Kevin Zhou — Advanced E&M II Problem 5 · Kevin Zhou #E6.5
Physics · electromagnetism
Problem
Problem 15. An alternating voltage V cosωt is applied to the terminals at A. The terminals at
0
B are connected to an audio amplifier of very high input impedance. (That is, current flow into the
amplifier is negligible.)
This circuit is the most primitive of “low-pass” filters.
(a) Calculate the “gain” ratio |V˜ |/V in this filter. Show that for sufficiently high frequencies,
1 0
the signal power is reduced by a factor of 4 for every doubling of the frequency.
(b) Design a low-pass filter without using a capacitor.
(c) Design a high-pass filter.
(d) Design a stronger low-pass filter, i.e. one which reduces the signal power by a greater factor
for every doubling of the frequency.
(e) Design a band-pass filter, which suppresses both low and high frequencies, but has a constant
gain for a wide range of medium frequencies. (It’s okay if the constant gain is less than 1, as
we can just pass the output through an amplifier.)
(f) Design a notchfilter, whichsuppresses a very smallrange offrequencies, while letting allother
frequencies through.