Page 78 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
67
CHAP. 5]
V cc ). The common reference for inputs, output, and power supplies resides outside the op amp and is
called the ground (Fig. 5-6).

Fig. 5-6

þ
The output voltage v o depends on v d ¼ v v . Neglecting the capacitive effects, the transfer
function is that shown in Fig. 5-7. In the linear range, v o ¼ Av d . The open-loop gain A is generally
very high. v o saturates at the extremes of þV cc and V cc when input v d exceeds the linear range
jv d j > V cc =A.

Fig. 5-7
Figure 5-8 shows the model of an op amp in the linear range with power supply connections omitted
5
for simplicity. In practice, R i is large, R o is small, and A ranges from 10 to several millions. The
model of Fig. 5-8 is valid as long as the output remains between þV cc and V cc . V cc is generally from 5
to 18 V.

5

EXAMPLE 5.5 In the op amp of Fig. 5-8, V cc ¼ 15 V, A ¼ 10 , and v ¼ 0. Find the upper limit on the magni-
þ
tude of v for linear operation.
þ
5 þ
jv o j¼j10 v j < 15 V jv j < 15 10 5 V ¼ 150 mV
5 þ
EXAMPLE 5.6 In the op amp of Fig. 5-8, V cc ¼ 5V, A ¼ 10 , v ¼ 0 and v ¼ 100 sin 2 t ðmVÞ. Find and sketch
the open-loop output v o .
þ

The input to the op amp is v d ¼ v v ¼ð100 sin 2 tÞ10 6 (V). When the op amp operates in the linear
5
range, v o ¼ 10 v d ¼ 10 sin 2 t (V). The output should remain between þ5 and 5 V (Fig. 5-9). Saturation starts
when v o ¼ 10 sin 2 t reaches the 5-V level. This occurs at t ¼ 1=12 s. The op amp comes out of 5-V saturation at