BLOCK-I. M. Sc. Previous PAPER-IV SOLID STATE ELECTRONICS

Transcription

1 BLOCK-I M. Sc. Previous PAPER-IV SOLID STATE ELECTRONICS UNIT: I TRANSISTOR AMPLIFIER, OPERATING POINT, BIAS AND THERMAL STABILITY 1.0 Introduction 1.1 Objectives 1.2 Transistor Biasing and Thermal Stabilization- Operating point and factors contributing to thermal stability 1.3 Biasing technique 1.4 Collector to base bias 1.5 Self bias and Voltage Divider Bias 1.6 Stabilization against variation in V BE and B Bias compensation. 1.7 Transistor Equivalent Circuits Y(Admittance) parameters 1.8 Hybrid Parameters 1.9 Conversion to CB to CE hybrid parameters and CB to CC hybrid parameters 1.10 R-C coupled CE amplifier and its frequency response 1.11 Low and high frequency compensation 1.12 Cascade Stages 1.13 Unit Summary 1.14 References UNIT: II FEEDBACK CIRCUITS 2.0 Introduction 2.1 Objectives 1

2 2.2 Feedback in amplifiers, Principle of Feedback Amplifiers and Negative Feedback 2.3 Gain stability effect of feedback on input and output impedances and Distortions 2.4 Current and voltage feedback circuits 2.5 Emitter follower 2.6 Positive feedback Amplifier Oscillator 2.7 Circuits and working of Hartley oscillator 2.8 Colpitt oscillator 2.9 Phase shift oscillator 2.10 UJT and its characteristics 2.11 UJT as relaxation oscillators 2.12 Transistor as a switch-astable multi-vibrator 2.13 Mono-stable multi-vibrators 2.14 Bi-stable multi-vibrator 2.15 Unit Summary 2.16 References 2

3 BLOCK I M. Sc. Previous PAPER-IV SOLID STATE ELECTRONICS INTRODUCTON Among the basic functions of a transistor is its amplification. For faithful amplification (amplified magnitude of signal without any change in shape), the following three conditions must be satisfied: (i) The emitter-base junction should be forward biased, (ii)the collector-base junction should be reverse biased, and (iii)there should be proper zero signal collector current. The proper flow of zero signal collector current (proper operating point of a transistor) and the maintenance of proper collector-emitter voltage during the passage of signal is known as transistor biasing. To achieve this, bias batteries may be used or associated circuit with the transistor may be employed. The latter method is more efficient and is frequently used. The circuit providing the desired biasing is known as biasing circuit. Transistor cannot be a direct substitute for a vacuum tube. A vacuum tube is a voltage operated device in which the input voltage controls the output current or voltage or both. This type of amplifier works best with a constant voltage source. On the other hand, transistor is a current operated device in which the input current controls the output current. This type of amplifier works best with a constant current source. 3

4 The second difference can be made on the basis of isolation of input and the output circuits. In transistor, these two circuits are not isolated; therefore, output circuit parameters will affect the input circuit parameters and vice versa. Third difference can be made with reference to the output and output impedances. In vacuum tube circuits, both the impedances are sufficiently high, while transistor circuits generally have a low to medium input impedance and moderate to high input impedance. The current flowing through these impedances determines the voltage or power gain of a transistor amplifier circuit. The process of injecting a fraction of output energy of some device back to the input is known as feedback in amplifiers. The principle of feedback is probably as old as the invention of first machine but it is only some 40 years ago that feedback has come into use in connection with electronic circuits. It has been found very useful in reducing noise in amplifiers and making amplifier operation stable. Depending upon whether the feedback energy aids or opposes the input single, there are two basic types of feedback in amplifiers viz positive feedback and negative feedback. 4

5 BLOCK-I UNIT: I TRANSISTOR AMPLIFIER, OPERATING POINT, BIAS AND THERMAL STABILITY Structure: 1.0 Introduction 1.1 Objectives 1.2 Transistor Biasing and Thermal Stabilization- Operating point and factors contributing to thermal stability 1.3 Biasing technique 1.4 Collector to base bias 1.5 Self bias and Voltage Divider Bias 1.6 Stabilization against variation in VBE and B Bias compensation. 1.7 Transistor Equivalent Circuits Y(Admittance) parameters 1.8 Hybrid Parameters 1.9 Conversion to CB to CE hybrid parameters and CB to CC hybrid parameters 1.10 R-C coupled CE amplifier and its frequency response 1.11 Low and high frequency compensation 1.12 Cascade Stages Unit Summary 1.14 References 5

6 BLOCK-I UNIT-I TRANSISTOR AMPLIFIER, OPERATING POINT, BIAS AND THERMAL STABILITY 1.0 INTRODUCTION Among the basic functions of a transistor is its amplification. For faithful amplification (amplified magnitude of signal without any change in shape), the following three conditions must be satisfied: (i) The emitter-base junction should be forward biased, (ii)the collector-base junction should be reverse biased, and (iii)there should be proper zero signal collector current. The proper flow of zero signal collector current (proper operating point of a transistor) and the maintenance of proper collector-emitter voltage during the passage of signal is known as transistor biasing. To achieve this, bias batteries may be used or associated circuit with the transistor may be employed. The latter method is more efficient and is frequently used. The circuit providing the desired biasing is known as biasing circuit. Transistor cannot be a direct substitute for a vacuum tube. A vacuum tube is a voltage operated device in which the input voltage controls the output current or voltage or both. This type of amplifier works best with a constant voltage source. On the other hand, transistor is a current operated device in which the input current controls the output current. This type of amplifier works best with a constant current source. 6

7 The second difference can be made on the basis of isolation of input and the output circuits. In transistor, these two circuits are not isolated; therefore, output circuit parameters will affect the input circuit parameters and vice versa. Third difference can be made with reference to the output and output impedances. In vacuum tube circuits, both the impedances are sufficiently high, while transistor circuits generally have a low to medium input impedance and moderate to high input impedance. The current flowing through these impedances determines the voltage or power gain of a transistor amplifier circuit. There are three basic types of transistor amplifier circuits: (i) grounded amplifier (ii) grounded base (iii) grounded collector. 1.1 OBJECTIVES When a transistor is not properly biased, it works inefficiently and produces distortion in the output signal. Hence a transistor should be biased correctly. A transistor is biased either with the help of battery or associating a circuit with the transistor. The latter method is generally employed. The circuit used with the transistor is known as biasing circuit. In transistor biasing, when a transistor is not properly biased, it works inefficiently and produces distortion in the output signal. In addition, amount of bias required is important for establishing Q-point which is dictated by the mode of operation desired. It is also desirable that the Q-point should be stable, i.e., it should not shift its position due to temperature rise etc. Special efforts are made for this purpose. The performance of a transistor circuit can be considered in Y parameters. Y parameters are measured under short circuit conditions. The hybrid parameters h 11 and h 21 are measured with output short circuited and h 12 and h 22 with input open circuited. It is convenient to short circuit the high impedance output of the capacitor and to open circuit the low impedance input with a inductor. 7

8 1.2 TRANSISTOR BIASING AND THERMAL STABILIZATION- OPERATING POINT AND FACTORS CONTRIBUTING TO THERMAL STABILITY The maintenance of the operating point stable is known as stabilization. There are two factors which are responsible for shifting the operating point. Firstly, many of the transistor parameters are markedly temperature sensitive and secondly when a transistor is replaced by another of the same type, there is a wide spread in the values of transistor parameters. The problem of operating point instability is not faced in case of vacuum tubes. The reason is that the tube parameters are almost independent of working temperature and it is also possible to manufacture tubes with identical characteristics. So, stabilization of the operating point is necessary due to the following reasons: (a) Temperature dependence of I c (b) Individual variations and (c) Thermal runaway. Dependence: (a) Temperature dependence of I c : The instability of I c is principally caused by the following three sources: (i) The collector leakage current I co is greatly influenced by temperature changes. The I co doubles for every 10 0 C rise in temperature. (ii) Increase of with increase of temperature. (iii) Variation of V BE (Base to emitter voltage) with temperature. Here it should be remembered that V CE also changes with temperature but the change is very small. Hence I C is almost independent of V CE. (b) Individual variations: When a transistor is replaced by another transistor of the same type, the value of and V BE are not exactly the same. Hence the operating 8

9 point is changed. So it is necessary to stabilize the operating point irrespective of individual variations in transistor parameters. (c) Thermal runaway. Depending upon the construction of a transistor, the collector junction can withstand a maximum temperature. The range of temperature lies between 60 0 C to C for Ge transistor and C to C for Si transistor. If the temperature increases beyond this range then the transistor burns out. The increase in the collector junction temperature is due to thermal runaway. When a collector current flows in a transistor, it is heated i.e., its temperature increases. If no stabilization is done, the collector leakage current also increases. This further increases the transistor temperature. Consequently, there is a further increase in collector leakage current. The action becomes cumulative and the transistor may ultimately burn out. The self-destruction of an un-stabilized transistor is known as thermal runaway. The following two techniques are used for stabilization: (1) Stabilization technique. The technique consists in the use of a resistive biasing circuit which permits such a variation of base current I B as to maintain I C almost constant in spite of variation of I CO, and V BE. (2) Compensation technique. In this technique, temperature sensitive devices such as diodes, transistors, thermistors etc. are used. Such devices produce compensating voltages and currents in such a way that the operating point is maintained stable. 1.3 BIASING TECHNIQUE From the point of view of simplicity and economy, only one source of supply (instead of two V BB and V CC ) in the output circuit (i.e., V CC ) is used. Some methods are used for providing bias for a transistor. The basic principle involved in all the methods is to obtain the required base current (i.e., collector current) from V CC in zero signal conditions. The value of collector load is selected in such a way that the voltage between collector and emitter should not fall below 0.5 volt for germanium transistor and 0.7 volt for silicon transistor. Some of the methods are as follows: 9

10 BASE RESISTOR METHOD Fig. shows an NPN transistor connected in CE configuration with resistor biased. In this method, a high resistance R B is connected between positive terminal of supply V CC and base of the transistor. Here it should be remembered that if the transistor is PNP, then R B is connected between negative terminal of supply V CC and base of the transistor. Here the required zero signal base current flows through R B and is provided by V CC. In fig. the base-emitter junction is forward biased because the base is positive w.r.t. emitter. By a proper selection of R B, the required zero signal base current (and hence I C = I B ) can be made to flow. Circuit analysis. Here we shall find the value R B such that required collector current flows under zero signal conditions. Let I C be the required zero signal collector current. Considering the closed circuit ABEGA and applying the Kirchhoff's voltage law, we have IBRB VBE VCC or IBRB VCC VBE 10

11 Further V R I B B CC IC V I B BE Substituting the value of I B from above eq. we get R B V CC V I C The value of V BE can be seen from the transistor manual. Using above eq. the value of R B can be calculated. As V BE is generally very small as compared to V CC, hence BE R B V I CC C From eq. the value of R B can be found directly. Hence this method is sometimes called as fixed-bias method. Stability factor S. The stability factor S is given by 1 S 1 di / di In base resistor method, the base current I B is independent of collector current I C. So the stability factor S is given by S 1 If =100, then S=101. This shows that I C changes 101 times as much as any change in I CO. Thus I C is very dependent upon I CO and hence upon temperature. The value of S is the highest that can be obtained. Hence the circuit has very poor stability. B C Example.1 for I C. Fig. shows the base bias with emitter feedback. Obtain an expression 11

12 Considering the closed circuit ABEGA, and applying the Kirchoff's law, we get From eq. VCC IBRB VBE IERE I B V V V R R CC BE CC B B So I B is independent of I C. Now I B = I C / and I E I C Substituting these values in eq. we get V R I / V I R CC B C BE C E or V V I R R / CC BE C E B I C VCC VBE RE RB / As V BE is negligibly small as compared to V CC, hence I C VCC RE RB / Example2. (i) A germanium transistor is to be operated at zero signal I C =1 ma. If the collector supply V CC = 10 V, what is the value of R B is base resistor method? Take = 100. (ii) If another transistor of the same batch with = 50 is used, what will be the new value of zero signal I C for the same R B. (i) The value of R B is given by 12

13 R B V Here, V CC = 10V, = 100 and I C = 1 ma. For a germanium transistor V BE = 0.3 V. CC V I C BE (ii) The value of I C is given by I C V CC V R B BE K = 0.5 ma 3 Example3. Fig. shows a silicon transistor with = 100 and biased by base resistor method. Determine the operating point. The Value of I C is given by I C V CC V R B BE Here, V CC = 10 V, V BE = 0.7 V (Silicon transistor), = 100 and R B = 930 K 10 I C ma 930K Now V CE = V CC - I C R L = 10-1 ma 4 K = (10-4) volt = 6V 13

14 Operating point is (6V, 1mA). 1.4 COLLECTOR TO BASE BIAS The circuit of an NPN transistor connected in CE configuration with collector to base bias is shown in fig. This circuit is same as base bias circuit except that the base resistor R B is returned to collector rather than to V CC supply. Using this circuit, there is considerable improvement in the stability. If the collector current I C tends to increase (either as a result of rise in temperature or as a result of transistor being replaced by another of larger ), the d.c. voltage drop across R L increase and consequently V CE decreases. As a result, the base current I B also reduces. This will tend to compensate for the original increase. The compensation is never exact. Circuit analysis. The required value of R B needed to give the zero signal current I C can be calculated as follows: Voltage drop across R L = (I C + I B ) R E I C R L From the figure, or I C R L + I B R B + V BE = V CC I B R B = V CC - V BE - I C R L VCC VBE ICRL R B = I or R Stability factor S. Applying KVL to the circuit of fig. we have 14 B B V V I R CC BE C L I C

15 or I I R I R V V B C L B B BE CC I R R I R V V B L B C L BE CC V V I R CC BE C L B RL RB I Since V BE is almost independent of collector current (V BE = 0.7 for Si and 0.3 V for di B RL Ge). Then from eq. we get di R R C L B 1 We know that S 1 di / di B C This value is smaller than 1 which is obtained for fixed-bias circuit. Thus there is an improvement in the stability. The circuit of fig. provides a negative feedback. This reduces the gain of the amplifier. So the increased stability of the collector to base bias circuit is obtained at the cost of a.c. voltage gain. 1.5 SELF BIAS VOLTAGE DIVIDER BIAS A very commonly used biasing arrangement is self-bias or emitter bias. The circuit arrangement is shown in fig. This is also known as universal bias stabilization circuit. In this method two resistance R 1 and R 2 are connected across supply voltage V CC and provide biasing. The emitter resistances R E provides stabilization. The name voltage divider is derived due to the fact that resistors R 1 and R 2 form a potential divider across V CC. The resistance R E causes a voltage drop in a direction so as to reverse-bias the emitter junction. Since the junction must be forward-biased, the base voltage is obtained from the supply through R 1 -R 2 network. The net forward bias across the emitter junction is equal to V b minus the d.c. voltage drop across R E. 15

16 The improvement in the operating point stability may be explained as follows: Let there be a rise in temperature. This causes a rise in I CO i.e. a rise in I C. Now the current in R E increases. As a result, the voltage drop across R E increases and consequently the base current decreases. This decreases the collector current. Thus the presence of R E reduces the increase in I C and improves the operating point stability. In case of amplifiers, to avoid the loss of ac signal gain (because of the feedback caused by R E ) a capacitor of large capacitance is connected across R E. The condenser offers a very small reactance to ac signal and hence it passes through the condenser. Circuit Analysis. Let current I 1 flows through R 1. As the base current I B is very small, the current flowing through R 2 can also be taken as I 1. The calculation of collector current I C is as follows: The current I 1 flowing through R 1 or R 2 is given by I 1 R V CC R 1 2 The voltage V 2 developed across R 2 is given by Applying KVL to the base circuit, we have V2 VBE VE VBE IERE or V V I R I I 2 BE C E E C 16

17 I C V V R 2 BE E Here I C is almost independent of transistor parameters and hence good stabilization is ensured. The collector emitter voltage V CE can be calculated as follows: V CE = I C R L + V CE + I C R E V CE = V CC - I C (R L +R E ) 1.6 STABILIZATION AGAINST VARIATION IN V BE AND B BIAS COMPENSATION So far we have studied the various biasing methods and operating point stability provided by them. We have seen that self bias circuit provides better operating point stability than a fixed bias circuit. In both arrangements the stabilization action occurs due to the negative feedback improves the stability of the operating point but at the same time it reduces the gain of the amplifier. In certain applications, the loss in the gain becomes serious drawback and is intolerable. In such cases, compensation techniques are used to reduce the drift of the operating point. Sometimes for excellent bias and thermal stabilization, both stabilization as well as compensation techniques are used. The stabilization techniques refer to the use of resistive biasing circuits which permit I B to vary so as to keep I C relatively constant. On the other hand, compensation techniques refer to the use of temperature-sensitive devices such as diodes, transistors, thermistors, sensistors etc. to compensate for the variation in currents. Here we shall discuss the following compensation techniques: (A) (B) (C) Diode compensation for instability due to V BE variation. Diode compensation for instability due to I CO variation. Thermistor Compensation (D) Sensitor compensation. 17

18 Diode compensation for instability due to V BE variation For germanium transistor, changes in I CO with temperature contribute more serious problem than for silicon transistor. On the other hand, in a silicon transistor, the changes of V BE with temperature possesses significantly to the changes in I C. A diode may be used as compensation element for variation in V BE or I CO. Fig. shows the circuit of self bias stabilization technique with a diode compensation for V BE. The Thevenin's equivalent circuit is shown in fig. The diode D used here is of the same material and type as the transistor. 18

