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Week 6aEECS40, Spring 2005 Week 6a OUTLINE Op-Amp circuits continued: examples Inverting amplifier circuit Summing amplifier circuit Non-inverting amplifier circuit Differential amplifier circuit Current-to-voltage converter circuit Reading Chapter 14. (Also, amplifiers are discussed in great detail in Ch. 11)

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Week 6aEECS40, Spring 2005 Negative feedback is used to “linearize” a high-gain differential amplifier. V0V0 + V+V+ VV V 0 (V) 5 55 Without feedback V0V0 + V IN 1 2 3 V0V0 1 2 3 4 5 4 5 Review: Negative Feedback With feedback

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Week 6aEECS40, Spring 2005 Application of Voltage Follower: Sample and Hold Circuit

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Week 6aEECS40, Spring 2005 Inverting Amplifier Circuit +–+– +vo–+vo– –+–+ vsvs RsRs RfRf inin i n = 0 i s = -i f v p = 0 v n = 0 +vp–+vp– +vn–+vn– isis ifif

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Week 6aEECS40, Spring 2005 Analysis using Realistic Op Amp Model In the analysis on the previous slide, the op amp was assumed to be ideal, i.e. R i = ; A = ; R o = 0 In reality, an op amp has finite R i, finite A, non- zero R o, and usually is loaded at its output terminals with a load resistance R L.

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Week 6aEECS40, Spring 2005 Summing Amplifier Circuit +–+– +vo–+vo– –+–+ vcvc RcRc RfRf inin +vp–+vp– +vn–+vn– icic ifif ibib iaia –+–+ vbvb –+–+ vava RbRb RaRa i n = 0 i a + i b + i c = -i f v p = 0 v n = 0 superposition !

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Week 6aEECS40, Spring 2005 A DAC can be used to convert the digital representation of an audio signal into an analog voltage that is then used to drive speakers -- so that you can hear it! 00 1 01 00 11 0 1 00 1.5 2 0 1 1 0 0 111 1 000 2.5 3 3.5 4 1 00 1 1 0 1 0 11 11 00 11 0 1 111 0 1111 4.5 5 5.5 6 6.5 7 7.5 Binary number Analog output (volts) 0000 000 1 0.5 MSB LSB S1 closed if LSB =1 S2 " if next bit = 1 S3 " if " " = 1 S4 " if MSB = 1 4-Bit D/A 8V + V0V0 5K 80K 40K 20K 10K S1 + -+ - S3 S2 S4 + Application: Digital-to-Analog Conversion “Weighted-adder D/A converter” (Transistors are used as electronic switches)

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Week 6aEECS40, Spring 2005 Digital Input 0 1 2 3 4 5 6 7 8 0246810121416 Analog Output (V) 1111 1000 0100 0000 0001 Characteristic of 4-Bit DAC

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Week 6aEECS40, Spring 2005 Noninverting Amplifier Circuit +–+– +vo–+vo– –+–+ vgvg RgRg RfRf i p = 0 v p = v g v n = v g i n = 0 R s & R f form a voltage divider + vpvp – RsRs + vnvn – inin ipip

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Week 6aEECS40, Spring 2005 Differential Amplifier Circuit +–+– +vo–+vo– –+–+ RbRb inin +vp–+vp– +vn–+vn– vbvb –+–+ vava RcRc RaRa i n = 0 i p = 0 RdRd ipip

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Week 6aEECS40, Spring 2005 More usual version of differential amplifier (Horowitz & Hill, “Art of Electronics”, p. 184-5 (part of their “smorgasbord” of op-amp circuits): Let R a = R c = R 1 and R b = R d = R 2 Then v 0 = (R 2 / R 1 )(v b – v a ) To get good “common-mode rejection” (next slide) you need well-matched resistors (R a and R c, R b and R d ), such as 100k 0.01% resistors Differential Amplifier (cont’d)

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Week 6aEECS40, Spring 2005 Differential Amplifier – Another Perspective Redefine the inputs in terms of two other voltages: 1. differential mode input v dm v b – v a 2. common mode input v cm (v a + v b )/2 so that v a = v cm – (v dm /2) and v b = v cm + (v dm /2) Then it can be shown that “common mode gain”“differential mode gain”

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Week 6aEECS40, Spring 2005 Differential Amplifier (cont’d) An ideal differential amplifier amplifies only the differential mode portion of the input voltage, and eliminates the common mode portion. –provides immunity to noise (common to both inputs) If the resistors are not perfectly matched, the common mode rejection ratio (CMRR) is finite:

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Week 6aEECS40, Spring 2005 Op-Amp Current-to-Voltage Converter

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Week 6aEECS40, Spring 2005 Summary Voltage transfer characteristic of op amp: A feedback path between an op amp’s output and its inverting input can force the op amp to operate in its linear region, where v o = A (v p – v n ) An ideal op amp has infinite input resistance R i, infinite open-loop gain A, and zero output resistance R o. As a result, the input voltages and currents are constrained: v p = v n and i p = -i n = 0 vovo vp–vnvp–vn V cc -V cc slope = A >>1 ~1 mV ~10 V

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Week 6aEECS40, Spring 2005

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Week 6aEECS40, Spring 2005

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Week 6aEECS40, Spring 2005

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Week 6aEECS40, Spring 2005 Differentiator (from Horowitz & Hill)

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Week 6aEECS40, Spring 2005 Op-Amp Imperfections Discussed in Hambley, pp. 651-665 (of interest if you need to use an op-amp in a practical application!) Linear range of operation: Input and output impedances not ideal values; gain and bandwidth limitations (including gain-bandwidth product); Nonlinear limitations: Output voltage swing (limited by “rails” and more; output current limits; slew-rate limited (how fast can the output voltage change); full-power bandwidth DC imperfections: Offset current (input currents don’t sum exactly to zero); offset voltage;

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