By Allan Waters (auth.)
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Extra info for Active Filter Design
3. 1 giving R 3 = KR 1 . 4. (l. 1 Basic Filter Grcuits 43 It can be seen that the resistor values are quite large because of the chosen value for the capacitor. tF could have been made. Selection of these capacitor values would have resulted in correspondingly reduced values of resistance. This is left as a simple exercise for the reader to perform. 3 The voltage-controlled-voltage-source second-order filter This type of circuit was first proposed by Sallen and Key and is relatively easy to design and implement.
12). 4. ;;;; 1), C~(w) = 1 and the function will vary between 1/(1 + e2 To and 1. Within the transition band and through the stop band, however, C~(w) increases with w such that for e 2 C~(w) > 1, IH(jw)l decreases rapidly. 10) AMIN = 10logto [1 + e2 C~(w)) for the edge of the stop band at w = w5 /wc normalised. 5 Effect of ripple width Unlike the Butterworth approximation, it cannot be assumed that the 3 dB or halfpower frequency is the cut-off frequency. The end of the pass band or ripple band is always at w = We.
Note also that there is an additional 90° phase shift through the op-amp over the working frequency range. It should fmally be mentioned here that the quality of the output signal depends on the op-amp's ability to cope with the rate at which the output signal varies with time. This capability is referred to as the slew rate of the op-amp and is the maximum rate-of-change of the output voltage which the device can handle. 10) Selection of op-amps with superior GB and SR is left to the designer, who must choose between cost and suitability of a device for his particular require- 34 Active Filter Design ment.