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Lecture 4 Operational AmplifiersNon-ideal behavior 1

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

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Op amps: Low-pass amplifier with high gain at dc and a single-pole frequency response. B = open loop bandwidth of op amp. ω T = unity gain bandwidth (frequency at which magnitude of gain is unity). At >> B, At ω =ω T, At >> B,product of magnitude of amplifier gain and frequency is a constant value of unity gain frequency. Hence, T is also called gain- bandwidth product. 4

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

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Frequency Response of Op Amps: Noninverting Amplifier 6

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|Vo/Vin| (dB) Ao 1 + R2/R1 f (log scale) f 3dB (no feedback) f 3dB (with feedback) -20 dB/dec Frequency Response of Op Amps: Noninverting Amplifier 7

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For a 741 Op amp, f t = 1MHz Gain = 10 5 (100dB) f 3dB = 1MHz/10 5 = 10 Hz Gain = 100 (40 dB) f 3dB = 1MHz/100 = 10KHz Gain = 10 (20dB) f 3dB = 1MHz/10 = 100KHz 8

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Frequency Response of Op Amps: Noninverting Amplifier (Example) 9 Problem: Characterize frequency response of noninverting amplifier. Given data: A o = 10 5 = 100 dB, f T = 10 7 Hz, desired A v = 1000= 60 dB Assumptions: Amplifier is described by single-pole transfer function. Analysis: Noninverting amplifier transfer function

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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/ s to 10V/ s. 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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