19 Hence the voltage V D across the diode has same temperature coefficient (- 2.5mV/deg.C) as V BE of the transistor. The diode D is forward-biased by the source V DD and resistor R D. Applying Kirchoff's voltage law to the base circuit of fig. we get V Th - V BE + V D = I B R Th + R E (I B + I C ) But 1 From eq. we have I I I C B CO V Th - V BE + V D = R E I C + (R Th + R E ) I B Substituting the value of I B from eq. (2), we get IC 1 ICO VTh VBE VD RE IC RTh RE or or 1 V V V R I R R I I R R Th BE D E C Th E C CO Th E 1 V V V I R R I R I R R Th BE D CO Th E C E C Th E I C 1 R 1 R V V V I R R Th BE D CO Th E Since variation in V BE with temperature is the same as the variation in V D with temperature, hence the quantity (V BE - V D ) remains constant in eq. So the current I C remains constant inspite of the variation in V BE. Although diode compensation for V BE variation is not perfect yet it is effective in canceling most of the operating point drift. EXERCISE ) Name three types of transistor amplifier circuits. 2) What do you understand by stabilization of operating point? 3) What do you understand by transistor biasing? What is its need? 19 Th E

20 4) Draw a self-bias circuit. 5) Draw a fixed-bias circuit. Explain why the circuit is unsatisfactory if the transistor is replaced by another of the same type. 6) What are the techniques needed for stabilization? 1.7 TRANSISTOR EQUIVALENT CIRCUITS- Y (ADMITTANCE) PARAMETERS The y- parameters are defined by choosing the input and output voltages V 1 and V 2 as independent variables and expressing the currents I 1 and I 2 in terms of these two voltages. Thus, where the I s and V s represent rms values of the small-signal currents and voltages. The circuit model satisfying these equations is indicated in Fig. 20

21 For a given device, single transistor or cascade pair, these parameters may be specified as explicit functions of frequency, or, as is more often the case, as graphs of the real and imaginary parts, the conductance G and the susceptance B, versus frequency. The data sheet of the MC 1550 gives the y-parameters measured on the general radio 1607A immittance bridge. Typical measured values are shown. The internal feedback factor y 12 is not shown because it was found to be less than ma/v and is neglected. Let us consider the two-port network terminated at the output by a load admittance Y L and driven by a current source I s with source admittance Y s. The equivalent admittance seen by the current source is Y eq = Y s + Y i. and the output admittance is Since y 12 ~ 0, then Y i ~ y 11 and Y O ~ y 22. EXERCISE ) Define the y- parameters (a) by equation (b) in words. 2) Explain y-parameters for circuit. 1.8 HYBRID PARAMETERS 21

22 The hybrid parameters are commonly known as h-parameters. These are generally used to determine amplifier characteristic parameters such as voltage gain, input and output resistances etc. Determination and Meaning of h-parameters Every linear circuit may be represented by a set of four h- parameters namely h 11, h 12, h 21 and h 22. The parameters h 11 and h 21 may be determined by short-circuiting the output terminal of a given circuit. On the other hand, h 12 and h 22 may be determined by open- circuiting the terminals of the given circuits. 1.Determination of h 11 and h 21. These are determined by short- circuiting the output terminals of a given circuit as shown in fig. A short-circuit at the output terminals makes the voltage V 2 equal to zero. We know that the input voltage is given by the relation. v 1 = h 11 = i 1 + h 12 v 2 Substituting the value of v 2 (equal to zero) in the above equation, the input voltage, v 1 = h 11 i 1 or h 11 = v 1 /i 1 Thus h 11 may be determined from the relation v 1 /i 1. The value of i 1 is obtained by applying a voltage at the input and then measuring the value of input current (i 1 ). Since h 11 is the ratio of voltage to current, therefore it has the units of ohms i.e., the same unit as that of a resistance. Similarly, we know that the output current is given by the relation, i 1 = h 21 i 1 or h 22 v 2 Again substituting the value of v 2 (equal to zero) in the above equation, the output current: i 1 = h 21 i 1 or h 21 = i 2 /i 1 Thus h 21 may be determined from the ration i 2 /i 1. The values of i 1 and i 2 may be obtained by applying a voltage at the input and then measuring the input current (i 1 ) and output current (i 2 ). Since h 21 is the ratio of currents, therefore it has no units. The parameter h21 is called the forward current gain of the circuit with output shortcircuited. 2.Determination of h 12 and h 22. These are determined by open circuiting the input terminals of a given circuit as shown in fig (b). An open circuit, at the input 22

23 terminals, makes the current (i 1 ) equal to zero. We also known that the input voltage is given by the relation, v 1 = h 11 i 1 + h 12 v 2 Substitution of the value of i 1 (equal to zero) in the above equation, the input voltage, v 1 = h 12 v 2 or h 12 = v 1 /v 2 Thus, h 12 may be determined from the ratio v 1 /v 2. The value of v 1 may be obtained by applying a voltage v 2 at the output and then measuring at the input voltage (v 1 ). Since, h 12 is a ratio of voltage, therefore it has no units. As h 12 is the ratio of input voltage (v 1 ) to the output voltage (v 2 ), therefore, its value is known as the reverse voltage gain in order to distinguish it from to forward voltage gain, whose value is equal to v 2 /v 1. Similarly, we know that the output current is given by the relation, i 2 =h 21.i 1 + h 22.v 2 Again substituting the value of (equal to zero) in the above equation, the output current, i 2 =h 22.v 2 or h 22 = i 2 /v 2 Thus, h 22 may be determined from the ratio i 2 /v 2. The value of current (i 2 ) may be obtained by applying a voltage at the output (v 2 ) and then measuring the output with input open. Since h 22 is the ratio of current to voltage, therefore it has the units of ohms () or Siemes (S). The parameter h 22 is also called output conductance with input open. 1.9 CONVERSION OF CB TO CE HYBRID PARAMETERS AND CB TO CC PARAMETERS CB to CE conversion: Figures show the transistor connected in common-emitter (CE) configuration and the hybrid equivalent circuit of such a transistor. 23

24 In a common emitter transistor configuration, the input signal is applied between the base and emitter terminals of transistor and output appears between the collector and emitter terminals. The input voltage (v eb ) and the output current (i c ) are given by the following equation: v be = h ie. i b + h re. v ce i c = h fe. i b + v ce CB to CC hybrid parameters: Figures show the transistor connected in a common- base (CB) configuration and its hybrid equivalent circuit. In a common-base configuration, the input signal is applied between emitter and base terminals and output appears between collector and base terminals. The input Voltage (v eb ) and the output current (i c ) are given by the following equations: v eb = h ib. i e + h re. v cb i e = h fh. i c + v cb 24

25 Approximate Conversion Formulae for h-parameters The transistors are used in most of the circuits in common emitter configuration. Therefore the manufacturers list only the common emitter h-parameters in their data sheets. However, if the transistor is to be used in a configuration, other than the common emitter, then we must use the specified conversion formulae for determining its h-parameters. The conversion formulas for common base and common collector configuration are as given below. 1.Conversion of formulas for common base configuration. The conversion formulas for determining the values of h-parameters of a transistor in common base configuration, from the common emitter h-parameter values, are as given below: h ib = h ie /1+ h fe, h rb = h ie. h oe /1+ h fe h fb = -h fe /1+h fe, h ob = h oe /1+h fe 2.Conversion formulae for common collector configuration. The conversion formulae for determining the values of h-parameters of a transistor n common collector configuration from the common emitter h-parameter value, are as given below: h ic = h ie, h re = 1-h re ~ 1 h fc = -(1+h fe ), h oc = h oe EXERCISE ) What do you understand by hybrid parameters? What are their dimensions? 25

26 2) How will you measure h- parameters of a linear circuit? 3) Draw the h- parameter equivalent circuit of a linear circuit. 4) How are h- parameters of a transistor measured? 5) Explain (a) conversion formulae for common base configuration (b) conversion formulae for common collector configuration R-C COUPLED CE AMPLIFIER AND ITS FREQUENCY RESPONSE A cascaded arrangement of common emitter transistor stages is shown in Fig.(a) and of common source FET stages is also shown in Fig. (b) The output Y 1 of one stage is coupled to the input X 2 of the next stage via a blocking capacitor C b which is used to keep the dc component of the output voltage at Y 1 from reaching the input X 2. Resistor R g is from gate to ground, and the collector (drain) circuit resistor is R c (R d ). The source resistor R s, the emitter resistor R e, and the resistors R 1 and R 2 are used to establish the bias. The bypass capacitors, used to prevent loss of amplification due to negative feedback, are C z in the emitter circuit and C s in the source circuit. Also present are junction capacitances, to be taken into account when we consider the high- frequency response, which is limited by their presence LOW AND HIGH FREQUENCY COMPENSATION In electrical engineering, frequency compensation is a technique used in amplifiers, and especially in amplifiers employing negative feedback. It usually has two primary goals: To avoid the unintentional creation of positive feedback, which will cause the amplifier to oscillate, and to control overshoot and ringing in the amplifier's step response. The low-frequency equivalent circuit is obtained by neglecting all shunting capacitances and all junction capacitances by replacing amplifier A 1 by its Norton s equivalent. For a transistor these quantities may be expressed in terms of the CE hybrid parameters: R i ~ h ie (for small values of R c ); R o 26

27 = 1/ h oe (for a current drive); and I = h fe I b where I b is the base signal current. The low 3-d B frequency is This result is easy to remember since the time constants equals C b multiplied by the sum of the effective resistances R o is to the left of the blocking capacitor, and R i to the right of C b. For an FET amplifier, R i = R g >> R d. Since R o < R d because R o is R d in parallel with then R i = R g >> R o and The input impedance of a transistor is much smaller than that of an FET, a coupling capacitor is required with the transistor which is 500 times larger than that required with the FET. Fortunately, it is possible to obtain physically small electrolytic capacitors having such high capacitance values at the low voltages at which transistors operate. Since the coupling capacitances required for good low-frequency response are far larger than those obtainable in integrated form, cascade integrated stages must be direct- coupled. For high- frequency calculations each transistor is replaced by its small- signal hybrid- II model. We have included a voltage source V s with R s = 50 and have assumed that capacitors C b and C z represent short circuits for high frequency CASCADE STAGES When the amplification of a single transistor is not sufficient for a particular purpose, or when the input or output impedance is not of the correct magnitude for the intended application two or more stages may be connected to the input of the next stage. To analyze such type of circuits, we make use of the general expressions for AI, Zi, Av, Yo. It is necessary that we have available the h parameters for the specific 27

28 transistors used in the circuit. The h-parameters values for a specific transistor are usually obtained from the manufacturer s datasheet. EXERCISES ) Explain in detail R-C coupled CE amplifier. 2) How is low-frequency equivalent circuit obtained? 3) What are cascade stages? 1.13 UNIT SUMMARY (i) The proper flow of zero signal collector current (proper operating point of a transistor) and the maintenance of proper collector-emitter voltage during the passage of signal is known as transistor biasing. (ii) The maintenance of the operating point stable is known as stabilization. (iii)the hybrid parameters are commonly known as h-parameters. These are generally used to determine amplifier characteristic parameters such as voltage gain, input and output resistances etc. (iv)the circuit providing the desired biasing is known as biasing circuit. (v) The circuit used with the transistor is known as biasing circuit REFERENCES (i) Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company Ltd. (ii) Electronic Devices and Circuits an Introduction by Mottershed (iii)transistor Physics by Sarkar (iv) Nashelsky Electronic Devices & Circuit Theory (PHI) by Robert Boylested and Louis (v) Principles of Electronics by V.K. Mehta, S. Chand & Company Ltd. SOLUTION EXERCISE ) Refer to article 1.0, 2) Refer to article 1.2, 3) Refer to article 1.0, 4) Refer to article 1.5, 5) Refer to article 1.3, 6) Refer to article 1.2 EXERCISE ) Refer to article 1.7, 2) Refer to article

29 EXERCISE ) Refer to article 1.8, 2) Refer to article 1.8, 3) Refer to article 1.8, 4) Refer to article 1.8 EXERCISE ) Refer to article 1.10, 2) Refer to article 1.11, 3) Refer to article 1.12 BLOCK-I UNIT: II FEEDBACK CIRCUITS Structure: 2.0 Introduction 29

30 2.1 Objectives 2.2 Feedback in amplifiers, Principle of Feedback Amplifiers and Negative Feedback 2.3 Gain stability effect of feedback on input and output impedances and Distortions 2.4 Current and voltage feedback circuits 2.5 Emitter follower 2.6 Positive feedback Amplifier Oscillator 2.7 Circuits and working of Hartley oscillator 2.8 Colpitt oscillator 2.9 Phase shift oscillator 2.10 UJT and its characteristics 2.11 UJT as relaxation oscillators 2.12 Transistor as a switch-astable multi-vibrator 2.13 Mono-stable multi-vibrators 2.14 Bi-stable multi-vibrator 2.15 Unit Summary 2.16 References BLOCK-I UNIT: II FEEDBACK CIRCUITS 2.0 INTRODUCTION 30

31 The process of injecting a fraction of output energy of some device back to the input is known as feedback in amplifiers. The principle of feedback is probably as old as the invention of first machine but it is only some 40 years ago that feedback has come into use in connection with electronic circuits. It has been found very useful in reducing noise in amplifiers and making amplifier operation stable. Depending upon whether the feedback energy aids or opposes the input single, there are two basic types of feedback in amplifiers viz positive feedback and negative feedback. 2.1 OBJECTIVES In feedback amplifiers, when the feedback voltage (or current) is so applied that it increases the input voltage (or current) i.e., it is in phase with the input, it is called as positive feedback or regenerative or direct feedback. Positive feedback increases the gain of the amplifier. However, it has the disadvantage of increased distortion and instability. So positive feedback is seldom employed in amplifiers. If the positive feedback is sufficiently large, it leads to oscillations and hence it is used in oscillators. When the feedback voltage is so applied that it decreases the input voltage i.e., it is out of phase with the input, it is called as negative feedback or degenerative feedback or inverse feedback. Negative feedback reduces the gain of the amplifier. However, the advantage of negative feedback are: reduction in distortion, stability in gain, increased bandwidth etc. So the negative feedback is frequently used in amplifier circuits. 2.2 FEEDBACK IN AMPLIFIERS, PRINCIPLE OF FEEDBACK IN AMPLIFIERS AND NEGATIVE FEEDBACK For an ordinary amplifier i.e., without feedback, let V o and V i be the output voltage and input voltage respectively. If A be the voltage gain of the amplifier, then A = V O / V i The gain A is often called as open loop gain. The principle of an amplifier with feedback is shown in fig. The amplifier has two parts: an amplifier and a feedback circuit. Let 31 be the output voltage with

32 feedback and a fraction B of this voltage is applied to the input voltage. Now the input voltage becomes (V i +BV O ) depending whether the feedback is positive or negative. This voltage is amplified A times by the amplifier. Considering positive feedback, we have A(V i +BV O ) = V O Or AV i +ABV O = V O Or AV i = V O [1-BA] The left hand side of eq. represents the amplifier gain A or A f with feedback i.e., For positive feedback Foe negative feedback 32

33 Here the term BA is called as feedback factor and B as feedback ratio. The term (1+ BA) is known as loop gain and amplifier gain A with feedback is closed loop gain(feedback loop is closed). Negative feedback: When the feedback energy (voltage or current) is out of phase with the input signal and thus opposes it, it is called negative feedback. This is illustrated in Fig. as you can see, the amplifier introduces a phase shift of into the circuit while the feedback network is so designed that it introduces a phase shift of (i.e., 0 0 phase shift). The result is that the feedback voltage V f is out of phase with the input signal V in. Negative feedback reduces the gain of the amplifier. However, the advantages of negative feedback are: reduction is distortion, stability in gain, increased bandwidth and improved input and output impedances. It is due to these advantages that negative feedback is frequently employed in amplifiers. 2.3 GAIN STABILITY EFFECT OF FEEDBACK ON INPUT AND OUTPUT IMPEDANCES AND DISTORTIONS Consider the negative voltage feedback amplifier shown in Fig. The gain of the amplifier without feedback is A v. Negative feedback is then applied by feeding a fraction m v of the output voltage e 0 back to amplifier input to the amplifier is the signal voltage e g minus feedback voltage m v e 0 i.e., 33

34 Actual input to amplifier = e 8 - m v e 0 The output e 0 must be equal to the input voltage e 8 - m v e 0 multiplied by gain A v of the amplifier i.e., (e 8 - m v e 0 ) A v = e 0 A v e 8 - A v m y e 0 = e 0 It may be seen that the gain of the amplifier without feedback is A v. However, when negative voltage feedback is applied, the gain is reduced by a factor 1 + A y m y. it may be noted that negative voltage feedback does not affect the current gain of the circuit. (i) Gain Stability An important advantage of negative voltage feedback is that the resultant gain of the amplifier can be made independent of transistor parameters or the supply voltage variations. A vf Ay 1 Am y v For negative voltage feedback in an amplifier to be effective, the designer deliberately makes the product A v m v much greater than unity. Therefore, in the 34

