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# filter parameter design and calculation

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#### lhlbluesky

##### Banned
i have some doubts about filter design.

1, for a standard two-order bandpass filter, the transfer function is vout(s)/vin(s)=H0*(W0/Q)*s/(s^2+W0/Q*s+W0^2), with Wo as center frequency, H0 as center frequency gain, Q as quality factor. if it is a three order or four order bpf, then how to calculate the parameter W0, H0, Q? for example, i have a four order bpf (two cascaded two-order bpf) with transfer function vout(s)/vin(s)=(H01*(W01/Q1)*s/(s^2+W01/Q1*s+W01^2))*(H02*(W02/Q2)*s/(s^2+W02/Q2*s+W02^2)), then what is the expression of total W0, H0, Q?

2, for twin-T notch filter(for example, c1=c2=50pF, c3=100pF, r1=r2=200k, r3=100k), Q is infinite ideally, but actually, it is not the case, in my simulation, Q=20, what is the expression of W0, H0, Q for twin-T notch filter? and what is the non-idealities?

3, if i want to get a band-rejection response with very sharp attenuation at both rising edge and falling edge, but not using multi-order structrue, is there such circuit?

thanks.

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