20. For the network in Fig. 21.99: a. Determine Vo at a frequency one octave abo

Question

20. For the network in Fig. 21.99:

a. Determine Vo at a frequency one octave above the critical frequency.

b. Determine Vo at a frequency one decade below the critical frequency.

c. Do the levels of parts (a) and (b) verify the expected frequency plot of Vo versus frequency for the filter?

For the network in Fig. 21.99: Determine Vo at a frequency one octave above the critical frequency. Determine Vo at a frequency one decade below the critical frequency. Do the levels of parts (a) and (b) verify the expected frequency plot of Vo versus frequency for the filter?

Explanation / Answer

With a first order low-pass filter, the signal will decrease by 6dB per octave above the critical frequency, and the signal will be untouched below the critical frequency. This is, of course, approximate, but very convenient in designing a filter.

For an RC filter, the critical frequency is equal to 1/RC.

First find the cutoff frequency,
fc = 1/(2*?*R*C)
fc = 1,592 hertz

A. one octave above, f = 3,184 hertz,
Xc = - j500 ohms
Z = 1,000 - j500
V out = (V in)( - j500/(1,000 -j500))
divide top and bottom by 500
note 2 -j = a magnitude of 2.236 at an angle of -26.6

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