0195136047.pdf

5.2 IDEAL OPERATIONAL AMPLIFIER 233

EXAMPLE 5.2.1

(a) Consider the circuit of theinverting amplifiershown in Figure E5.2.1(a), including an

ideal op amp. Show that the voltage gain of the overall circuitvo/viis independent of the

op-amp parameters.

(b) Without considering the op-amp gain to be infinite, investigate the effect of a finite value

ofA, the open-circuit voltage amplification of the op amp, on the voltage gain of the

overall circuit.

(c) LetRi=2kandRf=80 kin Figure E5.2.1(a). Find the voltage gain of the overall

circuit: (i) if the op-amp gain is infinite, and (ii) if the op amp gain is 100.

−

− +

−

+

+ +

+−

−

vo

vo

vd

vi

(a)

(b)

1

2

3

in = 0

= 0

if

if

ii

Ri

vi

−+

Rf

Ri

Rf

vi

vo

vp

vn

+

−

A(vp - vn)

Figure E5.2.1(a)Inverting ampli-

fier.(b)Equivalent circuit.

Solution

(a) Notice that a resistorRiis placed in the−lead, whereas the+lead is connected to the

common terminal (ground). Also, a feedback resistorRfis connected between the−lead

and the output lead. Noting thatin=0 andii=if, the KVL equation around the outside

loop yields

vi=Riii+Rfif+vo

Sincevd=0, it follows thatii=vi/Ri. Thus, one gets

vi=

(

Ri+Rf

)vi

Ri

+vo

Solving for the voltage gain,vo/vi=−Rf/Ri, where the negative sign implies that this

is aninverting amplifier,i.e., the output voltage is 180° out of phase with the input voltage.