0195136047.pdf

244 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

or

A ̄F= Ao

1 −jωRoC

=

Ao( 1 −jωRoC)

1 +(ωRoC)^2

∣

∣A ̄F

∣

∣=AF=√ Ao

1 +(ωRoC)^2

At the 3-dB point, or half-power frequencyfh,AF=Ao/

√

2, so that

ωhRoC=1orfh=

1

2 πRoC

DenotingA ̄F=AFejφ, whereφindicates that the output leads the input,

tanφ=−ωRoC

At very high frequencies, tanφ→−∞andφ→ 3 π/2, so that the output leads the input by

3 π/2 or lags it byπ/2. This is the largest phase shift possible.

5.4 Applications of Operational Amplifiers

An op amp along with a few external components (resistors and capacitors) is capable of

performing many different operations—hence the nameoperational.The linear operations of

integration, differentiation, addition, and subtraction that were needed in analog computers are

some of the early applications. Other linear applications include instrumentation amplifiers,

voltage-to-current and current-to-voltage converters, voltage followers, and active filters. Op

amps are also utilized in nonlinear applications such as limiters, comparators, voltage regulators,

signal rectifiers and detectors, logarithmic amplifiers, multipliers, and many digital circuits.

Negative feedback (which is said to be degenerative) is used to improve amplifier performance

by sacrificing gain. The opposite situation of positive feedback (which is said to be regenerative)

is also utilized, and gain is increased to the extent that an amplifier will produce an output signal

with no input. This leads to sinusoidal oscillators and nonsinusoidal waveform generators.

This section concentrates on a limited range of op-amp applications.

Inverting Amplifier

One common op-amp circuit is shown in Figure 5.4.1. For the case of finite voltage gainAoof an

op amp that is otherwise ideal, the output voltage becomes

−

+

vo

vi

i 2

i 1

v 1

v 2 = 0

1 (inverting terminal)

2 (noninverting

terminal)

3

R 1

R 2

+

−

Figure 5.4.1Inverting amplifier.