## PHYS345 Electricity and Electronics

Quiz 7: Simple Filters

You have in your possession a 0.01 mF capacitor. You would like to design a simple high-pass filter with a cutoff frequency of 8.0 kHz. What resistor would you select? Sketch the circuit.

What is the gain (in dB) of your filter at 4 kHz, 8 kHz, and 16 kHz?

As frequency increases, a capacitor has a vanishing reactance. So the capacitive reactance should be located at the input to design a high-pass filter. In fact the transfer function written below exhibits the frequency dependence associated with a high-pass filter.

 High-Pass RC Circuit Tranfer Function:

 H(w) = R / [R - j/wC] 1 / [1 - j/(wRC)] 1 / [1 - jwc/w]
where wc = (RC)-1.

Since the cutoff frquency fc = 8 kHz, wc = 50 k rad/s. Given C = 0.01 mF, R must be 2.0 k.

 H(x) = 1 / [1 - j/x] H(0.5) = 1 / [1 - j/0.5] |H(0.5)| = 0.447 = -7.0 dB H(1) = 1 / [1 - j] |H(1)| = 0.707 = -3.0 dB H(2) = 1 / [1 - j/2] |H(2)| = 0.894 = -1.0 dB

"http://www.physics.udel.edu/~watson/phys345/quiz/07.html"
Last updated October 21, 1999.
Copyright George Watson, Univ. of Delaware, 1999.