Chapter 2. Operational Amplifiers

Transcription

1 Chapter 2. Operational Amplifiers Tong In Oh 1

2 2.3 The Noninverting Configuration v I is applied directly to the positive input terminal of the op amp One terminal of is connected to ground Closed-loop gain (v O /v I ) Assuming that the op amp is ideal with infinite gain v Id = v O = 0 for A = A Virtual short circuit Figure 2.12 The noninverting configuration. Figure 2.13 Analysis of the noninverting circuit. The sequence of the steps in the analysis is 2 indicated by the circled numbers.

3 2.3.1 The Closed-Loop Gain Since the current into the op-amp inverting input is zero, the circuit composed of and R 2 acts as a voltage divider feeding a fraction of the output voltage back to the inverting input terminal of the op amp v 1 = v O ( +R 2 ) Action of the negative feedback Let v I increase v Id to increase v O correspondingly increase a fraction of the increase in v O feed to the inverting input terminal through voltage divider v Id back to zero Degenerative action of negative feedback: Degenerative feedback 3

4 2.3.2 Effect of Finite Open-Loop Gain Assuming the op amp to be ideal except for having a finite open-loop gain A G v o = 1+( R2 R1 ) v I 1+ 1+(R 2 R1 ) A Due to the same feedback loop, denominators are identical The numerator gives the ideal or nominal closed-loop gain A 1 + R 2 Percent gain error = 1+(R 2 R1 ) 100 A+1+( 2 R1 ) Input impedance: infinite (no current flows into the positive input) Output resistance: zero (take at the terminals of the ideal voltage source) 4

5 2.3.4 The Voltage Follower High input impedance: very desirable feature of the noninverting configuration Buffer amplifier (impedance transformer or power amplifier) R 2 = 0 and = to obtain the unity-gain amplifier Voltage follower since the output follows the input v O = v I, R in =, R out = 0 100% negative feedback, act to make v Id = 0 and hence v O = v I Figure 2.14 (a) The unity-gain buffer or follower amplifier. (b) Its equivalent circuit model. 5

6 2.4 Difference Amplifiers Difference or differential amplifiers Amplify only the differential input signal, v Id Reject completely the common-mode input signal, v Icm v O = A d v Id + A cm v Icm A d : differential gain A cm : common-mode gain Common-mode rejection ratio (CMRR) CMRR = 20 log A d A cm Need in the instrument front end Op amp itself (Difference amp) Impossible to use due to very high gain Devise a feedback for finite, predictable, and stable amp 6 Figure 2.15 Representing the input signals to a differential amplifier in terms of their differential and common-mode components.

7 2.4.1 A Single-Op-Amp Difference Amplifier Combining the noninverting and inverting amplifiers (reduce the gain of the positive path from (1 + R 2 / ) to (R 2 / ) R 4 = R 2 R 2 + R 4 = R 2 7 Figure 2.16 A difference amplifier.

8 v O1 = R 2 v I1 (v I2 = 0) v O2 = v I2 R R 2 = R 2 v I2 (v I1 = 0) v O = R 2 (v I2 v I1 ) = R 2 v Id Figure 2.17 Application of superposition to the analysis of the circuit of Fig

9 Common-mode Gain i 1 = 1 v Icm R 4 v Icm = v Icm 1 v O = R 4 v Icm i 2 R 2 v O = R 4 v Icm R 2 v Icm = R 4 1 R 2 R 4 v Icm A cm v O v Icm = R 4 1 R 2 R 4 If A cm nonzero, CMRR finite 9

10 High input resistance Differential input resistance R id R id v Id i I v Id = i I i I, R id = 2 Relatively low input resistance for large gain Not easy to vary the differential gain Figure 2.19 Finding the input resistance of the difference amplifier for the case = and R 4 = R 2. 10

11 2.4.2 The Instrumentation Amplifier Low input resistance problem of the difference amplifier voltage followers to buffer Gain adjusting without compromising the high input resistance by using followers with gain Input common-mode signal is amplified in the first stage Must be matched in the first stage To vary the differential gain, two resistors have to be varied simultaneously ( ) 11

12 Virtual short circuits at the inputs of op amp (A 1 and A 2 ) Produce a voltage difference between the output terminals of A 1, A 2 v O2 v O1 = 1 + 2R 2 2 v Id v O = R 4 v O2 v O1 = R R 2 v Id Gain varied by 2 v Icm, no longer amplifies at the 1 st stage Figure 2.20 A popular circuit for an instrumentation amplifier. (a) Initial approach to the circuit (b) The circuit in (a) with the connection between node X and ground removed and the two resistors and lumped together. This simple wiring change dramatically improves performance. (c) Analysis of the circuit in (b) assuming ideal op amps. 12