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Hi, I have a repeat in less than a month and could do with some help with this question from a past exam paper. Any help would be greatly appreciated.
The required order N of a low-pass Butterworth filter, with a 3dB frequency of 1 r/s, such that the attenuation at the reject frequency wr is ≤ α (dB) can be obtained using
N ≥ log(10α/10-1)/2log(wr)
1)
Determine the order and transfer function, using Table 1, of a Butterworth low-pass filter with a 3 dB cut-off frequency of 100kHz and a minimum attenuation of 20dB at 200kHz.
2)
Determine the unit step response of the filter.
3)
Hence calculate the filter overshoot.
Heres Table 1 given:
Order(N) : Factors
2 : (s2+√2s+1)
3 : (s+1)(s2+s+1)
4 : (s2+1.84776s+1)(s2+0.76537s+1)
5 : (s+1)(s2+0.6180s+1)(s2+1.6180s+1)
6 : (s2+1.9378s+1)(s2+1.4142s+1)(s2+0.5176s+1)
I am sorry if the table isn't easy to read.
Thanks.
The required order N of a low-pass Butterworth filter, with a 3dB frequency of 1 r/s, such that the attenuation at the reject frequency wr is ≤ α (dB) can be obtained using
N ≥ log(10α/10-1)/2log(wr)
1)
Determine the order and transfer function, using Table 1, of a Butterworth low-pass filter with a 3 dB cut-off frequency of 100kHz and a minimum attenuation of 20dB at 200kHz.
2)
Determine the unit step response of the filter.
3)
Hence calculate the filter overshoot.
Heres Table 1 given:
I am sorry if the table isn't easy to read.
Thanks.
