By Allan Waters (auth.)
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Extra resources for Active Filter Design
Check also the values of the pass-band and stop-band loss. [Ans. 1 Introduction It is useful to consider at this stage the basic theory concerning integrated circuit operational amplifiers, since they are the foundation of most of the filter circuits to be studied. The reader should refer to the more specialised texts for a fuller treatment of the subject matter. The operational amplifier ( op-amp) represents a basic integrated circuit building block and is a broad-band, high-gain, differential input device.
Active Filter Design 18 Here A MAX= 3 dB, AMIN = 100 dB, e = 1. 995 We have an odd function, hence 8n = ktr/n and a root on the negative real axis. ktr = (J n n k =0 80 = 0 k=1 (J1=tr/5=36° k =2 82 = 2tr/5 = 72° Roots are (s + ao)(s + a 1 + jwl)(s + a 1 - jwl)(s + a2 + jw2)(s + a2- jw2). 5. 7) e = (10°· 3 as expected for Butterworth. 3 The Chebyshev approximation It was seen that the Butterworth form gives a good approximation to the ideal around ( w = 0) but is less than ideal in the vicinity of the cut-off point ( w = We).
The end of the pass band or ripple band is always at w = We. For the conditione= 1 gives a ripple width of 3 dB and w = We as for the Butterworth approximation. 17) Active Filter Design 22 Finally it is necessary to determine the roots of the Chebyshev polynomial for various values of the order n of the filter. 18) and are sk = ak ± jwk, k =0, 1, 2 ... 19) 2n ok =(2k + 1) - 1T 2n for k = 0, 1, 2 ... 2n - 1 and 1 . }£___ sinha ) cosha which indicates that the poles (roots) of IH(s)l 2 lie on an ellipse.