# EXPERIMENT 1.2 CHARACTERIZATION OF OP-AMP

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1 1.17 EXPERIMENT 1.2 CHARACTERIZATION OF OPAMP OBJECTIVE 1. To sketch and briefly explain an operational amplifier circuit symbol and identify all terminals 2. To list the amplifier stages in a typical opamp and briefly discs each stage. 3. To explain the negative feedback control in opamp circuits. 4. To discuss the opamp modes and most important opamp parameters. 5. To measure the input bias current, input offset current, input offset voltage, input and output voltage ranges, the slew rate and bandwidth of op amp HARDWARE REQUIRED a. Power supply : Dual variable regulated low voltage DC source b. Equipments : CRO, AFO, DMM (Digital Multimeter), DRBs c. Resistors : d. Semiconductor : IC741 opamp e. Miscellaneous : Bread board and wires PRE LAB QUESTIONS 1. Determine the output voltage of an opamp for the input voltages of V i1 =150µV and V i2 =140µV. The amplifier has a differential gain of A d =4000 and the value of CMRR is Calculate the output voltage of an inverting amplifier for values of V S =1V, R f =500K and R 1 =100K. 3. Calculate the output voltage of a noninverting amplifier for values of V S =1V, R f =500K and R 1 =100K. 4. Calculate the output offset voltage of the circuit in Fig (a). The opamp spec lists V IO =1.2mV. 5. Calculate the offset voltage for the circuit in fig (a) for opamp spec listing I IO =100nA. 6. Calculate the total offset voltage for the circuit of fig (a) for an opamp with specified values of V IO =1.2mV and I IO =100nA.

2 k V1 2k + +VCC VCC Fig (a) 7. Calculate the input bias current at each input of an opamp and input offset current having specified values of IIO=5nA and IIB=30nA. 8. For an opamp having a slew rate of 2 V/µs, what is the maximum closed loop voltage gain that can be used when the input signal varies by 0.5V in 20µs. 9. How long does it take the output voltage of an opamp to go from 10V to +10V if the slew rate is 0.5V/µs. 10. Determine the input bias current and input offset current, given that the input currents of an opamp are 8.3µA and 7.9µA THEORY An opamp is a high gain, direct coupled differential linear amplifier choose response characteristics are externally controlled by negative feedback from the output to input, opamp has very high input impedance, typically a few mega ohms and low output impedance, less than 100Ω. Opamps can perform mathematical operations like summation integration, differentiation, logarithm, antilogarithm, etc., and hence the name operational amplifier opamps are also used as video and audio amplifiers, oscillators and so on, in communication electronics, in instrumentation and control, in medical electronics, etc Circuit symbol and opamp terminals The circuit schematic of an opamp is a triangle as shown below in Fig. 121 opamp has two input terminal. The minus input, marked () is the inverting input. A signal applied to the minus terminal will be shifted in phase 180 o at the output. The plus input, marked (+) is the noninverting input. A signal applied to the plus terminal will appear in the same phase at the output as at the input. +V CC denotes the positive and negative power supplies. Most opamps operate with a wide

3 1.19 range of supply voltages. A dual power supply of +15V is quite common in practical opamp circuits. The use of the positive and negative supply voltages allows the output of the opamp to swing in both positive and negative directions. +Vcc inverting input offset null output noninverting input + Vcc offset null Fig 121 opamp circuit symbol Negative feedback control The basic circuit connection using an opamp is shown below in fig. 122 Rf R1 +VCC Vs + VCC Fig 122 opamp circuit connection in the inverting mode An input signal, Vs is applied through resistor R, to the minus input. The output is then connected back to the same minus input through resistor R f. The plus input is connected to ground since the signal is essentially applied to the minus input the resulting output is opposite in phase to the input signal Note that the output is feedback to the minus input terminal (inverting input terminal) in order to provide negative feedback for the amplifier. This circuit arrangement is called inverting amplifier. For this amplifier, the output can be defined as R f V O = ( ) VS (121) R1 The minus sign indicates that the sign of the output is inverted as compared to the input. The equation for gain of this amplifier is Rf Gain = ( ) (122) R 1

4 1.20 It is also possible to operate the opamp as a noninverting amplifier by applying the signal to the plus input (noninverting input terminal), as shown below in fig Rf R1 +VCC + Vs VCC Fig 123 opamp circuit connection in the noninverting mode Note that the feedback network is still connected to the inverting input. For this amplifier circuit, the output of the amplifier is defined by Rf V = (1 + ) (123) O V S R1 R f and its gain is Gain = 1+ (124) R The opamp transfer characteristics The transfer characteristics of a typical opamp are sketched in fig. 124 and it shows three regions of operation, namely the linear region, the negative saturation region and the positive saturation region. range of input for linear operation +Vcc +Vsat +ve saturation linear region (V1 V2) ve saturation Vsat Vcc Fig 124 opamp transfer characteristics