35 above relation, I can be neglected as compared to A v m v and the expression becomes. A vf A y A m 1 m y v y It may be seen that the gain now depends only upon feedback fraction m y i.e., on the characteristics of feedback circuit. As feedback circuit is usefully a voltage divider (a resistive network), therefore, it is unaffected by changes in temperature, variation in transistor parameters and frequency, Hence, the gain of the amplifier is extremely stable. (ii) Reduces non-linear distortion. A large single stage has non linear distortion because its voltage gain changes at various points in the cycle. The negative voltage feedback reduces the non-linear distortion in large signal amplifiers. If can be proved mathematically that. D vf 1 D Am y v Where D = distortion in amplifier without feedback D vf = distortion in amplifier with feedback It is clear that by applying negative voltage feedback to an amplifier, distortion is reduced by a factor 1 + A y m v. (iii) Improves frequency response. As feedback is usually obtained through a resistive net work, therefore, voltage gain of the amplifier is independent of signal frequency. The result is that voltage gain of the amplifier will be substantially constant over a wide range of signal frequency. The negative voltage feedback, therefore, improves the frequency response of the amplifier. 35

36 (iv) Increases circuit stability. The output of an ordinary amplifier is easily changed due to variations in ambient temperature, frequency and signal amplitude. This changes the gain of the amplifier, resulting in distortion. However, by applying negative voltage feedback voltage gain of the amplifier is stabilized or accurately fixed in value. This can be easily explained. Suppose the output of a negative voltage feedback amplifier has increased because of temperature change or due to some other reason. This means more negative feedback since feedback is being given from the output. This tends to oppose the increase in amplification and maintains it stable. The same is true should the output voltage decrease. Consequently, the circuit stability is considerably increased. (v) Increases input impedance and decreases and decreases output impedance. The negative voltage feedback increases the input impedance and decreases the output impedance of amplifier. Such a change is profitable in practice as the amplifier can then serve the purpose of impedance matching. Input impedance. The increase in input impedance with negative voltage feedback can be feedback and Z m with negative feedback. Let us further assume that input current is i 1. Referring to e m e i Z 8 v 0 1 = 8 8 v 0 v 0 = in e ( e m e ) m e ( e m e ) A M ( e m e ) { e A ( e m e )} 8 v 0 v v 8 v 0 0 v 8 v 0 ( e m e )(1 A M ) = 8 v 0 v v 36

37 = 1 ( i Zin(1 Av Mv) { e8 mve0 i1z in) OR e i 8 1 Z (1 A M ) in v v But e 8 / i 1 = Z in the impedance of the amplifier with negative voltage feedback. Z Z (1 A M ) in in v v It is clear that by applying negative voltage feedback the input impedance of the amplifier is increased by a factor 1 AM v v As AM v v is much greater than unity, therefore, input impedance is increased considerably. This is an advantage, since the amplifier will now present less of a load to its Output impedance. We can show that output impedance with negative voltage feedback is given by : Z ' out Zout 1 AM v v Where Z ' out = Output impedance with negative voltage feedback 37

38 Z ' out = Output impedance without feedback It is clear that by applying negative feedback, the output impedance of the amplifier is decreased by a factor 1 AM v v. This is an added benefit of using negative voltage feedback. With lower value of output impedance, the amplifier is much better suited to drive low impedance loads. Distortions: Consider a large amplitude signal applied to a stage of an amplifier, so that the operation of an active device (i.e., transistor) extend slightly beyond its range of linear operation. As a result of this, the output signal is slightly distorted. Now if a negative feedback is introduced to the amplifier stage, the voltage gain reduces. But if the input signal is increased, by the same amount by which the gain is reduced, the output signal amplitude remains the same (i.e., as it was without feedback). Now if we measure the distortion in both cases, it will be found that distortion has reduced due to feedback by a factor (1 +. A). It may be noted that the input signal to the feedback amplifier may be the actual signal available from an external source or it may be an output of an amplifier preceding the feedback stage. To increase the input of the feedback amplifier by a factor (1+.A ), we can either increase the nominal gain of the pre-amplifying stages or add a new stage. It will be interesting to know that the full benefit of the feedback amplifier in reducing distortion, can be obtained. His can be done if the pre-amplifying stages do not introduce any additional distortion because of the increased output. 2.4 CURRENT AND VOLTAGE FEEDBACK CIRCUITS Voltage and current can be feedback to the input either in series to the parallel. In the feedback connections types, the term voltage refers to connecting the output voltage as input to the feedback network. The term current refers to tapping off some output current through the feedback network. The term series refers to connecting the feedback signal in series with the input signal voltage, and the term shunt refers to connecting the feedback signal in shunt (parallel) with an input current source. 38

39 It has been observed that the series feedback connections tend to increase the input resistance, while the shunt feedback connections tend to decrease the input resistance. Moreover, the voltage feedback will tend to decrease the output resistance, while the current feedback tends to increase the output resistance. (i) Voltage- series Feedback Connections It is also called a shunt-derived series-fed feedback connection. In this, a fraction of the output voltage is applied in series with the input voltage through the feedback network. However, the input to the feedback network is in parallel with output of the amplifier. It can be shown easily that the voltage- series feedback connection increase the input resistance and decreases the output resistance of the feedback amplifier. (ii)voltage- Shunt Feedback Connection It is also called a shunt-derived shunt-fed feedback connection. In this, a fraction of the output voltage is applied in parallel with the input voltage through the feedback network. It can be shown easily that the voltage- shunt feedback connection decreases both input and output resistances of the feedback amplifier by a factor equal to (1+.A). (iii) Current-series Feedback Connection It is also called a series-derived series-fed feedback connection. In this, a fraction of the output current is converted into a proportional voltage by the feedback network and then applied in series with the input. It can be shown easily that the current- series feedback connection increases both the input resistance and output resistance of the feedback amplifier by a factor equal to (1+.A). (iv) Current-Shunt Feedback Connection 39

40 It is also called a series-derived shunt-fed feedback connection. In this, a fraction of the output current is converted into a proportional voltage by the feedback network and then applied in parallel with the input voltage. It can be shown easily that the current- series feedback connection decreases the input resistance but increases the output resistance of the feedback amplifier by a factor equal to (1+.A). 2.5 EMITTER FOLLOWER It is a negative current feedback circuit. The emitter follower is a current amplifier that has no voltage gain. Its most important characteristic is that it has high input impedance and low output impedance this makes it an ideal circuit for impedance matching. Fig. shows the circuit of an emitter follower. As you can see, it differs from the circuitry of a conventional CE amplifier by the absence of collector load and emitter by pass capacitor. The emitter resistance R E itself acts as the load and a.c. output voltage (V out ) is taken across R E the biasing is generally provided by voltage-divider method or by base resistor method. The following points are worth noting about the emitter follower: (i)there is neither collector resistor in the circuit nor there is emitter by pass capacitor. These are the two circuit recognition features of the emitter follower. (ii)since the collector is at ac ground, this circuit is also known as common collector (CC) amplifier. 40

41 Operation. The input voltage is applied between base and emitter and the resulting a.c. emitter current produced an output voltage i e R E across the emitter resistance. This voltage opposes the input voltage, thus providing negative feedback. Clearly it is a negative current feedback circuit since the output voltage follows the input voltage. Characteristics. The major characteristics of the emitter follower are: (i)no voltage gain. In fact, the voltage gain of an emitter follower is close to 1. (ii)relatively high current gain and power gain. (iii)high input impedance and low output impedance. (iv)input and output ac voltages are in phase. EXERCISE ) What do you understand by feedback? 2) Discuss the principles of negative voltage feedback? 3) What is a feedback circuit? Explain how it provides feedback in amplifiers? 4) Describe the action of emitter follower with a neat diagram. 5) Why is voltage feedback employed in high gain amplifiers? 2.6 POSITIVE FEEDBACK AMPLIFIER-OSCILLATOR A transistor amplifier with proper positive feedback can act as an oscillator i.e. it can generate oscillations without any external signal source. Fig. shows a transistor 41

42 amplifier with positive feedback. Remember that a positive feedback amplifier is one that produces a feedback voltage (V f ) that is in phase with the original input signal. As you can see this condition is net in the circuit shown in fig. a phase shift of is produced by the amplifier and a further phase shift of input i.e. feedback voltage is in phase with the input signal. (i) (ii) We note that the circuit shown in is producing oscillations in the output. However, this circuit has an input signal. This is inconsistent with our definition of an oscillator i.e. an oscillator is a circuit that produces oscillations without any external signal source. When we open the switch S of Fig. we get the circuit shown in Fig. this means the input signal (V in ) is removed. However, V f (which is in phase with the original signal) is still applied to the input signal. The amplifier will be amplified and sent to the output. The feedback network sends a portion of the output back to the input. Therefore the amplifier receives another input cycle and another output cycle is produced this process will continue so long as the amplifier is turned on. Therefore, the amplifier will produces sinusoidal output with no external no external signal source. The following points may be noted carefully: a) A transistor amplifier with proper positive feedback will work as an oscillator. b) The circuit needs only a quick trigger signal to start the oscillations. Once the oscillations have started, no external signal source is needed. 42

43 c) In order to get continuous undraped output from the circuit, the following condition must be met. M y A y = 1 where A y = Voltage gain of amplifier without feedback M y = Feedback fraction. This relation is called Barkhausen Criterion. 2.7 CIRCUITS AND WORKING OF HARTLEY OSCILLATOR The Hartley oscillator is similar to Colpitt's Oscillator with minor modifications. Instead of using Tapped capacitors, two inductors L 1 and L 2 are placed across a common capacitor C and the centre of the inductors is tapped as shown in Fig. 43

44 The tank circuit is made up of L 1, L 2 and C. The frequency of oscillations is determined by the values of L 1, L 2 and C and is given by: Where L T = L 1 + L 2 + 2M Here M = mutual inductance between L 1 and L 2. Note that L 1 - L 2 - C is also the feedback network that produces a phase shift of Circuit Operation. When the circuit is turned on, the capacitor is charged. when this capacitor is fully charged, it discharges through coils L 1 and L 2 setting up oscillations of frequency determined by exp (i) the output voltage of the amplifier appears across L 1 and feedback voltage across L 2. The voltage across L 2 is out of phase with the voltage developed across L 1 (V out ) as shown in Fig it is easy to see that voltage feedback (i.e., voltage across L 2 ) to the transistor provides positive feedback. A phase shift of is produced by L 1 - L 2 voltage divider. In this way, feedback is properly phased to produce continuous un-damped oscillations. Feedback fraction m v :In Hartley oscillator, the feedback voltage is across L 2 and output voltage is across L 1. Feedback fraction m v = L L m v = COLPITT S OSCILLATOR 44

45 Fig. shows a Colpitt s oscillator. It uses two capacitors and placed across a common inductor L and the centre of the two capacitors is tapped. The tank circuit is made up of C 1, C 2 and L and is given by; f 1 2 LCT Where C T CC 1 2 C C 1 2 Note that C 1, - C 2 L is also the feedback circuit that produces a phase shift of Circuit Operation. When the circuit is turned on, the capacitors C 1 and C 2 are charged. the capacitors discharge through L, setting up oscillations of frequency determined by exp (i). The output voltage of the amplifier appears across C 1 and feedback voltage is developed across C 2. The Voltage across is out of phase with the voltage developed across C 1 (V out ) as shown in Fig. It is easy to see that voltage feedback (voltage across C 2 ) to the transistor provides positive feedback. A phase shift of is produced by the transistor and a further phase shift of is produced by C 1 - C 2 voltage divider. in this way, feedback is properly phased to produce continuous encamped oscillation. 45

46 Feedback fraction m y. The amount of Feedback voltage in Colpitt's oscillator depends upon feedback fraction m v of the circuit. For this Circuit, Feedback fraction m y = C C PHASE SHIFT OSCILLATOR The circuit of a phase shift oscillator of a conventional single transistor amplifier and a RC phase shift network. The phase shift network consists of three sections R 1, C 1, R 2, C 2 and R 3 C 3 At some particular frequency F 0, the phase shift in each RC section in 60 0 so that the total phase shift produced by the RC network is The frequency of oscillations is given by: f RC 6 Where R1 R2 R3 R C1 C2 C3 C 46

47 Circuit operation. When the circuit is switched on, it produces oscillations of frequency determined. The output E 0 of the amplifier is feedback to RC feedback network. This network produces a phase shift of and a voltage E i appears at its output which is applied to the transistor amplifier. Obviously, the feedback fraction m = E i / E 0. The feedback phase is correct. A phase shift of is produced by the transistor amplifier. A further phase shift of is produced by the RC network. As a result, the phase shift around the entire loop is Advantages: (i) It does not require transformers or inductors. (ii) It can be used to produce very low frequencies. (iii) The circuit provides good frequency stability Disadvantages: (i)it is difficult for the circuit to start oscillations as the feedback is generally small. (ii)the circuit gives small output. EXERCISE ) What is the need of an oscillator? Discuss the advantages of oscillators? 2) Explain phase shift oscillator in detail. 3) With a neat diagram, explain the action of Hartley and Colpitt s oscillator. 4) Why is amplifier circuit necessary in an oscillator? 2.11 UJT AND ITS CHARACTERISTICS 47

48 A uni-junction transistor (abbreviated as UJT) is a three terminal semiconductor switching device. This device has a unique characteristic that when it is triggered, the emitter current increases regenerative until it is limited by emitter power supply. Due to this characteristic, the uni-junction transistor can be employed in a variety of applications e.g. switching, pulse generator, saw-tooth generator etc. Construction. Fig. shows the basic structure of a uni-junction transistor. It consists of an n-type silicon bar with an electrical connection on each end. The leads to these connections are called base-leads base-one B 1 and base two B 2. Part way along the bar between the two bases, nearer to B 2 than B 1 a p-n Junction is formed between a p -type emitter and the bar. The lead to this junction is called the emitter lead E. Fig. shows the symbol of uni-junction transistor. Note that emitter is shown closer to B 2 than B 1. The following points are worth noting: (i)since the device has one p-n junction and three leads, it is commonly called a unijunction transistor (uni means single). (ii)with only one p-n-junction, the device is really a form of diode. Because the two base terminals are taken from one section of the diode, this device is also called double-based diode. 48

49 (iii)the emitter is heavily doped having many holes. The n region, however, is lightly doped. For this reason, the resistance between the base terminals is very high (5 to 10 K ) when emitter head is open. Characteristics of UJT The characteristics of UJT are: (i) In cut- off region, V E increases from zero, slight leakage current flows from terminal to the emitter. This current is due to minority carriers in reverse biased diodes. (ii) Above a certain value of V E forward I E begins to flow, increasing until the peak voltage V P and current I P are reached at point P. (iii) After the peak point P, an attempt to increase V E is followed by a sudden increase in emitter current I E with a corresponding decrease in V E. This is a negative resistance portion of the curve because with increase in I E, V E decreases. The device, therefore, has a negative resistance region which is stable enough to be used with a great deal of reliability in many areas, e.g. trigger circuits, saw-tooth generators, timing circuits. 49

50 (iv) The negative portion of the curve lasts until the valley point V is reached with valley point voltage V V and valley point current I V. After the valley point, the device is driven to saturation UJT AS RELAXATION OSCILLATOR The applications of UJT transistors are: (i) UJT relaxation oscillator (ii) Over- voltage detector Fig. shows UJT relaxation oscillator where the discharging of a capacitor through UJT can develop a saw tooth output. When battery V BB is turned on, the capacitor C charges through resistor R 1. During the charging period, the voltage across the capacitor rises in an exponential manner until it reaches the peak point voltage. At this instant of time, the UJT switches to its low resistance conducting mode and the capacitor is discharged between E and B 1. As the capacitor voltage flays back to zero, the emitter ceases to conduct and the UJT is switched off. The Next cycle then begins, allowing the capacitor C to charge again. The frequency of the output sawtooth wave can be varied by changing the value of R 1 since this controls the time constant R 1 C of the capacitor charging circuit. The time period and hence the frequency of the saw-tooth wave can be calculated as follows. Assuming that the capacitor is initially uncharged, the voltage, V C across the capacitor prior to break down is given by: where V C = (1 - e- t/r 1 C ) R 1 C = Charging time constant of resistor capacitor circuit t = time from the commencement of waveform. 50

51 The discharge of the capacitor occurs when V c is equal to the peak point voltage V BB i.e. V V e BB BB 1/ t R C 1 (1 ) OR 1 e OR e 1/ t R C 1 1/ t R C, 2.3R1 C log OR t R1 C loge 1 Time period t 1 Frequency of saw tooth wave, f t in 1 sec onds Hz EXERCISE ) Explain the construction and working of UJT. 2) Describe some characteristics of UJT. 3) Write a brief note on UJT relaxation oscillator TRANSISTOR AS A SWITCH - ASTABLE MULTI-VIBRATOR A multi-vibrator which generates square waves of its own, i.e. without any external triggering pulse is known as an astable or free running multi-vibrator. The astable multi-vibrator has no stable state. It switches back and forth from one state to the other, remaining in each state for a time determined by circuit constants. In other words, as first one transistor conducts (i.e. ON state) and the other stays in the OFF state for some time. After this period of time, the second transistor is automatically turned ON and the first transistor is turned OFF. Thus the 51

52 multivibrator will generate a square wave output of its own. The width of the square wave and its frequency will depend upon the circuit constants. Circuit details. Fig. shows the circuit of a typical transistor astable multi-vibrator using two identical transistors Q 1 and Q 2. The circuit essentially consists of two symmetrical CE amplifier stages, each providing a feedback to the other. Thus collector load of the two stages are equal i.e. R 1 = R 4 and the biasing resistors are also equal i.e. R 2 = R 3. The output of transistor Q 1 is coupled to the input of Q 2 through C 1 while the output of Q 2 is fed to the input of Q 1 through C 2. The square wave output can be taken from Q 1 or Q 2. Operation When V CC is applied, collector currents start flowing in Q 1 and Q 2. In addition the coupling capacitors C 1 and C 2 also start charging up. As the characteristics of no two transistors (i.e. VBB ) are exactly alike, therefore, one transistor say Q 1, will 52

