2. Operational Amplifiers. 2. Operational Amplifiers TLT-8016 Basic Analog Circuits 2005/2006 1

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1 . Operational Amplifiers. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006

2 Figure. Circuit symbol for the op amp. Operational amplifier: A differential amplifier with ery high oltage gain. Usually realized as integrated circuit.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006

3 Ideal operational amplifier: Infinite input impedance. Infinite open loop gain A OL for differential signal. Zero gain for the common - mode signal. Zero output impedance.. The Ideal Operational Amplifier Infinite bandwidth. Figure. Equialent circuit for the ideal op amp. A OL is ery large (approaching infinity). Common-mode input signal icm = ( ) + Differential input signal id = Figure.3 Op-amp symbol showing power supplies.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 3

4 . The Summing-Point Constraint Operational amplifiers are almost always used with negatie feedback, in which part of the opamp output signal is returned to the input in opposition to the source signal. Ideal op-amp circuits are analyzed by the following steps:. Verify that the negatie feedback is present. Usually this takes the form of a resistor network connected to the output terminal and to the inerting input terminal.. Assume that the differential input oltage and the input current of the op amp are forced to zero. (This is summing - point constraint.) 3. Apply standard circuit analysis principles, such as Kirchhoff s laws and Ohm s law, to sole for the quantities of interest.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 4

5 .3 The Inerting Amplifier i = i = in i (.) (.) i = in (.3) Figure.4 Inerting amplifier. o + i = 0 (.4) Figure.5 We make use of the summing-point constraint in the analysis of the inerting amplifier. o A = = in in Z = i = in = o i o is independent of the load resistance L. Thus the output acts as ideal oltage source and output impedance is 0. (.5) (.6) (.7). Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 5

6 The Virtual-Short-Circuit Concept The oltage between both inputs of the Op Amps is forced to be 0. There is no short circuit between both inputs because the current is also 0. Figure.5 We make use of the summing-point constraint in the analysis of the inerting amplifier. The circuit between both inputs is called irtual-short-circuit: = 0; i = 0.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 6

7 Exercise.. Summing Amplifier A circuit known as a summing amplifier is illustrated in Figure.7. (a) Use the ideal-op-amp assumption to sole for the output oltage in terms of the input oltages and resistor alues. (b) What is the input resistance seen by A? (c) By B? (d) What is the output resistance seen by L? i A A i f Solution: A ia = i i B f o = = i A A B B = i + i f B f = A A = + A B B f A + B f B + - A + - B i B B =0 - + f + o - L Input impedance seen by A : A Input impedance seen by B : B o doesn t depend on L, thus the output impedance is 0. Figure.7 Summing amplifier.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 7

8 Exercise.3. Find an expression for the output oltage of the circuit, shown in Figure.9. o Figure.9 Circuit of Exercise.3. Solution: The first Op Amp is connected as an inerting amplifier. Thus 0000 o = = = 0000 The second Op Amp is connected as summing amplifier 5 5 o = o = o = o o = 4. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 8

9 Positie Feedback Figure.0 Schmitt trigger circuit. The current equation at the noninerting input is The high gain increases the input oltage i, this increases further the output oltage and so on. Very soon the output oltage reaches the supply oltage, the amplifier enters in switching mode of operation and doesn t function any more as amplifier. i in + i o = 0 i = in o in + ( + ) = ( A ) OL i (.8). Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 9

10 .4 The Nonierting Amplifier The Voltage Follower A = when = 0 and/or =. The circuit is called oltage follower. Since i = 0 Figure. Noninerting amplifier. = in = + A o = = + in o Since i i = 0, i =. Since o doesn t depend on L ; o = 0. (.9) (.0) (.) Figure. Voltage follower.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 0

11 Exercise.5. Differential amplifier. Find an expression for the output oltage in in terms of the resistance and input oltages for the differential amplifier shown in Figure.4. i i o - L Solution: i = o + o = i = + From oltage diider principle + = + Figure.4 Differential amplifier. Since Op Amp input oltage is 0, - = + and o o + = = ( ) +. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006

12 .5 Design of Simple Amplifiers Amplifier Design Using Op Amp Example. Nonierting Amplifier Design Design a noninerting amplifier that has a oltage gain of 0 using an ideal op amp. The input signal lie in the range from - V to V. Use 5 % tolerance discrete resistors for the feedback network. Figure.0 If low-alue resistors are used, an impractically large current is required. Solution: A = 0 = + From the formula follows that only the ratio / is important to achiee the desired gain. The alues of and are restricted from additional practical considerations and must be in the range 00Ω.. MΩ. Figure. If ery high alue resistors are used, stray capacitance can couple unwanted signals into the circuit. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006

