Chapter 18 Operational Amplifiers

The typical op amp has a differential input and a single-ended output. Class B push-pull emitter follower Diff amp More stages of gain +V CC -V EE

Symbol +V CC -V EE Noninverting input Inverting input Output Op amp symbol and equivalent circuit A OL (v 1 -v 2 ) R out R in v1v1 v2v2 v out Equivalent circuit

The 741 op amp is an industry standard. A OL (v 1 -v 2 ) R out R in v1v1 v2v2 v out R in = 2 M  A OL = 100,000 R out = 75  I in(bias) = 80 nAI in(off) = 20 nAV in(off) = 2 mV CMRR = 90 dB f unity = 1 MHz

Bode plot of the 741 op amp 20 dB/decade rolloff f unity 10 Hz100 Hz1 kHz10 kHz100 kHz1 MHz 100 dB 80 dB 60 dB 20 dB 0 dB 40 dB

+V CC -V EE RBRB RBRB 10 k  C pinout and offset nulling Adjust for null

The internal frequency compensation capacitor found in most op amps also limits the rate at which the output can change. S R = 0.5 V/  s (for the 741) When a signal exceeds the slew-rate of an op amp, the output becomes distorted and amplitude limited. Slope > S R Slew rate distortion

dv dt dv dt > v t dv dt dv dt > v t The rate of voltage change (slope) is directly related to both amplitude and frequency: S S =  fV p The power bandwidth of an op amp is given by: f max =  fV p SRSR

R1R1 R2R2 The inverting amplifier The negative feedback produces a virtual ground at the inverting terminal. A virtual ground is a short for voltage but an open for current.

R1R1 R2R2 Analyzing the inverting amplifier v in v out i in v in = i in R 1 and v out = i in R 2 A CL = = R1R1 R2R2 v out v in z in(CL) = R 1

10 Hz100 Hz1 kHz10 kHz100 kHz1 MHz 100 dB 80 dB 60 dB 20 dB 0 dB Negative feedback increases the closed-loop bandwidth. f 2(CL)  f unity A CL 40 dB

Negative feedback reduces error V 1err = (R B1 - R B2 )I in(bias) V 2err = (R B1 + R B2 )I in(off) /2 V 3err = V in(off) V error = ± A CL (± V 1err ± V 2err ± V 3err ) V 1err eliminated with resistor compensation Use offset nulling in demanding applications

R1R1 R2R2 Resistor compensation for V 1err v in v out R B2 = R 1 R 2 R B2 has no effect on the virtual-ground approximation since no signal current flows through it.

R1R1 R2R2 The noninverting amplifier A virtual short is a short for voltage but an open for current. The negative feedback produces a virtual short.

Analyzing the noninverting amplifier R1R1 R2R2 v in v out i1i1 v in = i 1 R 1 and v out = i 1 (R 2 +R 1 ) i1i1 A CL = = R1R1 R 2 +R 1 v out v in = R1R1 R2R2 + 1 z in(CL)  

R1R1 RFRF The summing amplifier R2R2 v1v1 v out v2v2 R2R2 RFRF v2v2 R1R1 RFRF v1v1 + v out =

R high R low The voltage follower v out v in The virtual short tells us v out = v in A CL = 1 z in(CL)   z out(CL)  0 f 2(CL) = f unity

Other than the 741 BIFET op amps offer extremely low input currents. High-power op amps supply amperes of output current. High-speed op amps slew at tens or hundreds of volts/  s and some have hundreds of MHz of bandwidth. Precision op amps boast small offset errors and low temperature drift.

Other linear ICs Audio amps in the mW range optimized for low noise (preamplifiers) Audio amps in the watt range for driving loudspeakers Video amps with wide bandwidths RF and IF amps for receiver applications Voltage regulators