53 conduct more rapidly than the other. The rising collector current in Q 1 drives its collector more and more positive. The increasing positive output at point A is applied to the base of transistor Q 2 through C 1. This establishes a reverse bias on Q 2 and its collector current start decreasing. As the collector of Q 2 is connected to the base of Q 1 through C 2 therefore, base of Q 1 becomes more negative i.e. Q 1 is more forward biased. This further increases the collector current in Q 1 and causes a further decrease of collector current in Q 2. This series of actions is repeated until the circuit drives Q 1 to saturation and Q 2 to cut off. These actions occur very rapidly and may be considered practically instantaneous. The output of Q 1 (ON state) is approximately zero and that of Q 2 (OFF sate) is approximately V CC. This is shown by ab in Fig. When Q 1 is at saturation and Q 2 is cut off, the full voltage V CC appears across R 1 and voltage across R 4 will be zero. The charges developed across C 1 and C 2 are sufficient to maintain the saturation and cut off conditions at Q 1 and Q 2 respectively. This condition is represented by time interval bc in Fig. However, the capacitors will not retain the charges indefinitely but will discharge through their respective circuits. As C 1 discharges, the base bias at Q 2 becomes less positive and at a time determined by R 2 and C 1 forward bias is re-established at Q 2. This causes the collector current to start in Q 2. The increasing positive potential at collector of Q 2 is applied to the base of Q 1 through the capacitor C 2. Hence the base of Q 1 sends a negative voltage to the base of Q 2 through C 1 thereby causing further increase in the collector current of Q 2 with this set of actions taking place, Q 2 is quickly driven to saturation and Q 1 to cut off. This condition is represented by cd in Fig. The period of time during which Q 2 remains at saturation and Q 1 at cut off is determined by C 2 and R 3. On or Off time. The time for which either transistor remains ON or OFF is given by : ON time for Q 1 (or OFF time for Q 2 ) is T 1 = 0.694R 2 C 1 OFF time for Q 1 (or ON time for Q 2 ) 53

54 T 2 = 0.694R 3 C 2 Total time period of the square wave is T = T 1 + T 2 = (R 2 C 1 +R 3 C 2 ) As R 2 = R 3 = R and C 1 = C 2 = c, T = (RC + RC) = 1.4 RC seconds Frequency of the square wave is f T RC Hz It may be noted that in these expressions, R is in ohms and C in farad MONOSTABLE MULTIVIBRATOR A multi-vibrator in which one transistor is always conducting (i.e. in the ON state) and the other is non-conducting (i.e. in the OFF state) is called a mono-stable multivibrator. A mono-stable multi-vibrator has only one state stable. In other words, if one transistor is conducting and the other is non-conducting, the circuit will remain in this position. It is only with the application of external pulse that the circuit will interchange the states. However, after a certain time the circuit will automatically switch back to the original stable state and remains there until another pulse is applied. Thus a mono-stable multi-vibrator cannot generate square waves of its own like an astable multi-vibrator. Only external pulse will cause it to generate the square wave. Circuit Details. Fig. shows the circuit of a transistor mono-stable multi-vibrator. It consists of two similar transistors Q 1 and Q 2 with equal collector loads i.e. R 1 R 4. The values of V BB and R 5 are such as to reverse bias Q 1 and keep it at cut off. The pulse is given through C 2 to obtain the square wave. Again output can be taken from Q 1 or Q 2. 54

55 Operation. With the circuit arrangement shown, Q 1 is at cut off and Q 2 is at saturation. This is the stable state for the circuit and it will continue to stay in this state until a triggering pulse is applied at C 2. When a negative pulse of short duration and sufficient magnitude is applied to the base of Q 1 through C 2 the transistor Q 1 starts conducting and positive potential is established at its collector. The positive potential at the collector of Q 1 is coupled to the base of Q 2 through capacitor C 1. This decreases the forward bias on Q 2 and its collector current decreases. The increasing negative potential on the collector of Q 2 is applied to the base of Q 1 through R 3. This further increases the forward bias on Q 1 and hence its collector current. With this set of actions taking place, Q 1 is quickly driven to saturation and Q 2 cut off. With Q 1 at saturation and Q 2 at cut off, the circuit will come back to the original stage (i.e. Q 2 at saturation and Q 1 at cut off) after some time as explained in the following discussion. The capacitor C 1 (Charged to approximately V CC ) discharges through the path R 2 V CC Q 1. As C 1 discharges it sends a voltage to the base of Q 2 to make it less positive. This goes on until a point is reached when forward bias is reestablished on Q 2 and collector starts to flow in Q 2. The step by step events already explained occur and Q 2 is quickly driven to saturation and Q 1 to cut off. This is the stable state for the circuit and it remains in this condition until another pulse causes the circuit to switch over the states. 55

56 2.14 BISTABLE MULTIVIBRATOR A multi-vibrator which has both the states stable is called a bi-stable multi-vibrator. The bi-stable multi-vibrator has both the states stable. It will remain in whichever state it happens to be until a trigger pulse causes it to switch to the other state. For instance, suppose at any particular instant, transistor Q 1 is conducting and transistor Q 2 is at cut off. If left to itself, the bi-stable multi-vibrator will stay in this position forever. However, if an external pulse is applied to the circuit in such a way that Q 1 is cut off and Q 2 is turned on, the circuit will stay in the new position. Another trigger pulse is then required to switch the circuit back to its original state. Circuit details. The circuit of a typical transistor bi-stable multi-vibrator consists of two identical CE amplifier stages with output of one fed to the input of the other. The feedback is coupled through resistors (R 2 R 3 ) shunted by capacitors C 1 and C 2. The main purpose of capacitors C 1 and C 2 is to improve the switching characteristics of the circuit by passing the high frequency components of the square wave. This allows fast rise and fall time and hence distortion less square wave output. The output can be taken across either transistor. Operation. When V CC is applied, one transistor will start conducting slightly ahead of the other due to some difference in the characteristics of the transistors. This will drive one transistor to saturation and the other to cut off in a manner described for the circuit will stay in this condition. In order to switch the multi-vibrator to its other state, a trigger pulse must be applied. A negative pulse applied to the base of Q 1 through C 3 will cut it off or a positive pulse applied to the base of Q 2 through C 4 will cause it to conduct. Suppose a negative pulse of sufficient magnitude is applied to the base of Q 1 through C 3. This will reduce the forward bias on Q 1 and cause a decrease in its collector current and an increase in collector voltage. The rising collector voltage is coupled to the base of Q 2 where it forward biases the base-emitter junction of Q 2. 56

57 This will cause an increase in its collector current and decrease in collector voltage. The decreasing collector voltage is applied to the base of Q 1 where it further reverse biases the base emitter junction of Q 1 to cut off. The circuit will now remain stable in this state until a negative trigger pulse at Q 2 (or a positive trigger pulse at Q 1 ) changes this state. EXERCISE ) What is a multi-vibrator? Explain the principle on which it works? 2) With a neat sketch, explain the working of (i) a-stable multi- vibrator (ii) monostable multi-vibrator (iii) bi-stable multi- vibrator. 3) What is the basic difference between the three types of multi- vibrators? 2.15 UNIT SUMMARY (i) The process of injecting a fraction of output energy of some device back to the input is known as feedback in amplifiers. (ii) When the feedback energy (voltage or current) is out of phase with the input signal and thus opposes it, it is called negative feedback. (iii)the advantages of negative feedback are: highly stabilized gain, reduction in non-linear distortion, increased bandwidth i.e., improved frequency response, increased circuit stability, less amplitude distortion etc. (iv)the emitter follower is a current amplifier that has no voltage gain. (v)a transistor amplifier with proper positive feedback can act as an oscillator i.e. it can generate oscillations without any external signal source. (vi)a uni-junction transistor (abbreviated as UJT) is a three terminal semiconductor switching device. This device has a unique characteristic that when it is triggered, the emitter current increases regenerative until it is limited by emitter power supply. (vii)a multi-vibrator which generates square waves of its own i.e. without any external triggering pulse is known as an actable or free running multi-vibrator. 57

58 (viii)a multi-vibrator which has both the states stable is called a bi-stable multivibrator REFERENCES 1)Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company Ltd. 2)Electronic Devices and Circuits an Introduction by Mottershed 3)Transistor Physics by Sarkar 4)Nashelsky Electronic Devices & Circuit Theory (PHI) by Robert Boylested and Louis 5)Principles of Electronics by V.K. Mehta, S. Chand & Company Ltd. SOLUTION EXERCISE ) Refer to article 2.0, 2) Refer to article 2.2, 3) Refer to article 2.2, 4) Refer to article 2.5, 5) Refer to article 2.4 EXERCISE ) Refer to article 2.6, 2) Refer to article 2.10, 3) Refer to article 2.7 & 2.8, 4) Refer to article 2.3 EXERCISE ) Refer to article 2.11, 2) Refer to article 2.11, 3) Refer to article 2.11 EXERCISE ) Refer to article 2.12, 2) Refer to article 2.12, 2.13& 2.14, 3) Refer to article 2.12,2.13 &

59 BLOCK-II M. Sc. Previous PAPER-IV SOLID STATE ELECTRONICS UNIT: III OPERATIONAL AMPLIFIER Structure: 3.0 Introduction 3.1 Objectives 3.2 Differential amplifier circuits and working of operational amplifier and Circuit Symbol of an OP-AMP 3.3 Inverting and non-inverting OP-AMP amplifiers 3.4 Use of 741 IC as adder 3.5 Subtractor 3.6 Differentiator 3.7 Integrator 3.8 OP-AMP as constant current source 3.9 Comparator 3.10 Square wave generator 3.11 Triangular wave generator 3.12 Unit Summary 3.13 References UNIT:IV VOLTAGE MULTIPLIER CIRCUITS Structure: 4.0 Introduction 59

60 4.1 Objectives 4.2 Voltage multipliers circuits 4.3 Wave shaping circuits 4.4 Clipping Circuits 4.5 Clamping Circuits 4.6 Differentiating and Integrating circuits 4.7 Voltage regulated power supply and Regulation Sensitivity and Stability Factors 4.8 Unit Summary 4.9 References 60

61 BLOCK-II M. Sc. Previous PAPER-IV SOLID STATE ELECTRONICS INTRODUCTION The operational amplifier is a direct-coupled, high gain, negative feedback amplifier. They are made with different internal configurations in linear ICs. The operational amplifier is a complete amplifier. Furthermore, it is designed in such a way that external components like resistors, capacitors, etc. can be connected to its terminals. So the external characteristics can be changed. Due to this reason, the amplifier may fit to a particular application. The widespread applications of operational amplifiers are due to the use of negative feedback. We know that the performance of an amplifier with feedback solely controlled and determined by feedback elements only and is independent of the elements of the amplifier. As the feedback elements are generally passive hence the operation can be made very stable and predictable in performance. A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage by means of capacitors and diodes combined into a network. 61

62 BLOCK-II UNIT: III OPERATIONAL AMPLIFIER Structure: 3.0 Introduction 3.1 Objectives 3.2 Differential amplifier circuits and working of operational amplifier and Circuit Symbol of an OP-AMP 3.3 Inverting and non-inverting OP-AMP amplifiers 3.4 Use of 741 IC as adder 3.5 Subtractor 3.6 Differentiator 3.7 Integrator 3.8 OP-AMP as constant current source 3.9 Comparator 3.10 Square wave generator 3.11 Triangular wave generator 3.12 Unit Summary 3.13 References 62

63 BLOCK-II UNIT: III OPERATIONAL AMPLIFIER 3.0 INTRODUCTION The operational amplifier is a direct-coupled, high gain, negative feedback amplifier. They are made with different internal configurations in linear ICs. The operational amplifier is a complete amplifier. Furthermore, it is designed in such a way that external components like resistors, capacitors, etc. can be connected to its terminals. So the external characteristics can be changed. Due to this reason, the amplifier may fit to a particular application. The widespread applications of operational amplifiers are due to the use of negative feedback. We know that the performance of an amplifier with feedback solely controlled and determined by feedback elements only and is independent of the elements of the amplifier. As the feedback elements are generally passive hence the operation can be made very stable and predictable in performance. 3.1 OBJECTIVES The term operational amplifier was originally used for the d.c. amplifiers which perform mathematical operations as summation, subtraction, integration and differentiation in analog computers. Now-a-days, the operational amplifiers are put to a variety of other uses e.g. voltage regulators, in instrumentation and control 63

64 system, phase shift and oscillator circuits, pulse generators, square wave generator, comparator, analog to digital and digital to analog, converters, scale changer, analog computer and in many others. Although the scope of operational amplifier is much wider even the name OP-AMP continues. Operational amplifiers are used as comparator, pulse generator, square wave generator, Schmitt trigger etc. These days OP-AMP use integrated circuit technology and is referred to as basic linear or analogue integrated circuit. They possess all the merits of monolithic integrated circuits, e.g., small size, low cost, high reliability, low offset voltage and current and temperature tracking properties. 3.2 DIFFERENTIAL AMPLIFIER CIRCUITS AND WORKING OF OPERATIONAL AMPLIFIER AND CIRCUIT SYMBOL OF AN OP-AMP Standard triangular symbol is generally used for an OP-AMP. The early operational amplifier had only one input and one output terminal. The output was always inverted with respect to the input. The OP-AMPs now available are usually of differential type with two input terminals and a single output terminal. It is understood that all voltages are with respect to ground and hence the ground lines is not usually shown. The input terminals are marked with minus (-) and plus (+) signs. Terminals a (marked-) is called as inverting input terminal. The negative sign indicates that a signal applied at the terminal will appear amplified but in phase inverted (opposite polarity) at terminal c. Similarly, the terminal b (marked +) is called as noninverting input terminal. Here the positive sign indicates that a signal applied at the terminal b will appear amplified but in phase (same polarity) at the terminal c. It should be 64

65 clearly understood that minus and plus signs do not mean that the voltages V 1 and V 2 are negative and positive respectively. Moreover, it does not mean that the negative voltage is applied at terminal and positive voltage is applied at terminal b. The output voltage is directly proportional to the input voltage which is difference V 1 and V 2 thus VoV1. The constant of proportionality is the gain of the amplifier which is denoted by A. When no resistor or capacitor is connected from output terminal to any one of the input terminals (No feedback), the OP-AMP is said to be in open-loop condition. Here the word open signifies that feedback path or loop is open. CHARACTERISTICS OF AN IDEAL OP-AMP Ideal OP-AMP has the following characteristics: (i)an infinite voltage gain. (ii)an infinite bandwidth. (iii)the resistance measured between inverting and non-inverting terminals is input resistance. Infinite input resistance mean that input current is zero i.e., the amplifier is a voltage controlled device. (iv)zero output resistance. Zero output resistance means that V o is independent of the load resistance connected across the output. (v)perfect balance. The output is zero (V o =0) when equal voltages (V 1 = V 2 ) are applied at the two input terminals. A practical OP-AMP is, however, non-ideal. OPERATIONAL AMPLIFIER STAGES Fig. shows the block diagram of a typical OP-AMP. 65

66 It consists of two differential amplifiers followed by level shifter and an output stage. Input stage. The input stage is a dual-input, balanced output differential amplifier. The function of differential amplifier is to provide most of the voltage gain to OP- AMP. It also provides high resistance to OP-AMP. Intermediate stage. The intermediate stage is a dual input, unbalanced output differential amplifier. This is driven by the output of first stage and is used to provide some additional gain. There is a direct coupling between the first two stages. So the d.c. level at the output of intermediate stage is well above the ground level. This is undesirable. Level shifting stage. The level shifter (level translator) circuit is used after intermediate stage. Usually this is an emitter follower using constant current source. The function of level shifter is to shift the d.c. level at the output of intermediate stage downwards to zero volt with respect to ground. Output stage. The output stage is generally push-pull or complementary symmetry push-pull amplifier. Its function is to increase large output voltage swing capability, large output current swing capability of the amplifier and to provide low output resistance. EQUIVALENT CIRCUIT OF OP-AMP The equivalent circuit of an OP-AMP is shown. V 1 is the voltage at the inverting terminal and V 2 is the voltage at the non-inverting terminal. V id is the difference of 66

67 two input voltages i.e. (V 2 -V 1 ). R i is the input resistance which appears between the inverting and non-inverting input terminals. R o is the output resistance which is Thevenin equivalent resistance looking back into the output terminal of OP-AMP. The voltage source A V id is an equivalent Thevenin voltage source. The output voltage is directly proportional to the algebraic difference between the two input voltages. OPERATIONAL AMPLIFIER PARAMETERS Few commonly used electrical parameters of OP-AMP are defined as follows (1) Input offset voltage. When the input is OV, the output of OP-AMP should be zero. But in actual operation, there is some offset voltage at the output. The input offset voltage is defined as the voltage that must be applied between the two input terminals of an OP-AMP to nullify the output. Typically it lies in the range. 1 mv to 5mV. The smaller the value of input offset voltage, the better is the input terminal matched. (2) Input offset current. An output offset voltage will also result due to any difference in dc bias current at both inputs. The reason is that the two input transistors are never exactly matched. Each has a slightly different current. The input offset current is the difference between the two input currents. The input offset current typically lies in the range 20nA to 60nA. The smaller the input offset current, the better is the OP-AMP's performance. (3) Input bias current. The input bias current is the average of the currents that flow into the inverting and non-inverting input terminals of an OP-AMP. The smaller the input bias current, the smaller is the possible unbalance. 67