5 1.21 In the linear region, the output voltage V O is linearly related to the difference in the input voltage (V 1 V 2 ). The supply voltage limits the maximum value of the output voltage. The OUTPUT voltage is normally 2 to 3 volts lower than the power supply voltage, ie., V O < V CC Also, V O = A (V 1 V 2 ) (125) Therefore (V 1 V 2 ) < V CC /A (126) For V CC = 15V and A = 10 5, V 1 V 2 < 150µV. Thus, for very high gain opamps, the input voltages V 1 and V 2 are almost equal. Unequal input voltages characterize the operation in saturation region. If V 1 > V 2 by 150µV, will be saturated at a positive voltage and if V 1 < V 2 by the same amount, will be saturated at a negative voltage V sat. Although the opamp has distinct nonlinear characteristics bias as a linear devices under certain conditions and the principles of linear circuit theory can be used to design and analyses opamp is operated in the linear region. Since the magnitude of the input voltage for linear operations is quite small, opamps are seldom used in openloop configuration. Feedback from output to inverting () terminal tends to extend the range of input for linear operation Equivalent circuit of opamp In the linear region of operation, the opamp can be modeled as a VCVS. Fig. 125 shown an equivalent circuit of opamp. Fig 125 opamp equivalent circuit

6 1.22 Here R id is the differential input resistance, AV id is the Thevenin voltage source and R O is the Thevenin equivalent output resistance looking back into output terminals. The output voltage V O is V O = AV id = A (V 1 V 2 ) (127) where A is the openloop voltage gain of the opamp, V id is the differential input voltage, and V 1 and V 2 are the voltages w.r.t. ground potential at the noninverting and the inverting input terminals respectively. Thus the opamp amplifies the difference between the two input voltages. The input voltages V 1 and V 2 can be cither ac or dc voltages. In the openloop configuration, no connection exists between the output and input terminals. When connected in an openloop configuration, the opamp works as a high gain amplifier. Any input signal slightly above zero volts drives the output V O to saturation. For this reason, the opamp is seldom used in openloop configuration for linear applications. The property of opamp output saturating under openloop configuration is used in nonlinear circuit applications of opamp as a voltage comparator The ideal opamp The ideal behavior of an opamp implies that a. The output resistance is zero b. The input resistance seen between the two input terminals (called the differential input resistance) is infinity. c. The input resistances seen between each input terminal and the ground (called the common mode input resistance) are infinite. d. opamp has a zero voltage offset ie., for V 1 = V 2 = 0, output voltage V O = 0 e. Common mode gain A C is zero. f. Differential mode gain, A d is infinity. g. Common Mode Rejection Ratio (CMRR) is infinity h. Bandwidth is infinite, ie., A d is real and constant. i. Slew rate is infinite. j. Since V O = A d (V 1 V 2 ) and A d = V 1 V 2 = V O /A d = 0 ie., V 1 = V 2

7 1.23 The above condition implies that the inverting and noninverting terminals are at the same potential because of the very high (infinite) gain property. This condition along with the condition i 1 = i 2 = 0 are the keys to the simplified analysis of the opamp circuits opamp input modes and CMRR In opamp, a number of input signal combinations are possible: If an input signal is applied to either input with the other input connected to ground, the operation is referred to as single ended. If two opposite polarity input signals are applied, the operation in referred to as doubleended. If the same input is applied to both inputs, the operation is called common mode. Differential gain, Ad V2 V1 U1 + V 1 and V 2 are the two input signals and V O is the output. In an ideal opamp, V O is proportional to the difference between the two signal voltages. V O (V 1 V 2 ) (128) From equation 128 we can write, V O = A d (V 1 V 2 ) (129) Where A d is the constant of proportionality. A d is the gain with which differential amplifier the difference between two input signals. Hence, A d is called differential gain of the differential amplifier. The difference between the two inputs, V 1 V 2 is generally called difference voltage and denoted as V d. V O = A d V d (1210) Hence, the differential gain can be expressed as V O A d = (1211) Vd

