Given R = 20 kΩ and C = 1200 pF:
a. Sketch the normalized plot if the filter is used as both a high-pass and a low-pass filter.
b. Sketch the phase plot for both filters in part (a).
c. Determine the magnitude and phase of $A_\nu = V_o/V_i at f = \frac{1}{2} f_c$ for the high-pass filter.

Question

Given R = 20 kΩ and C = 1200 pF:
a. Sketch the normalized plot if the filter is used as both a high-pass and a low-pass filter.
b. Sketch the phase plot for both filters in part (a).
c. Determine the magnitude and phase of [latex]A_ u = V_o/V_i at f = \frac{1}{2} f_c[/latex] for the high-pass filter.

Accepted Answer

a. [latex]f_c=\frac{1}{2\pi RC}=\frac{1}{(2\pi)(20 kΩ)(1200 pF)}=6631.46 Hz [/latex]

The normalized plots appear in Fig. 22.28.

b. The phase plots appear in Fig. 22.29.

c. [latex]f=\frac{1}{2}f_c =\frac{1}{2}(6631.46 Hz) = 3315.73 Hz\[0.5cm] X_C=\frac{1}{2\pi fC}=\frac{1}{(2\pi)(3315.73 Hz)(1200 pF) } ≅ 40 kΩ\[0.5cm] A_\nu=\frac{V_o}{V_i}=\frac{1}{\sqrt{1+\left(\frac{X_C}{R} \right)^2 } } =\frac{1}{\sqrt{1+\left(\frac{40 kΩ}{20 kΩ} \right)^2 } } =\frac{1}{\sqrt{1+(2)^2} }\[0.5cm] =\frac{1}{\sqrt{5} }=0.4472\[0.5cm] \theta=\tan ^{-1}\frac{X_C}{R}= \tan ^{-1}\frac{40 kΩ}{20 kΩ} =\tan ^{-1}2= 63.43°\[0.5cm] and\hspace{30 pt} A_\nu=\frac{V_o}{V_i}=0.447 \angle 63.43° [/latex]

Question 22.6: Given R = 20 kΩ and C = 1200 pF: a. Sketch the normalized pl...

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