0195136047.pdf

234 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

The voltage gain is independent of the op-amp parameters. By selecting the resistors

to achieve the desired ratio, constructing a linear amplifier with a prescribed voltage

gain is rather simple. It may further be noted that the output impedance isZo =

0, with zero output impedance of the ideal op amp; the input impedance isZi =

vi/ii =Ri.

(b) The equivalent circuit of the inverting amplifier is shown in Figure E5.2.1(b). The current

through the feedback resistorifis given by

if=

vo−vi

Rf+Ri

The voltage at the inverting inputvnis

vn=vi+Riif

Combining these two equations, one gets

vn=vi+Ri

(

vo−vi

Rf+Ri

)

Sincevpis connected directly to ground,vp=0; the output voltagevois

vo=−Avn=−A

[

vi+Ri

(

vo−vi

Rf+Ri

)]

The voltage gain of the overall circuit is then given by

vo

vi

=−

1 −

(

Ri

Ri+Rf

)

1

A

+

(

Ri

Ri+Rf

)

IfAbecomes infinitely large, 1/A→0, and the preceding expression reduces to−Rf/Ri,

obtained in part (a). Clearly asA→∞, the inverting terminal voltagevn=−vo/Ais

going to be very small, practically on the order of microvolts. Then it may be assumed

in the inverting amplifier thatvnis virtually zero, i.e.,vn∼=0.

(c) (i) WhenAis infinitely large,

vo

vi

=−

Rf

Ri

=−

80

2

=− 40

(ii) WhenAhas a finite value of 100,

vo

vi

=−

1 −

(

Ri

Ri+Rf

)

1

A

+

(

Ri

Ri+Rf

)=−

1 −

2

82

1

100

+

2

82

=− 28. 4

The principle ofnegative feedbackis clearly illustrated in the operation of the inverting

amplifier in Example 5.2.1, since negative feedback is used to keep the inverting terminal voltage

as close as possible to the noninverting terminal voltage. One way of viewing negative feedback

is to consider it as a self-balancing mechanism which allows the amplifier to preserve zero