Ideal Op Amps Z in =  –Implies zero input current Z out = 0 (without feedback) –Implies a perfect voltage source Differential voltage gain G diff =  (without feedback) Common-mode voltage gain G CM = 0 –Above two features imply a perfect differential amplifier V out = 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 I B (Introductory Electronics, Simpson, 2 nd Ed.)

Compensating for I B (Introductory Electronics, Simpson, 2 nd Ed.)

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

Departure from Ideal: Offset Current I os (I io = I os ) (Introductory Electronics, Simpson, 2 nd Ed.)

Departure from Ideal: Offset Voltage V os (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.)

Departure from Ideal: Offset Voltage V os (Introductory Electronics, Simpson, 2 nd Ed.) (V io = V os )

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

Measuring I B, I os, V os (Lab 9–1) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd 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, 2 nd Ed.)

Departure from Ideal: Finite Slew Rate (Introductory Electronics, Simpson, 2 nd Ed.) (Lab 9–1)

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

Op-Amp Integrator with DC Error Compensation (Lab 9–2) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.)

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

Op-Amp Differentiator with Gain Rolloff (Lab 9–3) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.)

Active Rectifier (Lab 9–5) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.)

Effect of Finite Slew Rate on Active Rectifier (Lab 9–5) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.) output glitch

Improved Active Rectifier (Lab 9–6) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.) D1D1 D2D2 R1R1 R2R2

Active Clamp (Lab 9–7) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.) VCVC

Slew-Rate Limitations on Active Clamp (Lab 9–7) (The Art of Electronics, Horowitz and Hill, 2 nd Ed.) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.) V C = 10 V

AC Amplifier (The Art of Electronics, Horowitz and Hill, 2 nd Ed.) C RiRi R1R1 R2R2 (Additional Exercise 2) v in (capacitively coupled)

Single-Supply AC Amplifier (The Art of Electronics, Horowitz and Hill, 2 nd Ed.)