68 (4) Input offset voltage drift. It is the ratio of the change of input offset voltage to the change in temperature. (5) Input offset current drift. It is the ratio of the change of input offset current to the change in temperature. (6) Input resistance. This is the differential input resistance that can be measured at either of the input terminal with the other terminal connected to ground. The OP- AMP having bipolar input stage has an input resistance in the range of 100K to 1M. Usually, the voltage gain is large enough. Hence, the input resistance has little effect on the circuit performance. (7) Output resistance. It is the resistance measured between the output terminal of the OP-AMP and the ground. This is of the order of 40 to 100. This resistance does not significantly affect the closed-loop performance of the OP-AMP. (8) Slew rate (SR). It is defined as the maximum rate of change of output voltage per unit of time and is expressed in volts per microseconds, i.e., Slew rate indicates how rapidly the output of OP-AMP can change in response to change in input frequency. EXERCISE ) What is an OP-AMP? 2) What are the uses of an OP- AMP? Also give equivalent circuits of an OP-AMP? 3) What are the characteristics of an OP-AMP? 4) Define the terms: (i) input off- set voltage and current (ii) slew rate. 3.3 INVERTING AND NON-INVERTING OP-AMP AMPLIFIERS 68

69 (a) Differential amplifier. The open loop differential amplifier is shown in fig. Here V 1 and V 2 are signals applied to inverting and non- inverting terminals respectively. V 1 and V 2 may be either a.c. or d.c., as OP-AMP can amplify both types of signals. Here source resistances are not considered because they are negligibly small in comparison with the very high input resistance of OP-AMP. As the OP-AMP amplifies the difference between two input signals and hence this configuration is called as differential amplifier. The output voltage is given by V o = AV id = A (V 2 -V 1 ) where A is large signal voltage gain or open-loop gain. The common mode rejection ratio is defined as A d /A c where A d = ½ (A 1 A 2 ) and A c = (A 1 + A 2 ). (b) Inverting amplifier In this configuration, the input signal is applied to the inverting input terminal as shown in fig. The non-inverting terminals is grounded i.e., V 1 = 0. The output is given by 69

70 V o = AV id = A (V 2 -V 1 ) = -AV 1 ( V 2 = 0) The negative sign indicates that the output voltage is out of phase with respect to input i.e., output voltage is out of phase with respect to input. Thus in inverting amplifier, the input is amplified by gain. A with change is polarity. Hence, the name is given 'inverting amplifier'. (c)non-inverting amplifier In this configuration, the input signal is applied to the non-inverting input terminal of OP-AMP. The inverting input terminal is grounded. The output voltage is given by V o = AV id = A(V 2 -V 1 ) = AV 2 ( V 1 = 0) This shows that output voltage is gain A times the input voltage V 2 and is in phase with the input. As in non-inverting amplifier, the input signals is amplified by gain A without change in polarity and hence named as 'non-inverting amplifier'. INVERTING OP-AMP (NEGATIVE SCALER) Fig. shows the basic inverting amplifier with an input resistance R 1 and a feedback resistor R f. In this mode of operation, the positive input terminal of the amplifier is grounded and the input signal is applied to the negative input terminal. 70

71 Note that V 1 may be a dc voltage or an ac signal within the bandwidth of the amplifier. It is obvious from the figure that the feedback currents are algebraically added at point G. So this point is called as summing point. When input voltage v 1 is applied at the input terminal, the point G attains some positive potential. Now there exists a output voltage v o. Due to negative feedback, a fraction of the output voltage with phase inverted is fed back to point G, although not connected to ground, but is held virtually at ground potential irrespective of the magnitudes of the potentials v 1 and v o. The voltage at point G will become exactly zero when negative feedback voltage is exactly equal to positive voltage produced by v 1. Gain. The current i 1 flowing through point G is given by Similarly, At point G, The ratio of output voltage v 0 and input voltage v 1 is known as the gain of the amplifier. Hence the gain of inverting amplifier is given by 71

72 Thus the voltage gain is equal to the ratio of feedback resistance R f to the input resistance R 1. The negative signifies that output voltage is inverted with respect to input voltage. Input resistance. The input resistance of the whole amplifier is defined as the ratio of voltage v 1 to the input current. Thus Here R in refers to the voltage amplifier and not to the OP-AMP which has an infinite input impedance. Negative scalar. Here we shall show that OP-AMP works as a negative scalar. We denote the ratio of R f /R 1 by K 1 a real constant. Now from eq. v o = -Kv 1 Eq. shows that the input voltage scale has been multiplied by a factor - K to give the output voltage scale. Thus the circuit can act as scalar changer. In scalar changer, the precision resistors are used to get the accurate value of scalar factor K. Unity gain amplifier. The output of basic OP-AMP is given by v o R f v R 1 1 If R f = R 1, then A v v v R R o So, the circuit provides a unity voltage gain with phase inversion. NON-INVERTING AMPLIFIER (POSITIVE SCALER) 72

73 The circuit of non-inverting amplifier is shown in fig. Here the input voltage v 2 is applied to the no inverting terminal and hence the name non-inverting amplifier. The potential of point G is also v 2 since the gain of OP- AMP is infinite. The polarity of v o is the same as that of v 2. The voltage across R 1 is v 2 and across R f is (v o -v 2 ). Gain. The values of currents i 1 and i 2 are given as v vo v2 i and i R R1 f Applying Kirchhoff's first law at point G, we get (-i 1 ) + i 2 = 0 v R 2 o 2 1 v v R f 0 v v v 1 1 o 2 2 or v2 Rf R1 R f R1 Rf or v R o f R R 1 f v2 R1 R f or v o R1 Rf Rf 1 R2 R1 R1 or R f A 1 R 1 73

74 So the gain is one plus the ratio of two resistances R f and R 1. Here the output voltage is in phase with input voltage. This circuit offers a high input impedance and low output impedance. Voltage follower. It R 1 is infinite, then A v = 1 i.e. v o = v 2. Thus the output voltage follows the input voltage i.e., OP-AMP circuit acts as the voltage follower. Positive scalar. Here v o /v 2 = R f 1 R1 K v o = Kv 2 So the amplifier acts as positive scalar. The amplifier is used when we require an output which is equal to input multiplied by a positive constant. As the circuit has high input impedance and low output impedance, this is generally used as impedance matching device between high impedance source and low impedance load. EXERCISE ) Explain inverting and non- inverting amplifiers. 2) Define common mode rejection ratio. 3.4 USE OF 741 IC AS ADDER The most useful of the OP-AMP circuits used in analog computers is the summing amplifier circuit. Fig. shows a three input summing circuit. This circuit provides a means of algebraically summing three-input voltages, each multiplied by a constant gain factor. In the circuit G is a virtual ground and the output voltage is phase inverted. 74

75 As G is virtual ground, the different currents are given by v v v i i i andi o 1, 2, 3 R1 R2 R3 Rf v Applying Kirchhoff's current distribution law at point G, we get i 1 + i 2 + i 3 - i = 0 v1 v2 v3 vo or 0 R R R R f R R R v v v v f f f or R1 R2 R3 or v K v K v K v o If R1 = R 2 = R 3 = R and R f /R = K, then R vo K v v v v v v R f Thus the output voltage is proportional to the algebraic sum of three input voltages. Again if R f =R, we have o v v v v In this case, the output is equal to the average of the three inputs. 75 In this case, the output voltage v o is numerically equal to the algebraic sum of the input voltages. Hence the name summing or adder amplifier. If R f = R/3, then o 1/ 3 v v v v 1 2 3

76 3.5 SUBTRACTOR Fig. shows the circuit of the subtractor. The function of the subtractor is to provide an output which is equal to the difference of two input signals or proportional to the difference of two input signals. Here one signal is applied at the inverting terminal while the second signal is applied at the non-inverting terminal of an OP-AMP. Let (v o ) and (v o ) 2 be the output voltages produced by input voltages v 1 and v 2 respectively. Now Since R f >> R 1,i.e., R f / R 1 >>1. According to superposition theorem f vo v1 1 R R f f vo 1 v2 v2 2 R R v v v o o 1 o 2 R R Above Eq. shows that output voltage is proportional to the difference of two input voltages. 76

77 If R f = R 1, then from eq,we get v o = (v 2 -v 1 ) Thus the output voltage is equal to the difference of two input voltages. 3.6 DIFFERENTIATOR The function of the differentiator is to given an output voltage which is proportional to the rate of change of the input voltage. The circuit of a differentiator (fig.) is the same as that of an inverting OP-AMP except that the input resistance R 1 is replaced by a capacitor. When we feed linearly increasing the voltage to the differentiator, we get a constant d.c. output. So it is an inverse mathematical operation to that of an integrator. Assuming that G is at ground potential, we can write for capacitor q v1, where q = charge on capacitor C dv1 1 dq i dq wherei dt C dt C dt Again Substituting the value of i from above eq. s we get dv1 vo CR dt 77

78 This Eq. shows that the output voltage v o is equal to a constant -CR times the time derivative of the input voltage V INTEGRATOR The circuit of integrator is shown in fig. This circuit produces an output voltage which is proportional to the time integral of the input voltage. Due to this reason this is known as integrator. The integrator is an inverting OP-AMP in which feedback resistor R f has been replaced by a capacitor C. Feedback through the capacitor forces a virtual ground to exist at the inverting input terminal. Now the voltage across the condenser is simply the output voltage v o. The capacitive impedance X c can be expressed as X c 1 1 jc sc Where s = j = Laplace notation. v1 From the figure, i1 R vo and i2 scv X At point G, i1 i2 1 c o 78

79 Above Eq. can be rewritten in time domain as 1 v t v t dt ( ) o 1 RC ( ) 1 Above Eq. shows that the output is the integral of the input with an inversion and scale multiplier of 1/RC. When a step voltage is applied at the input terminal, the output voltage is a ramp or linearly changing voltage. Integrators are used in ramp or sweep generators, in filters, analog computers etc. 3.8 OP-AMP AS CONSTANT CURRENT SOURCE In any device, when the output current is proportional to the input signal voltage, the device is termed as voltage to current converter. The circuit of voltage to current converter is shown in fig. Here the resistance R f is replaced by a load resistance R L. The circuit is used in analog to digital converter. Let the current flowing through R L be i L. Hence i L v1 R 1 Thus the current i L is independent of the load resistance R L and is proportional to the input voltage v 1. Differentiating Circuit 79

80 A circuit in which output voltage is directly proportional to the derivative of the input is known as a differentiating circuit. Output d (Input) dt A differentiating circuit is a simple RC series circuit with output taken across the resistor R. The circuit is suitability designed so that output is proportional to the derivative of the input. Thus if a d.c. or constant input is applied to such a circuit, the output will be zero. It is because the derivative of a constant is zero. Fig. shows a typical differentiating circuit. The output across R will be the derivative of the input. It is important to note that merely using voltage across R does not make the circuit a differentiator; it is also necessary to set the proper circuit values. In order to achieve good differentiation, the following two conditions should be satisfied: (i) The time constant RC of the circuit should be much smaller than the time period of the input wave. (ii) The value of X C should be 10 or more times larger than R at the operating frequency. Fulfilled these conditions, the output across R in fig. will be the derivative of the input. Let e i be the input alternating voltage and let i be the resulting alternating current. The charge q on the capacitor at any instant is q = Ce c 80

81 dq d d dt dt dt Now i q Ce d dt or i C e Since the capacitive reactance is very much larger than R, the input voltage can be considered equal to the capacitor voltage with negligible error i.e. e c = e i d dt i C e c i c Output voltage, e o = ir d RC dt e i d e i RCis cons t dt ( tan ) Output voltage d (Input) dt Output waveforms. The output waveform from a differentiating circuit depends upon the time constant and shape of the input wave. Three important cases will be considered. EXERCISE-3.3 1) Explain the following (i) adder (ii) subtractor (iii) differentiator (iv)integrator. 3.9 COMPARATOR In electronics, a comparator is a device that compares two voltages or currents and switches its output to indicate which is larger. It is used in Analog-to-digital converter (ADCs). An operational amplifier (OP-AMP) has a well balanced difference input and a very high gain. This parallels the characteristics of 81

82 comparators and can be substituted in applications with low-performance requirements. In theory, a standard OP-AMP operating in open-loop configuration (without negative feedback) may be used as a low-performance comparator. When the noninverting input (V+) is at a higher voltage than the inverting input (V-), the high gain of the OP-AMP causes the output to saturate at the highest positive voltage it can output. When the non-inverting input (V+) drops below the inverting input (V-), the output saturates at the most negative voltage it can output. The OP-AMP's output voltage is limited by the supply voltage. An OP-AMP operating in a linear mode with negative feedback, using a balanced, split-voltage power supply, (powered by ± V S ) its transfer function is typically written as: V out = A o (V 1 V 2 ). However, this equation may not be applicable to a comparator circuit which is non-linear and operates open-loop (no negative feedback). In practice, using an operational amplifier as a comparator presents several disadvantages as compared to using a dedicated comparator: OP-AMPs are designed to operate in the linear mode with negative feedback. Hence, an OP-AMP typically has a lengthy recovery time from saturation. Almost all OP-AMPs have an internal compensation capacitor which imposes slew rate limitations for high frequency signals. Consequently an OP-AMP makes a sloppy comparator with propagation delays that can be as slow as tens of microseconds. 1.Since OP-AMP do not have any internal hysteresis an external hysteresis network is always necessary for slow moving input signals. 2.The quiescent current specification of an OP-AMP is valid only when the feedback is active. Some OP-AMPs show an increased quiescent current when the inputs are not equal. 3.A comparator is designed to produce well limited output voltages that easily interface with digital logic. Compatibility with digital logic must be verified while using an OP-AMP as a comparator. 4.Some multiple-section OP-AMP may exhibit extreme channel-channel interaction when used as comparators. 5.Many OP-AMP have back to back diodes between their inputs. OP-AMP inputs usually follow each other so this is fine. But comparator inputs are not usually the same. The diodes can cause unexpected current through inputs SQUARE WAVE GENERATOR. 82

83 When the input fed to a differentiating circuit is a square wave, output will consist of sharp narrow pulses as shown in Fig. During the OC part of input wave, its amplitude changes abruptly and hence the differentiated wave will be a sharp narrow pulse as shown in Fig. However, during the constant part CB of the input, the output will be zero because the derivative of a constant is zero. Let us look at the physical explanation of this behaviour of the circuit. Since time constant RC of the circuit is very small w.r.t. time period of input wave and X c >> R, the capacitor will become fully charged during the early part of each half-cycle of the input wave. During the remainder part of the half cycle, the output of the circuit will be zero because the capacitor voltage (e c ) neutralises the input voltage and there can be no current flow through R. Thus we shall get sharp pulse at the output during the start of each half-cycle of input wave while for the remainder part of the halfcycle of input wave, the output will be zero. In this way, a symmetrical output wave with sharp positive and negative peaks is produced. Such pulses are used in many ways in electronic circuits e.g. in television transmitters and receivers, in multi vibrators to initiate action etc TRIANGULAR WAVE GENERATOR. When the input fed to a differentiating circuit is a triangular wave, the output will be a rectangular wave as shown in Fig. During the period OA of the input wave, its amplitude changes at a constant rate and, therefore, the differentiated wave has a constant value for each constant rate of change. During the period AB of the input wave, the change is less abrupt so that the output will be a very narrow pulse of 83

84 rectangular form. Thus when a triangular wave is fed to a differentiating circuit, the output consists of a succession of rectangular waves of equal or unequal depending upon the shape of the input wave. When input is a sine wave. A sine wave input becomes a cosine wave and a cosine wave input becomes an inverted sine wave at the output. (i) The time constant RC of the circuit should be very large as compared to the time period of the input wave. (ii) The value of R should be 10 or more times larger than X C. Let e i be the input alternating voltage and let i be the resulting alternating current. Since R is very large is compared to capacitive reactance X C of the capacitor, it is reasonable to assume that voltage across R (i.e. e R ) is equal to the input voltage i.e. e i = e R Now e R ei i R R The charge q on the capacitor at any instant is q i dt Output voltage, q i dt e o C C 84

85 ei dt R C e i i R = 1 ei dt RC RC iscons tan t e idt Output voltage Input Voltage EXERCISE ) What is a comparator? 2) Explain square wave generator & triangular wave generator UNIT SUMMARY (i) The operational amplifier is a direct-coupled, high gain, negative feedback amplifier. They are made with different internal configurations in linear ICs. (ii) Slew rate (SR) is defined as the maximum rate of change of output voltage per unit of time and is expressed in volts per microseconds, i.e., (iii) Inverting Operational Amplifier works as a negative scalar. (iv) A circuit in which output voltage is directly proportional to the derivative of the input is known as a differentiating circuit. (v)a comparator is a device that compares two voltages or currents and switches its output to indicate which is larger. It is used in Analog-to-digital converter REFERENCES 85

86 1)Operational Amplifiers by Clayton 2)Electronic Devices and Circuits by Millman and Halkias (S. Chand & Company Ltd.) 3)Electronic Devices and Circuits an Introduction by Mottershed 4)Transistor Physics by Sarkar 5)Electronic Devices and Circuits by Sanjeev Gupta (Dhanpat Rai Publications) 6)A Textbook of Electronic Devices and Circuits by R.S. Sedha (S. Chand & Company Ltd.) SOLUTION EXERCISE ) Refer to article 3.0, 2) Refer to article 3.0, 3) Refer to article 3.1, 4) Refer to article 3.2 EXERCISE ) Refer to article 3.3, 2) Refer to article 3.3 EXERCISE ) Refer to article 3.4, 3.5, 3.6 & 3.7 EXERCISE ) Refer to article 3.9, 2) Refer to article 3.10, 3.11 BLOCK-II 86

