Question 8.29: An Audio System An audiophile has connected his new speakers...
An Audio System
An audiophile has connected his new speakers as shown in Figure 8.82. This is only one channel; other channels have the same connections (with the exception of the subwoofer). After verifying that the speakers are up to his standards, he wants to know how much the speakers will vibrate when he blasts them.
The input voltage is amplified using two amplifier stages. The first stage is a noninverting amplifier followed by an inverting amplifier. The output voltage from the first stage corresponds to:
V_{o1}=A_{v1} V_{i}where, A_{v1} is given by Equation (8.64). In addition, the output voltage from the second stage corresponds to:
A_{v}=\left(1+\frac{R_{f}}{R_1}\right) (8.64)
V_{o}=A_{v2} V_{o1}where, A_{v2} is calculated using Equation (8.55). Therefore, the relationship between the output and the input voltage corresponds to:
A_{v}=\frac{V_{o}}{V_{i}}=-\frac{R_{f}}{R_1} (8.55)
V_{o}=A_{v1} A_{v2} V_{i}Finally, the overall gain corresponds to:
A_{v}=\frac{V_{o}}{V_{i}}=A_{v1} A_{v2}Using Equations (8.55) and (8.64):
A_{v}=\left(1+\frac{40}{2}\right) \times-\frac{15}{3}=-105