By Allan Waters (auth.)
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Additional resources for Active Filter Design
A Butterworth low-pass filter has the following specifications: pass band up to 100 Hz with 3 dB of loss, stop band to be at least 80 dB down at 1 kHz. Calculate the order of the filter, the roots of the Butterworth polynomial, and the values of the pass-band and stop-band loss. [Ans. 2. Obtain the normalised Chebyshev coefficients for a fourth-order, 1 dB ripple width, low-pass filter. [Ans. 3. 5 kHz. Calculate the order of the filter and the Chebyshev polynomial. Check also the values of the pass-band and stop-band loss.
Obtain the relationship between the output and the two inputs. Assume that the opamps used have high open-loop gains and input impedance values. 15) Since a major assumption is that the gains of the op-amps are very high, then we may quote the following voltages: Vb = V2 , Va = V 1 , Ve = Vr. 17) The resistor R 1 is usually made variable in order to adjust the gain. A typical instrumentation op-amp would have A 0 = 2 x 10 5 , Ri = 10 12 ohms. Active Filter Design 36 This circuit is an example of a differential-in and differential-out (A 1 , A 2 ) amplifier with negative feedback and equalised amplification.
5 Obtain the order of the filter and confirm that the stop band requirement is fulfilled. 4 dB Note that this fourth-order Chebyshev circuit satisfies the requirements better than the previously considered sixth-order Butterworth circuit, at the expense of some pass-band ripple. 5 dB up to 3 kHz stop-band minimum to be 60 dB at 30kHz Calculate the order of the filter and the roots of the polynomial. 5 dB, A MIN > 60 dB. 35. a= .!.. 3. It should again be noted that we have also obtained important design coefficients which will later be used in the design of filters having specified ripple widths.