Chapter 30, Problem 104GP

(II) The RC circuit shown in Fig. 30–40 is called a high-pass filter because it passes high-frequency ac signals with less attenuation than low-frequency ac signals. (a) Show that the voltage gain is $A=V_{\text{out}}/V_{\text{in}}=2\pi fRC/\left(4{\pi }^2{f}^2{R}^2{C}^2+1\right)\frac{1}{2}$. (b) Discuss the behavior of the gain A for $f\to 0$ and $f\to \infty$. (c) Choose R = 850 Ω and C = 1.0 × 10^–6F, and then graph log A versus log f with suitable scales to show the behavior of the circuit at high and low frequencies.