13 Example. Amplifier Design Suppose that we need an amplifier with input resistance of 500 kω or greater and a oltage gain of -0. The feedback resistors are to be implemented in integrated form and hae alues of 0 kω or less to consere chip area. Choose a suitable circuit configuration and specify the resistance alues. Finally, estimate the resistor tolerance needed so that the gain magnitude maintained within 5 % of its nominal alues. These alues exceed the maximum alues allowed. A oltage follower at the input must be added as a buffer amplifier. Values for and : = kω; = 0kΩ. esistor tolerances: not more than ±.5%; practically ±%. Solution: To attain desired input resistance = 500 kω The formula for the gain is A = Figure. To attain large input resistance with moderate resistances for an inerting amplifier, we cascade a oltage follower with an inerter. To achiee the desired gain 3 = 0 = = 5MΩ. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 3

14 .6 Op-amp Imperfections in the Linear ange of Operation The nonideal characteristics of real op amps fall into three categories:. Nonideal properties in the linear range of operation.. Nonlinear characteristics. 3. DC offsets. Input Impedance and Output Impedance Input impedance BJT input stage: > 00kΩ, typically few MΩ; FET input stage: ~0 Ω Output impedance: ~00Ω or less. If the gain the Op Amp is high, the influence of the input and output impedance is small.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 4

15 Gain and Bandwidth Limitations When the Op Amp is included in a feedback loop in order to realise a finite gain amplifier, the bandwidth of the finite gain amplifier is extended proportionally to the feedback. Figure.5 Bode plot of open-loop gain for a typical op amp. A OL ( f A ) = 0 OL (.4) + j( f / f ) BOL Figure.7 Bode plots.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 5

16 Some Popular Op Amps Table.4 Typical specifications for two popular Op Amps Type LM74 LF4 A 0OL F t.5mhz 4.0MHz S 0.5V/µs 5V/µs Input resistance MΩ 0 Ω Output resistance 50Ω 50Ω mv 0.8mV V off I B I off 80nA 50pA 0nA 5pA. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 6

17 Output Voltage Swing.7 Large Signal Operation Output Current Limits The maximum that an Op Amp can supply to a load is restricted. For µa74 this limitation is ±5mA. If a small-alue load resistance drew a current outside this limits, the output waeforme would become clipped. Figure.8 For a real op amp, clipping occurs if the output oltage reaches certain limits. For µa74: If the supply oltages are +5V and 5V the amplitude of the output oltage without clipping is 4V typically (guaranteed is V).. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 7

18 Slew-ate Limitations Slew-rate: the speed of the change of the output oltage. Maximum slew rate S is limited for eery Op Amp. d o S (.45) dt Figure.3 An example of the effect of the slew-rate limitation on the output wae-shape in a certain finite gain amplifier, realized with Op Amp. 4 s (t) is the expected output wae shape based on the oltage gain. o (t) is the real output wae-shape, distorted due to the limited slew rate of the Op Amp.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 8

19 .8 DC Imperfections Dc currents flow into Op Amp inputs (they are the base currents of the input transistors). Two input currents: I B+ and I B-. Their aerage is called bias current I B I B+ + I B I B = (.47) The difference between I B+ and I B- is called offset current I off (.48) I off = I B+ I B Figure.33 Current sources and a oltage source model the dc imperfections of an op amp. Output oltage may not be zero for zero input oltage. The Op Amp behaes as if a small dc source known as offset oltage V off is in series with one of the input terminals.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 9

20 . Integrators and Differentiators ( t ) i ( t ) in in = (.50) c( t ) = t iin( C 0 x ) dx (.5) o( t ) = c( t ) (.5) o( t t ) = in( C 0 x ) dx (.53) Figure.60 Integrator.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006 0

21 Differentiators Circuit d ( t ) C in o = (3) dt Figure.8 Differentiator.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006

22 Operations on the Input signals, Which Can Be ealized With Op Amps Linear operations: Multiplication with a constant (amplification); Summation Subtracting Differentiation Integration Other nonlinear operations are also possible.. Operational Amplifiers TLT-806 Basic Analog Circuits 005/006