87 UNIT: IV VOLTAGE MULTIPLIER CIRCUITS Structure: 4.0 Introduction 4.1 Objectives 4.2 Voltage multipliers circuits 4.3 Wave shaping circuits 4.4 Clipping Circuits 4.5 Clamping Circuits 4.6 Differentiating and Integrating circuits 4.7 Voltage regulated power supply and Regulation Sensitivity and Stability Factors 4.8 Unit Summary 4.9 References BLOCK-II 87

88 UNIT:IV VOLTAGE MULTIPLIER CIRCUITS 4.0 INTRODUCTION A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage by means of capacitors and diodes combined into a network. 4.1 OBJECTIVES Voltage multipliers can be used to generate bias voltages ranging from a few volts for electronic appliances, to millions of volts for purposes such as high-energy physics experiments and lightning safety testing. 4.2 VOLTAGE MULTIPLIER CIRCUITS Assuming that the peak voltage of the AC source is +U s we can describe the (simplified) working of the cascade as follows: 1. Negative peak ( U s ): The C 1 capacitor is charged through diode D 1 to 0 V(potential difference between left and right plate of the capacitor is U s ) 2. Positive peak (+U s ): the potential of C 1 adds with that of the source, thus charging C 2 to 2U s through D 2 3. Negative peak: potential of C 1 drops to 0 V thus allowing C 3 to be charged through D 3 to 2U s. 4. Positive peak: potential of C 1 rises to 2U s (analogously to step 2), also charging C 4 to 2U s. The output voltage (the sum of voltages under C 2 and C 4 ) raises till 4U s. 88

89 In reality more cycles are required for C 4 to reach the full voltage. Each additional stage of two diodes and two capacitors increases the output voltage by twice the peak AC supply voltage. EXERCISE4.1 1) What is a voltage multiplier? 2) What is the use of voltage multiplier? 4.3 WAVE SHAPING CIRCUITS Electronic circuits used to create or modify specified time-varying electrical voltage or current waveforms using combinations of active electronic devices, such as transistors or analog or digital integrated circuits, and resistors, capacitors, and inductors. Most wave-shaping circuits are used to generate periodic waveforms. The common periodic waveforms include the square wave, the sine and rectified sine waves, the saw tooth and triangular waves, and the periodic arbitrary wave. The arbitrary wave can be made to conform to any shape during the duration of one period. This shape then is followed for each successive cycle. A number of traditional electronic and electromechanical circuits are used to generate these waveforms. Sine-wave generators and LC, RC, and beat-frequency oscillators are used to generate sine waves; rectifiers, consisting of diode combinations interposed between sine-wave sources and resistive loads, produce rectified sine waves; multivibrators can generate square waves; electronic integrating circuits operating on square waves create triangular waves; and electronic relaxation oscillators can produce saw tooth waves. In many applications, generation of these standard waveforms is now implemented using digital circuits. Digital logic or microprocessors generate a sequence of numbers which represent the desired waveform mathematically. These numerical values then are converted to continuous-time waveforms by passing them through a digital-to-analog converter. Digital waveform generation methods have the ability to generate waveforms of arbitrary shape, a capability lacking in the traditional approaches. 4.4 CLIPPING CIRCUITS The circuit with which the waveform is shaped by removing (or clipping) a portion of the applied wave is known as a Clipping circuit. 89

90 Clippers find extensive use in radar, digital and other electronic systems. Although several clipping circuits have been developed to change the wave shape, we shall confine our attention to diode clippers. These clippers can remove signal voltages above or below a specified level. The important diode clippers are (i) positive clipper (ii) biased clipper (iii) combination clipper. (i) Positive clipper. A positive clipper is that which removes the positive half-cycles of the input voltage. Fig. shows the typical circuit of a circuit of a positive clipper using a diode. As shown, the output voltage has all the positive half-cycle removed or clipped off. The circuit action is as follows. During the positive half cycle of the input voltage, the diode is forward biased and conducts heavily. Therefore, the voltage across the diode (which behaves as a short) and hence across the load R L is zero. Hence output voltage during positive half-cycle is zero. During the negative half-cycle of the input voltage, the diode is reverse biased and behave as an open. In this condition, the circuit behaves as a voltage divider with an output given by: Output voltage = RL V R R L m Generally, R L is much greater than R. Output voltage = - V m It may be noted that if it is desired to remove the negative half-cycle of the input, the only thing to be done is to reverse the polarities of the diode in the circuit shown in Fig. Such a clipper is then called a negative clipper. (ii) Biased clipper. Sometimes it is desired to remove a small portion of positive or negative half-cycle of the signal voltage. For this purpose, biased clipper is used. 90

91 Fig. shows the circuit of a biased clipper using a diode with a battery of V volts. With the polarities of battery shown, a portion of each positive half-cycle will be clipped. However, the negative half-cycle will appear as such across the load. Such a clipper is called biased positive clipper. The circuit action is as follows. The diode will conduct heavily so long as input voltage is greater than +V. When input voltage is greater than +V, the diode behave as a short and the output equals +V. The output will stay at +V so long as the input voltage is greater than +V. During the period the input voltage is less than +V, the diode is reverse biased and behaves as an open. Therefore, most of the input voltage appears across the output. In this way, the biased positive clipper removes input voltage above +V. During the negative half-cycle of the input voltage, the diode remain reverse biased. Therefore, almost entire negative half-cycle appears across the load. If it is desired to clip a portion of negative half-cycles of input voltage, the only thing to be done is to reverse the polarities of diode or battery. Such a circuit is then called a biased negative clipper. (iii) Combination clipper. It is a combination of biased positive and negative clippers. With a combination clipper, a portion of both positive and negative halfcycle of input voltage can be removed or clipped as shown in Fig. 91

92 The circuit action is as follows. When positive input voltage is greater than +V 1, diode D 1 conducts heavily while diode D 2 remains reverse biased. Therefore, a voltage +V 1 appears across the load. This output stays at +V 1 so long as the input voltage exceeds +V 1. On the other hand, during the negative half-cycle, the diode D 2 will conduct heavily and the output stays at -V 2 so long as the input voltage is greater than -V 2. Note that +V 1 and -V 2 are less than +V m respectively. Between +V 1 and -V 2 neither diode is on. Therefore, in this condition, most of the input voltage appears across the load. It is interesting to note that this clipping circuit can give square wave output if V m is much greater than clipping levels. Applications of Clippers: Clippers are used to perform 1) Changing the shape of a waveform 2)Circuit transient protection. 4.5 CLAMPING CIRCUITS A circuit that places either the positive or negative peak of a signal at a desired d.c. level is known as a Clamping circuit. A clamping circuit (or a clamper) essentially adds a d.c. component to the signal. Fig. shows the key idea behind clamping. The input signal is a sine wave having a peak-to-peak value of 10V. The clamper adds the d.c. component and pushes the signal upwards so that the negative peaks fall on the zero level. As you can see, the waveform now has peak values of + 10V and 0V. It may be seen that the shape of the original signal has not changed; only there is vertical shift in the signal. Such a clamper is called a positive clamper. The negative 92

93 clamper does the reverse i.e. it pushes the signal downwards so that the positive peaks fall on the zero level. The following points may be noted carefully. (i) The clamping circuit does not change the peak-to-peak or r.m.s. value of the waveform. Thus referring to Fig. above, the input wave form and clamped output have the same peak-to-peak value i.e., 10V in this case. If you measure the input voltage and clamped output with an a.c. voltmeter, the readings will be the same. (ii) A clamping circuit changes the peak and average values of a waveform. This point needs explanation. Thus in the above circuit, it is easy to see that input waveform has a peak value of 5V and average value over a cycle is zero. The clamped output varies between 10V and 0V. Therefore, the peak value of clamped output is 10V and average value is 5V. Hence we arrive at a very important conclusion that a clamper changes the peak value as well as the average value of a waveform. The operation of a clamper is based on the principle that charging time of a capacitor is made very small as compared to its discharging time. Positive clamper The input signal of a positive clamper is assumed to be a square wave with time period T. The clamped output is obtained across R L. The circuit design incorporates two main features. Firstly, the values of C and R L are so selected that time constant is very large. This means the voltage across the capacitor will not discharge during the interval the diode is non conducting. During the negative half cycle of the input signal, the diode is forward biased and during the positive half cycle of the input signal, the diode is reverse biased. The resulting waveform is shown in fig. and V out = 2V. 93

94 Negative clamper The clamped output of negative clamper is taken across R L. During the positive half cycle of the input signal, the diode is forward biased and during the negative half cycle of the input signal, the diode is reverse biased. 94

95 The resulting waveform shown in fig. and V out = -2V. EXERCISE ) What is clipper? 2) Describe (i) positive clipper (ii) biased clipper (iii) combination clipper. 95

96 3) What do you understand by clamping circuit? 4) Explain the action of positive clamper and negative clamper? 4.6 DIFFERENTIATING AND INTEGRATING CIRCUITS By introducing electrical reactance into the feedback loops of OP-AMP amplifier circuits, we can cause the output to respond to changes in the input voltage over time. Drawing their names from their respective calculus functions, the integrator produces a voltage output proportional to the product (multiplication) of the input voltage and time; and the differentiator (not to be confused with differential) produces a voltage output proportional to the input voltage's rate of change. Capacitance can be defined as the measure of a capacitor's opposition to changes in voltage. The greater the capacitance, the more the opposition. Capacitors oppose voltage change by creating current in the circuit: that is, they either charge or discharge in response to a change in applied voltage. So, the more capacitance a capacitor has, the greater its charge or discharge current will be for any given rate of voltage change across it. The equation for this is: The dv/dt fraction is a calculus expression representing the rate of voltage change over time. If the DC supply in the above circuit were steadily increased from a voltage of 15 volts to a voltage of 16 volts over a time span of 1 hour, the current through the capacitor would most likely be very small, because of the very low rate of voltage change (dv/dt = 1 volt / 3600 seconds). However, if we steadily increased the DC supply from 15 volts to 16 volts over a shorter time span of 1 second, the rate of voltage change would be much higher, and thus the charging current would be much higher (3600 times higher, to be exact). Same amount of change in voltage, but vastly different rates of change, resulting in vastly different amounts of current in the circuit. To put some definite numbers to this formula, if the voltage across a 47 µf capacitor was changing at a linear rate of 3 volts per second, the current "through" the capacitor would be (47 µf)(3 V/s) = 141 µa. We can build an OP-AMP circuit which measures change in voltage by measuring current through a capacitor and outputs a voltage proportional to that current. 96

97 EXERCISE ) Explain differentiating and integrating circuits. 4.7 VOLTAGE REGULATED POWER SUPPLY REGULATION SENSITIVITY AND STABILITY FACTORS A voltage regulator is an electrical regulator designed to automatically maintain a constant voltage level. A voltage regulator may be a simple "feed-forward" design or may include negative feedback control loops. It may use an electromechanical mechanism, or electronic components. Depending on the design, it may be used to regulate one or more a.c. or d.c. voltages. Electric voltage regulators: A simple voltage regulator can be made from a resistor in series with a diode (or series of diodes). Due to the logarithmic shape of diode V-I curves, the voltage across the diode changes only slightly due to changes in current drawn. When precise voltage control is not important, this design may work fine. Feedback voltage regulators operate by comparing the actual output voltage to some fixed reference voltage. Any difference is amplified and used to control the regulation element in such a way as to reduce the voltage error. This forms a negative feedback control loop; increasing the open-loop gain tends to increase regulation accuracy but reduce stability (avoidance of oscillation, or ringing during step changes). There will also be a trade-off between stability and the speed of the response to changes. If the output voltage is too low (perhaps due to input voltage reducing or load current increasing), the regulation element is commanded, up to a point, to produce a higher output voltage by dropping less of the input voltage (for linear series regulators and buck switching regulators), or to draw input current for longer periods (boost-type switching regulators); if the output voltage is too high, the regulation element will normally be commanded to produce a lower voltage. However, many regulators have over-current protection, so that they will entirely stop sourcing current (or limit the current in some way) if the output current is too high, and some regulators may also shut down if the input voltage is outside a given range. 97

98 Regulator with an operational amplifier The stability of the output voltage can be significantly increased by using an operational amplifier. In this case, the operational amplifier drives the transistor with more current if the voltage at its inverting input drops below the output of the voltage reference at the non-inverting input. Using the voltage divider (R1, R2 and R3) allows choice of the arbitrary output voltage between U z and U in. Voltage Stabilizers: Many simple DC power supplies regulate the voltage using a shunt regulator such as a zener diode, avalanche breakdown diode, or voltage regulator tube. Each of these devices begins conducting at a specified voltage and will conduct as much current as required to hold its terminal voltage to that specified voltage. The power supply is designed to only supply a maximum amount of current that is within the safe operating capability of the shunt regulating device (commonly, by using a series resistor). In shunt regulators, the voltage reference is also the regulating device. If the stabilizer must provide more power, the shunt regulator output is only used to provide the standard voltage reference for the electronic device, known as the voltage stabilizer. The voltage stabilizer is the electronic device, able to deliver much larger currents on demand. EXERCISE

99 1) What is a voltage regulator? 2) Explain in detail the action of voltage regulator. 3) What do you understand by voltage stabilizer? 4.8 UNIT SUMMARY (i) The operational amplifier is a direct-coupled, high gain, negative feedback amplifier. They are made with different internal configurations in linear ICs. (ii) Slew rate (SR) is defined as the maximum rate of change of output voltage per unit of time and is expressed in volts per microseconds, i.e., (iii) Inverting Operational Amplifier works as a negative scalar. (iv) A circuit in which output voltage is directly proportional to the derivative of the input is known as a differentiating circuit. (v)a comparator is a device that compares two voltages or currents and switches its output to indicate which is larger. It is used in Analog-to-digital converter. (vi) A voltage multiplier is an electrical circuit that converts AC electric power from a lower voltage to a higher DC voltage by means of capacitors and diodes combined into a network. (vii)wave- shaping circuits are used to generate periodic waveforms. (viii) The circuit with which the waveform is shaped by removing (or clipping) a portion of the applied wave is known as clipping circuit. (ix) A circuit that places either the positive or negative peak of a signal at a desired d.c. level is known as a clamping circuit. (x) A voltage regulator or an electrical regulator designed to automatically maintain a constant voltage level. 4.9 REFERENCES 1)Operational Amplifiers by Clayton 99

100 2)Electronic Devices and Circuits by Millman and Halkias (S. Chand & Company Ltd.) 3)Electronic Devices and Circuits an Introduction by Mottershed 4)Transistor Physics by Sarkar 5)Electronic Devices and Circuits by Sanjeev Gupta (Dhanpat Rai Publications) 6)A Textbook of Electronic Devices and Circuits by R.S. Sedha (S. Chand & Company Ltd.) SOLUTION EXERCISE ) Refer to article 4.0, 2) Refer to article 4.1 EXERCISE ) Refer to article 4.4, 2) Refer to article 4.4, 3) Refer to article 4.4, 4) Refer to article 4.5 EXERCISE ) Refer to article 4.6 EXERCISE ) Refer to article 4.7, 2) Refer to article 4.7, 3) Refer to article

101 BLOCK-III M.Sc. Previous PAPER-IV SOLID STATE ELECTRONICS UNIT:V COMMUNICATION ELECTRONICS Structure: 5.0 Introduction 5.1 Objectives 5.2 Modulation and Types of modulation analysis and production of AM and FM wave Generation DSB/SC modulation of AM waves 5.3 Demodulation of AM waves Generation of DSBSC waves and Coherent detection of DSB/SC waves 5.4 SSB modulation 5.5 Generation and detection of SSB waves 5.6 Vestigial sideband modulation 5.7 Frequencies division multiplexing 5.8 Unit Summary 5.9 References UNIT:VI ELECTRONIC DEVICES Structure: 6.0 Introduction 6.1 Objectives 101

102 6.2 Electronic devices: JFET, MOSFET AND MESFET 6.3 Structure & working of their characteristics under different conditions 6.4 Microwave devices tunnel diode and Gunn diode 6.5 Impatt diode and parametric devices 6.6 Unit Summary 6.7 References UNIT: VII PHOTONIC DEVICES Structure: 7.0 Introduction 7.1 Objectives 7.2 Radiotive and non- radiotive transmitter 7.3 LDR 7.4 Photodiode Detectors 7.5 Solar cells 7.6 LED diode lasers condition for population inversion light contentment factor 7.7 Threshold current for lasing 7.8 Unit Summary 7.9 References 102

103 5.0 INTRODUCTION BLOCK-III UNIT: V COMMUNICATION ELECTRONICS For the transmission of message to distant parts of the globe, sound waves are first converted into electrical signals with the help of microphone. To release this audio signal into space, antenna is employed for effective radiation of energy. But the frequency of audio signal is always quite low and consequently, it cannot be fed as such to the antenna for communication. Therefore, before applying the audio signal to the antenna, a process is performed in which the audio signal is superimposed on a high frequency wave, called carrier wave. In this process, as mentioned, a separate high frequency wave is needed because we cannot change any of the characteristics, e.g., amplitude, frequency and phase of the audio signal as it would amount to a change in the message to be communicated. But the amplitude, of frequency or phase of the high frequency wave is modified in accordance with the audio signal, so that the resultant wave inherits the frequency of modulated wave is quite high, effective radiation from antenna takes place. 5.1 OBJECTIVES The purpose of modulation is to alter the frequency level of intelligence. There are two main reasons for this alteration in frequency level: (i)at high frequencies, the intelligence practically can be transmitted by radiation. (ii)different messages having different frequency levels can be transmitted simultaneously without any interference. 5.2 MODULATION AND TYPES OF MODULATION ANALYSIS AND PRODUCTION OF AM AND FM WAVE AND GENERATION DSB/SC MODULATION OF AM WAVES Modulation is defined as a process by which a high frequency carrier is made to vary in some manner as function of the instantaneous value of message to be transmitted. The most common type of modulation is amplitude modulation, phase modulation and frequency modulation. 103

