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The cutoff frequency of the low pass Butterworth filter is the arithmetic mean of the two cutoff frequencies as found above.
The arithmetic mean of the two cutoff frequencies as found above is the final cutoff frequency of the low pass Butterworth filter.
Which of the following is a frequency domain specification?
What is the value of gain at the pass band frequency, i.e., what is the value of KP?
We know that the formula for gain is:
What is the value of gain at the stop band frequency, i.e., what is the value of KS?
We know that the formula for gain is:
We know that,
We know that:
What is the order N of the low pass Butterworth filter in terms of KP and KS?
Explanation:
What is the expression for cutoff frequency in terms of pass band gain?
We know that:
What is the expression for cutoff frequency in terms of stop band gain?
We know that:
What is the lowest order of the Butterworth filter with a pass band gain KP= 1 dB at ΩP= 4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS= 8 rad/sec?
We know that the equation for the order of the Butterworth filter is given as:
From the given question:
KP= 1 dB, ΩP= 4 rad/sec, KS= 20 dB and ΩS= 8 rad/sec
Upon substituting the values in the above equation, we get N = 4.289
Rounding off to the next largest integer, we get N=5.
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