0195136047.pdf

242 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

−

−

+

RS

RL

Ri

(a)

(b)

vS

vo

RL

+

vS RS

vo

+

−

A(v+ − v−)

Figure E5.3.1

Solution

Replacing the op amp by its model, we have the circuit shown in Figure E5.3.1(b). The nodal

equation at the node labeled+is

vS−v+

RS

+

vo−v+

Ri

= 0

Also,

vo=A(v+−v−) and v−=vo

Thus,

vo=A(v+−vo)

Solving, one gets

vo=vS

A

A+ 1

Ri

Ri+[RS/( 1 +A)]

Evaluatingvo/vSfor the given two conditions, we have

(a)vo/vS= 0. 999989

(b)vo/vS= 0. 999994

Thus, we see that the output voltage (using negative feedback) is very nearly independent ofRi,

Ro,andA,provided the op amp’s parameters remain in their allowable ranges.

EXAMPLE 5.3.2

Find the maximum frequency of an output sine wave which can be produced at an amplitude of

1.5 V if the op-amp slew rate is 0.5 V/μs.