8 1.24 Common mode gain, A C If we apply two input voltages which are equal in all respects to the differential amplifier, ie., if V 1 =V 2, then ideally the output voltage, V O = A d (V 1 V 2 ) must be zero. But the output voltage of the practical differential amplifier not only depends on the difference voltages, but also depends on the average common level of the two inputs. Such an average level of the two input signals is called common mode signal denoted as V C. ( V 1 + V2 ) V C = (1212) 2 Practically, the differential amplifier produces the output voltage proportional to such common mode signal, also. The gain with which it amplifier the common mode signal to produce the output is called as common mode gain of the differential amplifier denoted as Ac. V O = A C V C (1213) So the total output of any differential amplifier can be expressed as V O = A d V d +A C V C (1214) Common Mode Rejection Ratio (CMRR) In an ideal different amplifier, A d is infinite while A C must be zero. However, in a practical differential amplifier; A d is very large and A C is very small. ie., the differential amplifier provides very large amplification for difference signals and very small amplification for common mode signals. Many disturbance signals/noise signals appear as a common input signal to both the input terminals of the differential amplifier. Such a common signal should be rejected by the differential amplifier. The ability of a differential amplifier to reject a commonmode signal is expressed by a ration called Common Mode Rejection Ratio, denoted as CMRR. CMRR is defined as the ratio of the differential voltage gain Ad to common mode voltage gain Ac. d CMRR = (1215) Ideally A C is zero. Hence, the ideal value of CMRR is. A A C

9 op amp internal circuit Commercial integrated circuit OPamps usually consists of your cascaded blocks as shown in figure 126 shown below. V 2 V 1 Differential Amplifier Differential Amplifier Buffer and Level Translator Output driver Fig 126 Internal block schematic opamp The first two stages are cascaded difference amplifier used to provide high gain. The third stage is a buffer and the last stage is the output driver. The buffer is usually an emitter fallowing whose input impedance is very high so that it prevents loading of the high gain stage. The output stage is designed to provide low output impedance. The buffer stage along with the output stage also acts as a level shifter so that output voltage is zero for zero inputs opamp characteristics An ideal opamp draws no current from the source and its response is also independent of temperature. However, a real opamp does not work this way. Current is taken from the source into opamp inputs. Also the two inputs respond differently to current and voltage due to mismatch in transistors. A real opamp also shifts its operation with temperature. These nonideal characteristics are: 1. Input bias current 2. Input offset current 3. Input offset voltage 4. Thermal drift 5. Slew rate 6. input and output voltage ranges Input bias current The opamp s input is a differential amplifier, which may be made of. BJT or FET. In either case the input transistors must be biased into this linear region by supplying currents into the bases. In an ideal opamp, no current is drawn from the input terminals. However, practically, input terminals conduct a small value of dc current to bias the input transistors when base currents flow through external resistances, they produce a small differential input voltage or unbalance; this

10 1.26 represents a false input signal. When amplified, this small input unbalance produces an offset in the output voltage. The input bias current shown on data sheets is the average value of base currents entering into the terminals of an opamp. + + ( I B I B ) I B = (1216) 2 For 741, the bias current is 500nA or less. The smaller the input bias current, the smaller the offset at the output voltage. Input offset current The input offset current is the difference between the two input currents driven from a common source I OS = I + B + I B (1217) It tells you how much larger one current is than the other. Bias current compensation will work if both bias currents I + B and I B are equal. So, the smaller the input offset current the better the OP amp. The 741 opamps have input offset current of 20nA. Input offset voltage Ideally, the output voltage should be zero when the voltage between the inverting and noninverting inputs is zero. In reality, the output voltage may not be zero with zero input voltage. This is due to unavoidable imbalances, mismatches, tolerances, and so on inside the opamp. In order to make the output voltage zero, we have to apply a small voltage at the input terminals to make output voltage zero. This voltage is called input offset voltage.i.e., input offset voltage is the voltage required to be applied at the input for making output voltage to zero volts. The 741 opamp has input offset voltage of 5mV under no signal conditions. Therefore, we may have to apply a differential input of 5mV, to produce an output voltage of exactly zero. Thermal drift Bias current, offset current and offset voltage change with temperature. A circuit carefully mulled at 25 o C may not remain so when the temperature rises to 35 o C. This is called drift often, offset current drift is expressed in n A/ o C and offset voltage drift in mv/ o C. These indicate the change is offset for each degree celsius change in temperature. There are very few techniques that can be used to minimize the effect of drift.

