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Week 6a

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 6a

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  1. 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)

  2. V V0 V+ V0 VIN + +   Review: Negative Feedback • Negative feedback is used to “linearize” a high-gain differential amplifier. With feedback Without feedback V0(V) V0 5 5 4 3 2 1 VIN 2 5 1 3 4 5

  3. Application of Voltage Follower: Sample and Hold Circuit

  4. Inverting Amplifier Circuit if Rf is Rs in + – + vn – + vo – – + vs + vp – in = 0  is = -if vp= 0  vn = 0

  5. Analysis using Realistic Op Amp Model • In the analysis on the previous slide, the op amp was assumed to be ideal, i.e. Ri = ; A = ; Ro = 0 • In reality, an op amp has finite Ri, finite A, non-zero Ro, and usually is loaded at its output terminals with a load resistance RL.

  6. Summing Amplifier Circuit Ra ia if Rf Rb in va – + ib + – + vn – + vo – vb – + ic + vp – superposition ! Rc vc – + in = 0  ia + ib + ic= -if vp= 0  vn = 0

  7. 0 0 1 0 1 10K 0 0 1 1 1.5 S4 0 1 0 0 2 20K 0 1 0 1 2.5 S3 0 1 1 0 3 40K S2 8V 0 1 1 1 3.5 + - 5K 80K 1 0 0 0 4 - 1 0 0 1 4.5 + - V0 S1 1 0 1 0 5 + 1 0 1 1 5.5 4-Bit D/A 1 1 0 0 6 1 1 0 1 6.5 1 1 1 0 7 1 1 1 1 7.5 Application: Digital-to-Analog Conversion 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! Analog Binary output number (volts) 0 0 0 0 0 0 0 0 1 .5 “Weighted-adderD/A converter” S1 closed if LSB =1 S2 " if next bit = 1 S3 " if " " = 1 S4 " if MSB = 1 (Transistors are used as electronic switches) LSB MSB

  8. Characteristic of 4-Bit DAC 8 7 6 5 Analog Output (V) 4 3 2 1 0 0 2 4 6 8 10 12 14 16 0000 0001 1111 1000 0100 Digital Input

  9. Noninverting Amplifier Circuit Rf Rs in + – + ip + vo – vn + – Rg – + vg vp – ip = 0  vp= vg vn= vg in = 0  Rs & Rf form a voltage divider

  10. Differential Amplifier Circuit Ra Rb in + vn – va + – – + Rc ip + vo – + vp – – + vb Rd in = 0  ip= 0 

  11. Differential Amplifier (cont’d) More usual version of differential amplifier (Horowitz & Hill, “Art of Electronics”, p. 184-5 (part of their “smorgasbord” of op-amp circuits): Let Ra = Rc = R1 and Rb = Rd = R2 Then v0 = (R2 / R1)(vb – va) To get good “common-mode rejection” (next slide) you need well-matched resistors (Ra and Rc, Rb and Rd), such as 100kW 0.01% resistors

  12. Differential Amplifier – Another Perspective Redefine the inputs in terms of two other voltages: 1. differential mode inputvdmvb– va 2. common mode inputvcm (va+ vb)/2 so that va = vcm – (vdm/2) and vb = vcm + (vdm/2) Then it can be shown that “common mode gain” “differential mode gain”

  13. 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:

  14. Op-Amp Current-to-Voltage Converter

  15. 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 vo = A (vp – vn) • An ideal op amp has infinite input resistanceRi, infinite open-loop gainA, and zero output resistance Ro. As a result, the input voltages and currents are constrained: vp = vn and ip = -in = 0 vo Vcc slope = A >>1 ~10 V vp–vn -Vcc ~1 mV

  16. Differentiator (from Horowitz & Hill)

  17. 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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