Chap' 2 Operational Amplifiers

1
Chap. 2Operational Amplifiers

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• sfhung.ece96g_at_g2.nctu.edu.tw
• EE901, 54397
• office hour 5CDX

2
Ideal OP Amplifier

• Input impedance Ri ? 8
• Input current i1 i2 ? 0
• Output impedance Ro ? 0
• Common-mode gain Acm ? 0
• CMRR ? 8
• Open-loop gain A ? 8
• v1 v2 are virtual short
• Bandwidth ? 8

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Differential and Common-Mode Signals

• Define
• then

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Inverting Configuration

• Open-loop gain A is infinite

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Inverting Configuration

• Open-loop gain A is finite
• If A ? 8,

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Noninverting Configuration

• Open-loop gain A is infinite

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Voltage Follower

• Unit-gain amplifier

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Exercises 2.9

• Use the superposition principle to find the
  output voltage.

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Difference Amplifiers

• For practical circuits
• Ad differential gain
• Acm common-mode gain
• Common-mode rejection ratio (CMRR)

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Problem 2.2

• The circuit uses an op amp that is ideal except
  for having a finite gain A. Measurements indicate
  vo4.0V when vi4.0V. What is the op amp gain A?

vo/A
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Problem 2.8

• Assuming ideal op amps, find the voltage gain
  vo/vi and input resistance Rin of each circuit.

inverting
0V
0V
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Problem 2.22

• The circuit is frequently used to provide an
  output voltage vo proportional to an input signal
  current ii. Derive expressions for the
  transresistance Rmvo/ii and the input resistance
  Rivi/ii for (a) A is infinite(b) A is finite

-vo/A
0V
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Problem 2.31

• (a) Find the resistances R1, R2, R3, and R4.(b)
  Find the currents I1, I2, I3, and I4 in terms of
  the input current I.(c) Find the voltages in
  terms of (IR).

-4IR
-2IR
-IR
-8IR
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Problem 2.49

• Derive an expression for the voltage gain, vo/vi.

noninverting
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Problem 2.51

• The circuit utilizes a 10-kO potentiometer to
  realize an adjustable-gain amplifier. (a) Derive
  an expression for the gain as a function of the
  potentiometer setting x. (b) Assume the op amp
  to be ideal. What is the range of gains obtained?
  (c) Show how to add a fixed resistor so that the
  gain range can be 1 to 21 V/V. What should the
  resistor value be?

noninverting
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Problem 2.62

• (a) Express vo as a function of v1 and v2. (b)
  What is the input resistance seen
• by v1 alone?
• by v2 alone?
• by a source connected between the two input
  terminals?
• by a source connected to both input terminals
  simultaneously?

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Problem 2.62

• (a) Express vo as a function of v1 and v2.

By superposition
v2/2
0V
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Problem 2.62

• (b) What is the input resistance seen
• by v1 alone?
• by v2 alone?
• by a source connected between the two input
  terminals?
• by a source connected to both input terminals
  simultaneously?

0V
vi/2
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Problem 2.70

• The circuit is a modified version of the
  difference amplifier. The modified circuit
  includes a resistor RG, which can be used to vary
  the gain. Show that the differential voltage gain
  is given by

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Problem 2.78

• The two circuits are intended to function as
  voltage-to-current converters that is, they
  supply the load impedance ZL with a current
  proportional to vI and independent of the value
  of ZL. Show that this is indeed the case, and
  find for each circuit iO as a function of vI.
  Comment on the differences between the two
  circuits.

v1
-v2
ZLio