lhlbluesky_lhl wrote on Dec 30th, 2012, 5:47pm: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?
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?
to 1.) There is no third-order bandpass - only even orders are possible. This results from the lowpass-to-bandpass transformation.
More than that, because a fourth-order bandpass has TWO conjugate-complex pole pairs it is not possible to define a single "overall" Q value.
Normally. the center frequency of a fourth-order BP is the geometrical mean value of both pole frequencies. The gain at the center frequency depends on the used approximation (Butterworth, Chebyshev,...)
to 2.) For a notch filter only the Q value for the zero approaches infinite. The pole Q has a finite value. The values for Ho, wo and Qp can be derived directly from the transfer function (similar to the bandpass case). Of course, Ho is ideally zero.
to 3.) Such a 2nd-order design requires a very large pole Q.