11 1.27 Slew rate Among all specifications affecting the ac operation of the opamp, slew rate is the most important because it places a severe limit on a large signals operation. Slew rate is defined as the maximum rate at which the output voltage can change. The 741 opamp has a typical slew rate of 0.5 volts per microsecond (V/µs). This is the ultimate speed of a typical 741; its output voltage can change no faster than 0.5V/µs. If we drive a 741 with large step input, it takes 20µs (0.5 V/µsX10V) for the output voltage to change from 0 to 10V. Band width Slew rate distortion of a sine wave starts at a point where the initial slope of the sine wave equals the slew rate of the opamp. The maximum frequency at which the opamp can be operated without distortion is f max SR = (1218) (2π ) V P where SR=slew rate of opamp, V P = peak voltage of output sine wave. As an example, if the output sine wave has a peak voltage of 10V and the opamp slew rate is 0.5 V/µs, the maximum frequency for large signal operation is f max 0.5V / µ s = = 7.96 KHz 2 π 10V Frequency ƒ max is called bandwidth of opamp. The 741 opamp has a bandwidth of approximately 8 KHz. This means the undistorted band width for large signal operation is 8 KHz. Input and output voltage ranges Maximum positive and negative input voltage applied to the opamp for undistorted output gives the input voltage range. Maximum positive and negative undistorted output voltage of the opamp gives the output voltage range OP amp applications 1) Signal conditioners (a) Linear eg. Adder, subtractor, differentiator, integrator, VI converter, etc. (b) NonLinear eg., log amplifier, antilog amplifier, multiplier, divider, etc. 2) Signal Processors (a) Linear eg., voltage follower, instrumentation amplifier, etc. (b) NonLinear eg., log amplifier, antilog amplifier, multiplier, divider, etc.

12 EXPERIMENT Use opamp dc power supply voltages ±15V wherever not specified 1. Input bias current and input offset current DC voltage at the noninverting terminal V + V 220k 220k + +Vcc Vcc Fig 127 Input bias and input offset current DC voltage at the inverting V I + + V B = I B = terminal 220K 220K I B Input bias current ( I = + B + 2 I B ) Input offset current + I OS = I B I B Table Connect the circuit of figure Using a DMM, measure the dc voltage at the () terminal & record the values in Table By ohm s law, calculate the input currents; I + B and I B. Average these values to find out the input Bias current. Also, find the difference between these two currents to know the input offset current. Record these values in Table Input offset voltage 100k +Vcc Vcc Fig 128 Input offset voltage

13 1.29 V out V in = V ou t/1000 Table Connect the circuit of Figure Measure the DC output voltage at pin 6 using multimeter and record the result in Table Calculate the input offset voltage using the formula Vi = ut / 1000 and record the value in table Slew rate and bandwidth +Vcc + 1Vpp 20KHz Vcc Fig 129(a) Slew rate and bandwidth Fig 129(b )Model graph

14 1.30 V T SR = V/ T BW Table Connect the circuit of Figure 129(a). 3.2 Using an AFO, provide a 1V peak to peak square wave with a frequency of 25 KHz. 3.3 With an oscilloscope, observe the output of OPAMP. Adjust the oscilloscope timing the get a couple of cycles. 3.4 Measure the voltage change V and time change T of the output waveform. Record the results in Table Calculate the slew rate using the formula SR = V / T 3.5 Using the circuit of figure 3, set the AFO at 1KHz. Adjust the signal level to get 20V peak to peak (20 V PP ) out of the opamp. 3.6 Increase the frequency and watch the waveform somewhere above 10 KHz, slew rate distortion will become evident. That maximum frequency ƒ max at which the opamp can be operated is called bandwidth of an opamp record the value in Table Input and output voltage ranges 4.1 Assemble the voltage follower circuit as shown in Figure 1210 with R 1 = R 2 = 100 kω. Use opamp dc power supply voltages of ±9 V. R2 +Vcc R1 Vs + Fig 1210 Circuit to find the input voltage range 4.2 Apply ±5 V, 100 Hz sinusoidal input, Vs. Observe on a CRO the voltages at the noninverting input and output pins simultaneously. Increase the signal amplitude until distortion is observed Vcc

15 1.31 at the peak value of the output. Measure the positive and negative input voltage peak values. This gives the opamp input voltage range. 4.3 Change the circuit of Figure 1210 to an inverting amplifier. Connect R 1 between the source and inverting input. Ground the noninverting input. Choose R 1 = 10 kω, R 2 = 100 kω. Repeat observations of step 3.2 starting with ±0.5 V, 100 Hz sinusoidal input. Measure the positive and negative output voltage peak values. This gives the opamp output voltage range. 126 POSTLAB QUESTIONS Check your understanding by answering these questions 1. The input stage of a 741 opamp is a 2. The output stage of a 741 opamp is a 3. The input bias current of an opamp is the of the two input base currents under nosignal condition. 4. The input current is the difference of the two input base currents. 5. The input voltage is the differential input voltage needed to null or zero the quiescent output voltage. 6. The CMRR of an opamp is the ratio of voltage gain to voltage gain. 7. A 741 has a slew rate of V/µs. 8. The bandwidth is the undistorted frequency out of an opamp. It depends on the rate of the opamp and the of the output signal. 9. Identify the type of input mode for each opamp in fig (b) Vin1 Vin Vin2 Vin Fig (b)

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