Active Filter Design by Allan Waters (auth.)

By Allan Waters (auth.)

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5 kHz. Calculate the order of the filter and the Chebyshev polynomial. 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.

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). Filter Types 19 This is because F(w 2 ) = w 2 n is chosen such that the zeros of F(w 2 ) are at one point (w = 0). An alternative approximation, called the Chebyshev approximation, spreads the zeros ofF( w 2 ) across the pass band and constrains H(jw) to attain its maximum value at a number of points within the pass band.

Let w~ = 1 rad/s, C 1 = C2 = 1 F. 16) Notice that there are six unknowns and therefore a certain degree of component selectivity will have to be made since a unique solution is not possible. 16) we obtain which may be written boR? 17) So far we have normalised the capacitors C 1 , C2 and obtained the normalised values for the resistors R 1 , R 2 • We now have to obtain values for the gain resistors R 3 , R 4 for the good circuit design condition of minimum de offset. 8 shows the re-drawn circuit for the de condition where the capacitors are now represented by open circuits.

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