5.3 PRACTICAL PROPERTIES OF OPERATIONAL AMPLIFIERS 235
potential difference between its input terminals. The effect of the feedback connection from
output to inverting input is then to force the voltage at the inverting input to be equal to that at
the noninverting input. This is equivalent to stating that for an op amp with negative feedback,
vn∼=vp. The analysis of the op amp is greatly simplified if one assumes thatin=0 andvn=vp.
The voltage gain of the overall circuit of Figure E5.2.1(a) is called theclosed-loop gain, because
the presence of a feedback connection between the output and the input constitutes a closed loop
as per the terminology used in the field of automatic control, which is presented in Section 16.2.
EXAMPLE 5.2.2
(a) Consider the circuit of thenoninverting amplifierin Figure E5.2.2, including an ideal op
amp. Obtain an expression for the voltage gain of the overall circuit.
(b) LetRi=10 kandRf=240 kin Figure E5.2.2. Find the voltage gain of the overall
circuit.
+
− −
−
+
+ +
−
vo
vd = 0
vi
1
2
3
if
ip = 0
ii
in = 0
Rf
Ri
Figure E5.2.2Noninverting amplifier.
Solution
(a) Note that the input is directly connected to the+terminal. ResistorsRiandRfare
connected as in the previous example. Since the input currentip=0, the input impedance
is infinite. Becausein=0,ii=if. The KVL equation around the loop containingRiand
Rfgives
vo=−(Ri+Rf)ii
Because of the virtual short circuit,vi=−Riii. Thus, for the case of a simplenoninverting
amplifier,one gets
vo
vi
= 1 +
Rf
Ri
(b) For the given values ofRiandRf,
vo
vi
= 1 +
240
10
= 25
5.3 Practical Properties of Operational Amplifiers
To achieve voltage gain and consequently power gain, the op amp must be biased by a dc source.
The biasing network is comprised of the power supply and the passive circuit elements surrounding
