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CHAP. 5]



Vcc ). 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

The output voltage vo depends on vd ¼ vþ  v . Neglecting the capacitive effects, the transfer function is that shown in Fig. 5-7. In the linear range, vo ¼ Avd . The open-loop gain A is generally very high. vo saturates at the extremes of þVcc and Vcc when input vd exceeds the linear range jvd j > Vcc =A.

Fig. 5-7

Figure 5-8 shows the model of an op amp in the linear range with power supply connections omitted for simplicity. In practice, Ri is large, Ro is small, and A ranges from 105 to several millions. The model of Fig. 5-8 is valid as long as the output remains between þVcc and Vcc . Vcc is generally from 5 to 18 V. EXAMPLE 5.5 In the op amp of Fig. 5-8, Vcc ¼ 15 V, A ¼ 105 , and v ¼ 0. tude of vþ for linear operation. jvo j ¼ j105 vþ j < 15 V

Find the upper limit on the magni-

jvþ j < 15  105 V ¼ 150 mV

EXAMPLE 5.6 In the op amp of Fig. 5-8, Vcc ¼ 5 V, A ¼ 105 , v ¼ 0 and vþ ¼ 100 sin 2 t ðmVÞ. Find and sketch the open-loop output vo . The input to the op amp is vd ¼ vþ  v ¼ ð100 sin 2 tÞ106 (V). When the op amp operates in the linear range, vo ¼ 105 vd ¼ 10 sin 2 t (V). The output should remain between þ5 and 5 V (Fig. 5-9). Saturation starts when vo 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