1. Lecture 4 Operational Amplifiers—Non-ideal behavior1

2. Goals Study non-ideal op amp behavior.
Demonstrate circuit analysis techniques for non-ideal op amps.
Understand frequency response limitations of op amp circuits. 2

3. Frequency Response of Op Amps: General Case
vo = A (v+ - v-)
(A) is function of frequency
General purpose op-amp has a single-pole response
100db
Gain = 105
0 dB
Gain = 1 3
Band-width
Unity gain frequency

4. Frequency Response of Op Amps: General Case
Op amps: Low-pass amplifier with high gain at dc and a single-pole frequency response.
wB = open loop bandwidth of op amp. ωT = unity gain bandwidth (frequency at which magnitude of gain is unity).
At w >>wB,
At ω =ωT,
At w >>wB,product of magnitude of amplifier gain and frequency is a constant value of unity gain frequency.
Hence, wT is also called gain-bandwidth product. 4

5. Frequency Response of Op Amps: General Case (Example)
Frequency values are often expressed in Hz.
Problem: Find transfer function describing frequency-dependent amplifier voltage gain. 5

6. Frequency Response of Op Amps: Noninverting Amplifier6

7. Frequency Response of Op Amps: Noninverting Amplifier
|Vo/Vin| (dB) Ao
-20 dB/dec
1 + R2/R1
f (log scale)
f3dB
(no feedback)
f3dB
(with feedback) 7

8. Gain = 105 (100dB)  f3dB = 1MHz/105 = 10 Hz
For a 741 Op amp, ft = 1MHz
Gain = 105 (100dB)  f3dB = 1MHz/105 = 10 Hz
Gain = 100 (40 dB)  f3dB = 1MHz/100 = 10KHz
Gain = 10 (20dB)  f3dB = 1MHz/10 = 100KHz 8

9. Frequency Response of Op Amps: Noninverting Amplifier (Example)
Problem: Characterize frequency response of noninverting amplifier.
Given data: Ao= 105= 100 dB, fT= 107 Hz, desired Av= 1000= 60 dB
Assumptions: Amplifier is described by single-pole transfer function.
Analysis:
Noninverting amplifier transfer function 9

10. Slew Rate (SR)
Slew rate: maximum rate of change at the output of the OPAMP 10

11. Large Signal Limitations: Slew Rate (SR) and Full-Power Bandwidth
Slew rate: Maximum rate of change of voltage at output of op amp.Typical values range from 0.1V/ms to 10V/ms.
For given frequency, slew rate limits maximum signal amplitude that can be amplified without distortion.
For no signal distortion,
Full-power bandwidth is highest frequency at which a full-scale signal can be developed. 11