Ideal Op Amps• Zin =

– Implies zero input current

• Zout = 0 (without feedback)– Implies a perfect voltage source

• Differential voltage gain Gdiff = (without feedback)

• Common-mode voltage gain GCM = 0

– Above two features imply a perfect differential amplifier

• Vout = 0 when both inputs are at the same voltage (zero “offset voltage”)– Implies perfect transistor matching at the inputs

• Output can change instantaneously (infinite “slew rate”)

Op Amp “Golden Rules”Op Amp “Golden Rules”

I.I. The output The output attemptsattempts to do whatever is to do whatever is necessary to make the voltage difference necessary to make the voltage difference between the two inputs zero (consequence between the two inputs zero (consequence of very high voltage gain).of very high voltage gain).

ButBut asymmetries between the input asymmetries between the input terminals cause output error signals!terminals cause output error signals!

II.II. The inputs draw “no” current (consequence The inputs draw “no” current (consequence of very high input impedance).of very high input impedance).

In reality, the inputs draw In reality, the inputs draw somesome current! current!

Departure from Ideal: Input Bias Current IB

(Introductory Electronics, Simpson, 2nd Ed.)

Compensating for IB

(Introductory Electronics, Simpson, 2nd Ed.)

Compensating for IB

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Departure from Ideal: Offset Current Ios

(Iio = Ios)

(Introductory Electronics, Simpson, 2nd Ed.)

Departure from Ideal: Offset Voltage Vos

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Departure from Ideal: Offset Voltage Vos

(Introductory Electronics, Simpson, 2nd Ed.)

(Vio = Vos)

Compensating for Vos

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Measuring IB, Ios, Vos (Lab 9–1)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Effects of Op Amp Imperfections

• The circuits below will always give a saturated output after a short time. Why?

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Departure from Ideal: Finite Slew Rate

(Introductory Electronics, Simpson, 2nd Ed.)

(Lab 9–1)

Op-Amp Integrator

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Op-Amp Integrator with DC Error Compensation(Lab 9–2)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Op-Amp Differentiator

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Op-Amp Differentiator with Gain Rolloff(Lab 9–3)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Active Rectifier(Lab 9–5)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

Effect of Finite Slew Rate on Active Rectifier(Lab 9–5)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

output glitch

Improved Active Rectifier(Lab 9–6)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

D1

D2

R1

R2

Active Clamp(Lab 9–7)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

VC

Slew-Rate Limitations on Active Clamp(Lab 9–7)

(The Art of Electronics, Horowitz and Hill, 2nd Ed.)

(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

VC = 10 V

AC Amplifier

(The Art of Electronics, Horowitz and Hill, 2nd Ed.)

C

Ri

R1

R2

(Additional Exercise 2)

vin

(capacitively coupled)

Single-Supply AC Amplifier

(The Art of Electronics, Horowitz and Hill, 2nd Ed.)