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**Lecture 4 Operational Amplifiers—Non-ideal behavior**

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**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

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**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

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**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

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**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

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**Frequency Response of Op Amps: Noninverting Amplifier**

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**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

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**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

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**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

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

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**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

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