104 Consider the following waveform which represents a high frequency sinusoidal carrier of frequency ω e e (t) A ( t) cos e ( t) Basically, there are three parameters which may be varied as function of the message to be transmitted. (i)the first choice would be to let the amplitude A(t) vary as the function of the message, i.e., the modulating signal. This choice is certainly feasible and is given the name amplitude modulation. (ii)the second choice would be to let the phase vary which conveys the message. Again, this is also done and is denoted by the term phase modulation. (iii)lastly, if the derivative of with respect to time is assumed to vary, resulting in frequency variations, the modulation process is called frequency modulation. Amplitude modulation is often referred as linear modulation. Phase and frequency modulation belongs to the general class of non-linear modulation popularly referred as angle modulation or exponential modulation. Amplitude Modulation When amplitude of a sinusoidal signal is varied in accordance with the amplitude of the message signal the sinusoidal signal is said to be amplitude modulated or A.M. Let the carrier and modulated signals be represented respectively by V c (t)= A c cos (ω c t + ) 104

105 V m (t)= A m cos (ω m t) Where A c is amplitude of carrier is the initial face angle of the carrier A m is the amplitude of modulating signal ω c is angular frequency of the carrier ω m is angular frequency of the modulating signal The A m signal is then represented by v(t) = A c ( 1+ m cos ω m t) cos ω c t The deviation in amplitude from the carrier amplitude is controlled by the constant m. Power of an A.M. can be determined by the equation by the equation From the equation v(t) = A c ( 1+ m cos ω m t) cos ω c t = A c cos ω c t + A c m cos ω m t cos ω c t = A c cos ω c t + A c m (cos ω m t cos ω c t) From 2 cos A cos B = cos (A+B) + cos (A-B), above equation can be written as v(t) = A c cos ω c t+ m/2[(a c (cos (ω c+ ω m )t+ A c cos (ω c - ω m ) t] The first term represents the carrier signal with amplitude A c. The second term represents for sinusoidal signals. The sideband having frequency higher (ω c+ ω m ) than that of the carrier is called upper sideband. The sideband having frequency lower (ω c - ω m ) than that of the carrier is called upper sideband. Generation of FM waves A wave whose frequency is varied in proportion to the instantaneous amplitude of the information wave is frequency modulation. The result of this encoding or 105

106 modulation process is a complex modulated wave whose instantaneous frequency is a function of the amplitude of the modulating wave and differs from the frequency of the carrier from instant to instant as the amplitude of the modulating wave varies. Let the modulation signal V m (t) be sinusoidal of frequency and a amplitude, then this signal is represented by the equation V m (t)= A m cos (ω m t). And ω t (t) = ω c + k A m cos ω m t = ω c + ω cos ω m t, where ω = k A m and f = k A m /2 The instantaneous frequency deviation is ω cos ω m t which is proportional to the magnitude of modulating signal A m cos (ω m t). This shows instantaneous frequency lines in the range f c + f to f c - f. Comparison between frequency modulation and Amplitude Modulation Frequency Modulation: (i) There is a substantial reduction in interference effects. That is, noise can be easily minimized in f.m. systems. The presence of the noise at the receiver input in addition to the desired signal tends to alter the input voltage both in instantaneous amplitude and instantaneous phase. In frequency modulation system, amplitude variations can be eliminated by slicing them with the help of limiter, so that always constant amplitude is applied to the discriminator. (ii) No restriction is placed on the modulation index. The instantaneous frequency deviation is proportional to the instantaneous magnitude of the modulating signal. (iii)the average power in frequency modulated wave is the same as that contained in the unmodulated wave. Amplitude Modulation: (i) In this type of modulation, alternation of the amplitude of the desired signal by the noise at the receiver input severely affects the response and amounts to marked distortion. 106

107 (ii) In amplitude modulation, use of an excessively large modulating signal may result in distortion because of over modulation. Modulation index can have a maximum value unity for distortion-less modulation. (iii) The average power in modulated wave is greater than that contained in unmodulated wave. This added power is provided by the modulating source. GENERATION DSB/SC MODULATION OF AM WAVES Generation of Amplitude Modulation-DSB/SC AM-DSB/SC is an abbreviation of amplitude-modulated, double-sideband, suppressed carrier. As shown in Fig., let us assume F(f) to be the Fourier transform of the information or modulation source, e m (t). Then X(f) shown in Fig (b) will represent the translated spectrum, that is, the spectrum of e(t) cos ω c t. The receiver accomplishes frequency conversion of X(f) by multiplying e(t) cos ω c t by cos ω c t. The resulting spectrum is denoted by Y(f), in Fig. Recovery of e m (t) may now be accomplished by filtering as indicated by dotted lines in Fig. The actual system which accomplishes this is shown in Fig. The disadvantage of this system is the necessity of knowing cos ω c t at the receiver. This method of detection is called synchronous detection since the detector 107

108 must have a carrier wave that is in synchronism with that used at the transmitter. The synchronism may be accomplished by transmitting a pilot carrier. The system performance of AM-DSB/SC is identical to AM-DSB (described in the preceding article) except for the power wasted by the carrier ; that is, if an AM-DSB and an AM-DSB/SC system have equal power in the sidebands, then the output signal-to-noise ratios are equal. If an AM-DSB and an AM-DSB/SC system have the same total transmitted powers, then the output signal-to-noise ratios differ by a factor of three, that is, This difference can be explained by noting that for equal powers the AM-DSB system only has 1/3 rd of the signal power of the AM-DSB/SC system. For AM/DSB, 1.5 watts transmitted means 1.0 watts in the carrier and 0.5 watts in the side bands. Hence the transmitted sideband powers differ by a factor of three and we would therefore expect the output signal-to-noise ratio to differ by the same factor. Demodulation is the act of extracting the original information-bearing signal from a modulated carrier wave. A demodulator is an electronic circuit (or computer 108

109 program in a software defined radio) that is used to recover the information content from the modulated carrier wave. Demodulation of AM waves: An AM signal encodes the information onto the carrier wave by varying its amplitude in direct sympathy with the analogue signal to be sent. There are two methods used to demodulate AM signals. AM-DSB has the advantage that it does not require synchronous detection as in the case of AM/DSB/SC and AM-SSB to be studied in subsequent articles. As shown in Fig AM-DSB/SC has information contained in both the amplitude and phase considering e m (t) sinusoidal. Synchronous (often referred as coherent) detection is necessary to extract the information in phase and amplitude. Since e m (t) changes sign, it causes the carrier to change phase. Hence we modulate by a source that does not change sign. This can be achieved by adding a bias component to e m (t) positive and then modulate. This is shown in Fig. As we already know this type of modulation is known as AM-SSB. It may be mentioned here that the Fourier transform of [K+e m (t)] cos ω c (t) is identical to the AM-DBS system except that now we have a carrier component at f c. 109

110 The detection problem is, however, completely different, because now all the information is in the amplitude and an amplitude-sensitive device may be used to recover e m (t). Thus the advantage of AM-DSB is the case with which reception occurs. The disadvantage is the large amount of power wasted in the carrier components. EXERCISE ) What is modulation? Why is modulation necessary in communication system? 2) Explain amplitude modulation. Derive the voltage equation of an AM wave. 3) What do you understand by sideband? 4) What do you understand by frequency modulation? Explain its advantages over amplitude modulation. 5) Explain with diagram the generation of DSB/SC modulation of A.M. waves. 5.3 DEMODULATION OF AM WAVES AND GENERATION & COHERENT DETECTION OF DSB/SC (DOUBLE-SIDEBAND) WAVES The envelope detector is a very simple method of demodulation. It consists of a rectifier (anything that will pass current in one direction only), and a low-pass filter. The rectifier may be in the form of a single diode, or may be more complex. Many natural substances exhibit this rectification behavior, which is why it was the earliest modulation and demodulation technique used in radio. The filter is usually a RC low-pass type, but the filter function can sometimes be achieved by relying on the limited frequency response of the circuitry following the rectifier. The crystal set exploits the simplicity of AM modulation to produce a receiver with very few parts, using the crystal as the rectifier, and the limited frequency response of the headphones as the filter. The product detector multiplies the incoming signal by the signal of a local oscillator with the same frequency and phase as the carrier of the incoming signal. After filtering the original audio signal will result. This method will decode both AM and SSB, although if the phase cannot be determined a more complex setup is required. 110

111 An AM signal can be rectified without requiring a coherent demodulator. For example, the signal can be passed through an envelope detector (a diode rectifier and a low-pass filter). The output will follow the same curve as the input baseband signal. There are forms of AM in which the carrier is reduced or suppressed entirely, which require coherent demodulation. 5.4 SSB MODULATION AM-SSB is an abbreviation for amplitude modulation single sideband. Instead of transmitting the total spectrum about f c, that is both sidebands, only one sideband is transmitted. This system is shown in Fig. The advantages of this system over AM- DSB/SC are that the required channel bandwidth is reduced by a factor of ½. The disadvantage of this system is the same as that of AM-DSB-SC that is this also requires synchronous detection with the recent developments of atomic clocks as frequency standards it has become possible to eliminate the pilot carriers. However, as already explained, AM-DSB does not require synchronous detection. Let us now consider an AM-SSB system with emphasis on system performance. Let us first consider a simplified means of producing an AM-SSB wave. Shown in Fig is the phase-shift method of generating SSB wave. Thus e s (t) represents a single sideband at f=f c =f m. Assuming as the transmitted wave the total transmitted power will be 2 Em P t 2 111

112 and all this power is useful signal power; that is, it is all in the sideband. Next consider the simplified AMSSB receiver shown in Fig. Let the input to the multiplier circuit be the AM-SSB signal + noise. Representing the noise as a finite number of discrete components, we have e in f E c m cos( ) t (2k 1) f t 2 c m fm / f k 1 2 n cos 2 It may be mentioned here that only noise terms cover one sideband since the amplifier need only half a bandwidth of f m. After mixing, we have e fm / f 2 ( t) Em cos ( c m ) t cos et 2 k1 n cos 2 f c (2k 1) 2 f t cosct Assuming the filter to pass only those terms having frequencies less than f m, we get f m / f Em (2k 1) e0 ( t) cos mt ncos 2 2 k 1 2 f The first term represents desired signal, thus S 0 E m 8 2 The second term represents noise. Each discrete component has a mean-square value n 2 /2, and there is f m /-f of them. Thus, Since the noise at the input to the mixer is 2ηf m, we have 112

113 N 0 N m 4 Using Eqs. we get S N 0 0 Pt 2 nf m S N in in Thus the pre-detection and post detection signal-to-noise are equal. Advantages of Single Side Band Modulation: (i) Bandwidth is SSB transmission is half than in double-side band system e.g. bandwidth occupied by one radio telephone channel is reduced to half i.e. only 3kc/s instead of 6kc/s. (ii) In SSB system, no carrier is transmitted and therefore possibility of interference with other channels is avoided. (iii)the improvement in signal to noise ratio is from 10 to 12 db at the receiver output over that in double sideband system. (iv) SSB system eliminates the possibility of distortion due to selective fading. (v)ssb system provides an improvement in signal to noise of at least 9 dbs. Disadvantages of Single Side Band transmission: (i) The transmitter and receiver become more complex and performance required is of high standard. (ii) For demodulation process, carrier is inserted at the receiver. The frequency of this reinserted carrier must be within 15 c/s of the suppressed carrier frequency in each case of speech and 4c/s in case of music. Such a requirement complicates the demodulating process; because to meet it, this is necessary to transmit a pilot signal or the carrier voltage itself at a very low level for synchronizing the receiver oscillator frequency. This signal has to be filtered at the receiver with the use of highly selective filters, amplified and then either reinserted to provide the carrier or is used to control the carrier frequency produced by the local oscillator. Design of these highly selective filters is thus involved in SSB receiver. This complexity contributes to an addition in cost. Applications of Single Side band Transmission: Because of complexity and cost of SSB receiver, this system is not used for commercial broadcasting. It finds use in other fields such as: (i) Police wireless communication 113

114 (ii) SSB telegraph system (iii) Point-to-Point radio telephone communication (iv) In V.H.F. and U.H.F. communications 5.5 GENERATION AND DETECTION OF SSB WAVES There are two methods for production of SSB signals. First method is based on the frequency-domain description of the SSB signal which suggests that the SSB signal can be obtained from the corresponding DSB/SC through proper filtering. This method is called frequency discrimination method or filter method. Second method is based on the time domain description of the SSB signal and generally requires 90o phase shift networks for the modulating and carrier signals. This method is called phase discriminator method or phase shift method. Third method makes use of product modulators (balanced modulator) and low pass filter and is applicable to modulating signals having a finite energy gap near zero frequency. Since this method was devised by Weaver is known as Weavers method or third method. We will now discuss these three methods in detail. (i) Filter method. This method simply involves in the generation of a DSB/SC signal for the given carrier signal and the given modulating signal and then filtering out the undesired sideband. The method looks fairly simple; but the filtering will present serious problem when the highest frequency of the lower sideband (LSB) is very near to the lower frequency of the upper sideband (USB) that is when the frequency separation between LSB and USB is too small. The separation is twice the minimum frequency in the modulating signals x(t). Thus if a tuned circuit is used as a band pass filter to reject one of the 114

115 sidebands, the Q of the tuned circuit is determined by the carrier frequency f c and the value of the lowest modulating signal frequency. When the required carrier frequency is high and the modulating signal effect is very low, filtering of one of the sidebands would become virtually impossible. To solve this problem repeated filtering is used. (ii) Phase shift method. This method uses two identical product modulators and two quadrature (90 o ) phaseshift networks, one of which is for the carrier frequency and the other is for the modulating signal. For successful operation, it is necessary that for the product modulators to be identical, phase shifts to be precisely 90 o and for the phase shifter, for the modulating signal, to have a flat amplitude response over the modulating signal frequency range. The two inputs to one of the modulators are the modulating signal x(t) and the carrier signal v c (t) while the two inputs to the other product modulator are the 90 o phase-shifted x(t) the 90 o phase shifted v c (t). The sum and difference of the two outputs of the product modulators, represent the individual sidebands. Any deviation from the flat amplitude response of 90 o phase-shifter for the modulating signal, will result in the appearance of the undesired sideband. This can be avoided by using two phase-shifters, instead of one, for the modulating signal. The phase shifts introduced by these phase shifters can now be functions of frequency but in such a way that the difference between the phase shifts at all 115

116 frequencies over the modulating signal frequency range, is equal to 90 o while three amplitude responses are identical (not necessarily flat). EXERCISE ) Give a brief note on demodulation of AM waves. 2) What is SSB modulation? 3) Discuss a suitable method of generating an SSB signal. 4) What are the advantages and disadvantages of SSB modulation? 5) Explain methods for production of SSB signals. 5.6 VESTIGIAL SIDE BAND MODULATION (VSB) It is an abbreviation of vestigial sideband. Consider a modulating signal of large band width having significant low frequency content. Principal examples are television, video, facsimile, and high speed data signals. Practical SSB systems have poor low frequency response. On the other hand, DSB work quite well for low message frequencies but transmission bandwidth is twice that of SSB. Thus a compromise modulation scheme is desired which s VSB. VSB is derived by filtering DSB (or AM) in such a fashion that one sideband is passed almost completely while just a trace, or vestige, of the other sideband is included. The key to VSB is the sideband filter, typical transfer function is shown in Fig. Fig. VSB filter characteristics 116

117 117 While the exact shape of the response is not crucial, it must have odd symmetry about the carrier frequency and a relative response of ½ at the point. Therefore, taking the upper side band case, ) ( ) ( ) ( ) ( ) ( c c c c f f H f f u f f H f f u f H where and as shown in Fig. Fig. VSB modulator The VSB sideband filter is thus a practical sideband filter with transition width 2, and a VSC modulator takes the form of SSB modulator shown in Fig. If carrier suppression is not wanted, the balanced modulator is replaced by an AM modulator. Because the width of the partial sideband is one-half the filter transition width, the transmission bandwidth is VSB and SSB spectra are quite similar, particularly when (((W, which is often true. The similarities exist in the time domain as well, and we can write xc(t) as where the quadrature component consists of x (t) plus ) ( ) ( f f H t t x t x t t x A x e e c c c sin ) ( ) '( )cos ( 2 1 f f H 0 ) ( df e f f H j t x t j ) ( ) ( 2 ) ( W W 1

