0195136047.pdf

5.2 IDEAL OPERATIONAL AMPLIFIER 231

+

− −

−

+

+ +

−

vo = A(vp − vn); A ≥ 105

vd = vp − vn

vp

−

+

vn

Ground Zo

Zi

A

i Figure 5.2.1Operational amplifier.

denoted by a ground symbol. The output voltage is related to the difference between the two input
voltages as

vo=A(vp−vn) (5.2.1)

whereAis the open-loop voltage gain. Thus, the op amp is basically a form of differen-
tial amplifier, in which the differencevp−vnis amplified. For an output voltage on the
order of 12 V, the difference voltagevdis on the order of 0.12 mV, or 120μV. The input
impedanceZiis on the order of 1 M, while the output impedanceZois on the order of 100
to1k.
The practical op-amp characteristics are approximated in theideal op ampshown in Figure
5.2.2. Because of the high input impedance, very large gain, and the resulting small difference
voltagevdin practical op amps, the ideal op amp is approximated by the following two charac-
teristics:

1. The input currentsipandinare zero,ip=in=0.


2. The difference voltagevdis zero,vd=0.

The principle ofvirtual short circuit,illustrated by the preceding, is utilized in analyzing circuits
containing ideal op amps. The accompanying principle of negative feedback is explained later.
The ideal op-amp technique is based on the approximations thatA∼=∞,Zi∼=∞, andZo∼=0.
The output voltage can always be found from the ideal op-amp technique in the usual op-amp
feedback circuits, since the precise values ofA, Zi,andZohave negligible influence on the answer,
as shown in Example 5.2.1.
The op amp is composed of a number of transistor stages on a single chip and pro-
vides the characteristics of a voltage-controlled voltage source. The so-called ideal op amp
is characterized by infinite bandwidth. However, it is pertinent to mention that the band-
width of an op amp without feedback is quite small. In commercially available op amps,
while the open-loop voltage gainAis rather large (usually 10^5 or greater), the range of fre-
quency for which this gain is achieved is limited. The asymptotic Bode diagram shown in
Figure 5.2.3 illustrates the frequency characteristic for the open-loop voltage gain. For fre-
quencies belowfh, the open-loop gain is a constantAo; for frequencies beyondfh, the open-
loop gain decreases. The frequencyfhis known as theopen-loop bandwidth,as it separates

+

−

−

+

+

−

vo

vd = 0

vp

−

+

vn

ip = 0

in = 0

Figure 5.2.2Ideal operational amplifier.