• Zin = 
Ideal Op Amps
– 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”
I.
The output attempts to do whatever is
necessary to make the voltage difference
between the two inputs zero (consequence
of very high voltage gain).
 But asymmetries between the input
terminals cause output error signals!
II.
The inputs draw “no” current (consequence
of very high input impedance).
 In reality, the inputs draw some 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
(Vio = Vos)
(Introductory Electronics, Simpson, 2nd Ed.)
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
(Lab 9–1)
(Introductory Electronics, Simpson, 2nd Ed.)
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)
output glitch
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
Improved Active Rectifier
(Lab 9–6)
R2
D1
R1
D2
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
Active Clamp
(Lab 9–7)
VC
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
Slew-Rate Limitations on Active Clamp
(Lab 9–7)
VC = 10 V
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
AC Amplifier
(Additional Exercise 2)
vin
(capacitively
coupled)
Ri
R2
R1
C
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
Single-Supply AC Amplifier
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)