118 If << W, VSB approximates SSB and x(t)= 0 : conversely for large (, VSB approximate DSB. The transmitted power is not easy to determine but depends on the vestige width. Frequency and Phase Modulation Frequency modulation and phase modulation are normally abbreviated as FM and PM respectively. They belong to the general class of angle modulation (or exponential modulation). Phase modulation and frequency modulation are not essentially different in the sense that variation in the phase of a carrier is accompanied by a corresponding change in frequency. This is because of the relationship between phase and frequency ω of the carrier that is d dt As shown in fig, if a carrier has been angle modulated, it will be impossible to determine whether PM and FM had been used. Therefore, the term FM and PM are only used to indicate which parameters of the carrier are made to vary as function of the modulating signal e m (t). Since the carrier waveforms for PM and FM are very similar, the methods of producing and detecting those waveforms must have a great deal in common. Fig. illustrates the basic difference between the two. Fig. shows some form of phase modulation will be achieved. However, it will be very complex and non-linear form having no practical use. Yet it suggests two identical frequencies, (i.e. one source for both with a phase-shifting network in one of the channel). 118

119 The carrier of the amplitude-modulated signal has been removed so that only the two sidebands are added to the unmodulated voltage. This has been accomplished by the balanced modulator and the addition takes place in the combining network. As can be seen the resultant of the two sideband voltages will always be in quadrature with the carrier voltage. Moreover as the modulation increases, so will be phase deviation, and hence phase modulation has been obtained. Thus the resultant voltage coming from the combining network is phase modulated, but there is also a little amplitude modulation present. The AM can be removed by an amplitude limiter. Since frequency-modulation is what we want, the modulatory voltage have to be equalized before it enters the balanced modulator. As we know PM may be changed into FM by prior boosting of the modulation. A simple RL equalizer shown in Fig. can be used. The most convenient operating frequency for the crystal oscillator and phase modulator is in the vicinity of 1 MHz. Since transmitting frequencies are normally much higher than this, frequency multiplies are used. Frequency Discriminator A frequency discriminator is a device which produces an output voltage proportional to the input-frequency. The discriminator is usually tuned about a given frequency, say the difference frequency in this case, and the output voltage is proportional to the deviation of the input frequency from this point. One type of such discriminator circuit is shown. The upper and lower turned circuits T 1 and T 2, tuned above and below the centre frequency f 0, respectively. The voltage e 1 and e 2 are shown as function of input frequency. Since e 0 = e 1 + e 2, the total output signal is linear about f 0 if T 1 and T 2 are properly tuned and adjusted. 119

120 If the difference between the carrier and the standard falls as f 0 then no output is produced by the discriminator. Should the oscillator change, thus causing the transmitted carrier to change the difference frequency will also change and will be something other than f 0. Consequently, on output will be created from the discriminator. This output will be in the form of a d. c. voltage and is used to control the bias on the reactance tube circuit and restore the proper carrier frequency. When the transmitter is modulated the discriminator output will consist of a d.c. component (if correction is necessary) plus a.c. component. Filtering must be used to remove a.c. component. The receiver is similar to that used in a conventional AM-DSB system except for bandwidth requirements of the amplifiers and the use of frequency instead of an amplitude sensitive detector. If the carrier has been phase modulated, the output from the detector must be integrated to recover the modulating voltage. The detector is shown in Fig. Its gain vs frequency characteristic is shown in Fig. Bandwidth Requirements Because of the similarity between PM and FM, only FM bandwidth requirement will be discussed here. FM is produced by varying the instantaneous frequency of the carrier to be modulated the instantaneous deviation being directly proportional to the instantaneous value of the message or modulating wave. If the frequency of the carrier is to be a function of e m (t), then the carrier phase is a function of 120

121 Thus we may write where K has the units of radians per volt per second. Considering a modulating signal to be sinusoidal, we have and the FM wave may be expressed as Here KE m represents the maximum frequency deviation of the carrier. Let where m f is termed the modulation index for an FM. Eq. then becomes, es ( s) Ee cos( et mf sinm t ) cos (mf sin ω mt ) and sin (mf sin ω mt ) may be expanded in terms of Bessel s function as follows: Substituting these values in Eq. we have 121

122 It is seen that each pair of side-bands is proceeded by J coefficients. These are Bessel s functions of the first kind and of the order denoted by the subscript, with the arguments mf. J n (mf) may be shown to be a solution of an equation of the form 2 2 d y dy ( m f ) m f ( m 2 n f d 2 d mf fm The solution, i.e., the formula for the Bessel function, is 2 ) y FREQUENCIES DIVISION MULTIPLEXING FDM is the technique used to divide the bandwidth available in a physical medium into a number of smaller independent logical channels with each channel having a small bandwidth. The method of using a number of carrier frequencies each of which is modulated by an independent speech signal is in fact frequency division multiplexing. When many channels are multiplexed together, 400Hz is allocated to each channel to keep them well separated. First the voice channels are raised in frequency, each by a different amount. Then they can be combined, because no two channels how occupy the same portion of the spectrum. Notice that even though there are gaps (guard bands) between the channels, there is some overlap between adjacent channels, because the filters do not have sharp edges. This overlap means that a strong spike at the edge of one channel will be felt in the adjacent one as nonthermal noise. 122

123 Frequency-division multiplexing works best with low-speed devices. The frequency division multiplexing schemes used around the world are to some degree standardized. A wide spread standard is Hz each voice channels ( 300Hz for user, plus two guard bands of 500Hz each) multiplexed into the 60 to 108 KHz band. Many carriers offer a 48 to 56 kbps leased line service to customers, based on the group. Other standards upto voice channels also exist. Example: The allocated spectrum is about 1MHz, roughly 500 to 1500 KHz. Different (stations, each operating in a portion of the spectrum with the inter-channel separation great enough to prevent interference. This system is an example of frequency division multiplexing. Advantages of FDM 1. Here user can be added to the system by simply adding another pair of transmitter modulator and receiver demodulators. 2.FDM system support full duplex information flow which is required by most of application. 3.Noise problem for analog communication has lesser effect. Disadvantages of FDM 1.In FDM system, the initial cost is high. This may include the cable between the two ends and the associated connectors for the cable. 2.In FDM system, a problem for one user can sometimes affect others. 3.In FDM system, each user requires a precise carrier frequency. EXERCISE ) Discuss with a diagram the communication system with a VSB. 2) What is frequency division multiplexing (FDM)? 3) Discuss its advantages and disadvantages. 5.8 UNIT SUMMARY (i) Frequency modulation is produced when the instantaneous frequency of carrier is varied in accordance with the modulating signal, while the amplitude of the carrier remains constant. 123

124 (ii)am-ssb is an abbreviation for amplitude modulation single sideband. (iii)fdm is the technique used to divide the bandwidth available in a physical medium into a number of smaller independent logical channels with each channel having a small bandwidth. (iv) Frequency modulation and phase modulation are normally abbreviated as FM and PM respectively. (v) A frequency discriminator is a device which produces an output voltage proportional to the input-frequency. 5.9 REFERENCES 1)Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company Ltd. 2)Electronic Devices and Circuits an Introduction by Mottershed 3)Transistor Physics by Sarkar 4)Operational Amplifiers by Clayton 5)Nashelsky Electronic Devices and Circuit Theory by Robert Boylested and Louis SOLUTION EXERCISE ) Refer to article 5.1& 5.2, 2) Refer to article 5.2, 3) Refer to article 5.2, 4) Refer to article 5.2 EXERCISE ) Refer to article 5.3, 2) Refer to article 5.4, 3) Refer to article 5.5, 4) Refer to article 5.4, 5) Refer to article 5.5 EXERCISE ) Refer to article 5.6, 2) Refer to article 5.7, 3) Refer to article

125 BLOCK-III UNIT-VI ELECTRONIC DEVICES 6.0 INTRODUCTION An electronic device is any physical entity in an electronic system used to affect the electrons or their associated fields in a desired manner consistent with the intended function of the electronic system. Components may be packaged singly or in more complex groups as integrated circuits. Some common electronic components are capacitors, inductors, resistors, diodes, transistors, etc. Components are often categorized as active (e.g. transistors and thermistors) or passive (e.g. resistors and capacitors). 6.1 OBJECTIVES Components are generally intended to be connected together, usually by being soldered to a printed circuit board (PCB), to create an electronic circuit with a particular function (for example amplifier, radio receiver, or oscillator). 6.2 ELECTRONIC DEVICES: JFET, MOSFET AND MESFET Field - Effect Transistor There are two main types of field - effect transistors: 1. Junction field - effect transistor (JFET). 2. Metal Oxide semiconductor field -effect transistor (MOSFET) Junction field - effect Transistor The Junction field - effect transistors (JFET's) can be divided depending upon their structure into the following two categories: 1. N-channel JFET and 2. P-channel JFET. The basic construction of an N-channel JFET is as shown in figure. It consists of an N-type Semiconductor bar with two p-type heavily doped regions diffused on 125

126 opposite sides of its middle part and the P-type regions from two PN junctions. The space between the junctions (i.e., N-type region) is called a channel. Both the P-type regions are connected internally and single wire is taken out in the form of a terminal called the gate (G). The electrical connections (called ohmic contacts) are made to both ends of the N-Type semiconductor and are taken out in the form of two terminals called drain (D) and Source (S). The Drain (D) is a terminal through which electrons leave the semiconductor bar and source (S) is a terminal through which the electrons enter the semiconductor. Whenever a voltage is applied across the drain and source terminals, a current flows through the N-channel. The current consists of only one type of carriers (i.e., electrons). Therefore the field-effect transistor (FET) is called a unipolar device. This distinguishes a FET from a BJT (i.e., a bipolar junction transistor) where the current consists of the flow of both the electrons and holes. MOSFETs The MOSFETS is an abbreviation for metal-oxide semiconductor field-effect transistor. Like JEET, the MOSFT has a source, gate and drain. However, unlike JFET, the gate of a MOSFET is insulated from the channel. Because of this, the MOSFET is sometimes known as IGFET which stands for insulated-gate field - effect transistor. Other names used for MOSFET are MISFET (metal-insulatorsemiconductor field -effect transistor) and MOST (metal - oxide semiconductor Transistor). There are two basic types of MOSFETs; depletion type and enhancement- type MOSFETs. Depletion- Type MOSFET 126

127 Figure shows the basic structure of an N- channel depletion type MOSFET. It consists of a conducting bar of N-type material with an insulated gate on the left and P-region on the right. Free electrons can flow from source to drain through the N- type material. The P-region is called substrate. It physically reduces the conducting path to a narrow channel. A thin layer of silicon dioxide is deposited on the left side of the channel. This layer insulates the gate form the channel. Because of this, a negligible gate current flows even when the gate voltage is positive. It will be interesting to know that a PN junction, which exists in a JFET, has been eliminated in the MOSFET. The basic construction of a depletion-type P-channel MOSFET is similar to that of N-channel except that the conducting bar is of P-type material and the substrate is of N-type material. Enhancement- type MOSFET The enhancement-type MOSFET has no depletion mode it operates only in enhancement mode. It differs in construction from the depletion-type MOSFET in the sense that it has no physical channel MESFETS (METAL SEMICONDUCTOR FIELD EFFECT TRANSISTORS) These are unipolar microwave transistors that have several advantages compared to bipolar microwave transistors. They have higher efficiency, f max operation frequencies, input impedances and lower noise figures. In fact these are replacing bipolar transistors and even parametric amplifiers (to be discussed later) in several applications such as radars. Although junction FET s (JFETs) and insulated gate 127

128 FETs (GFET s) are also suitable for microwave amplification and oscillation, MESFETs with silicon and gallium arsenide (GaAs) are very popular. GaAs MESFETs due to their higher mobility (6 times larger than silicon) larger peak drift velocity (2 times larger than Si), smaller parasitic resistances, larger transconductances and smaller transit time are almost always preferred. They use metal semiconductor schottky junction for the gate contact and hence the name MESFET. 6.3 STRUCTURE, WORKING AND THEIR CHARACTERISTICS UNDER DIFFERENT CONDITIONS Construction of MESFET: The schematic diagram of a GaAs MESFET along with its symbol is shown in Fig. It uses inter-digitated structure. A moderately doped n type GaAs epitaxial layer is grown on a high resistivity, semi-insulating GaAs substrate. The two ohmic contacts for source and drain are made on the top of epitaxial layer using Au-Ge, Au-Te or Au-Te-Ge alloys. In between these two contacts another contact made of metal aluminium semiconductor schottky junction is added that is called the gate. Operation The MESFET operates with drain at positive potential with respect to source and the gate is reverse biased so that the majority-carriers (the electrons) flow in the n type epitaxial layer from the source. This creates depletion layer (completely depleted of carrier-electrons) in the channel and gradually pinches off. The cross-section of 128

129 current flow in the n-layer gets constricted due to insulating nature of the depletion region (i.e., the gain controls the current flow from the drain to the source). As the reverse bias between the source and gate is increased, the height of the charge depletion region also increases. The non-pinched off region now has lesser channel height increasing channel resistance. Thus the drain current I sub ds is modulated by the gate voltage Vgs. The VI characteristics V ds vs I ds for various values of V gs are as shown in Fig. It is clearly seen that the drain current I ds is completely controlled by the field effect of the gate voltage V gs (hence the name FET). Pinch off occurs when the I ds increases continuously and the ohmic voltage drop between source and channel reverse biases the function. When the channel is pinched off I ds remains almost constant even if V ds is increased. The pinch off voltage is the gate reverse that removes all the free charges from the channel and is given by the relation. Characteristics of JFET We known that a family (or a set) of curves which relate device current and voltages are knows as characteristics curves. Following are the two important characteristics of a JFET. 1. V-I or drain characteristics. These curves given relationship between the drain current (I D ) and drain-to-source voltage (V DS ) for different values of gate-tosource voltage (V GS ). 129

130 2. Transfer Characteristics. These curves given relationship between drain current (I D ) and gate-to-source voltage (V GS ) for different values of drain-to-source (V DS ) voltage. Drain Characteristics These curves may be obtained by using the circuit arrangement shown in figure. First of all, we adjust the gate-to-source voltage (V GS ) to zero Volt. Then increase the drain-to-source voltage (V DS ) in small suitable steps and record the corresponding values of drain current (I D ) attach step. Now if we plot a graph with drain-to-source voltage along the horizontal axis and drain current along the vertical axis, we shall obtain a curve marked V GS =0 and in a similar procedure may be used to obtain curves for different values of gate-to-sources voltage. Transfer Characteristics These are also called transonductance curves, which give us the relationship between drain current (I D ) and gate-to-source voltage (V GS ) for a constant value of 130

131 drain-to-source voltage (V DS ). The transfer characteristics may be obtained by adjusting the drain-to-source voltage to some suitable value and increase the gate-tosource voltage in small suitable steps. Now records the corresponding values of drain current at each step. If we plot a graph with gate-to-source voltage (V GS ) along the horizontal axis and the drain current (I D ) along the vertical axis, we shall obtain a curve as shown in figure A similar procedure may be used to obtain curves at different values of gate-to-source voltage. Drain Characteristic of Depletion - Type MOSFET. Figure shows the drain characteristic for the N-channel depletion - type MOSFET in the common source configuration. These curves are plotted for both negative and positive values of gate-to-source voltage (V GS ). The curves shown above the curve for V GS =0 have a positive zero whereas those below it have a negative value of V GS. When V GS is zero and negative, the MOSFET operates in the depletion-mode. On the other hand, if VGS is zero and positive, the MOSFET operates in the enhancement- mode. It may be noted that the drain characteristics of depletion-type MOSFET's are 131

132 similar to that of JFET. The only difference is that JFET does not operate for positive values of gate-to-source voltage. (V GS ). Transfer characteristics of Depletion - type MOSFET Figure shows the transfer characteristic (also called transconductance curve) for an N-channel depletion-type MOSFET. It may be noted form this curve that the region AB of the characteristic is similar to that of JFET. But here, this curve extends for the positive values of gate-to-source voltage similar to that of JFET. But here, this curve extends for the positive values of gate-to-source voltage (V GS ) also. The value I DSS represents the current form drain-to-source with V GS =0. The drain current at any point along the transfer characteristic (i.e., the curve ABC) is given by the relation, I D = I DSS [1-V GS /V GS (off)] 2 It may be noted that even if V GS = 0, the device has a drain current equal to I DSS. Due to this fact, it is called normally - ON MOSFET. Drain Characteristics for Enhancement - type MOSFET Figure shows the drain characteristics for N-Channel enhancement-type MOSFET. It may be noted form this fig., that when the gate-to-source voltage (V GS ) is less than threshold voltage, V GS(th), there is no drain current. However, in actual practice, an extremely small value of drain current does flow through the MOSFET. This current flow is due to the presence of thermally generated electrons in the P-type substrate. When the value of V GS is kept above V GS(th), a significant drain current flows, where V GS(th) is threshold voltage. 132

133 The values of drain current increase with the increase in gate-to-source voltage. It is because of the fact that the width of inversion layer widens for increased values of V GS and therefore allows more number of free electrons to pass through it. The drain current reaches its saturation value above a certain value of drain-to-source voltage (V DS ). Transfer characteristic of Enhancement-type MOSFET. In this, there is no drain current when the gate-to-source voltage, V GS = 0. However, if V GS is increased above the threshold voltage, V GS(th), the drain current increases rapidly. The drain current at any point along the curve is given by the relation, I D = K [V GS - V GS(th) ] 2 where K is a constant, whose value depends on the type of MOSFET. It value can be determined form the data sheet by taking specified value of drain current called I D(ON) at the given value of V GS and then substituting these values in the above equation. Incidentally, may be noted that enhancement-type MOSFET does not have an I DSS parameter like JFET and depletion-type MOSFET. Applications of MESFET GaAs MESFETs due to their excellent performance characteristics have found a number of microwave applications 1. As front end low noise amplifier of microwave receivers in both radar and communications 2. As power amplifiers for output stage of microwave links 133