The effects of error in the element values and the converter transfer characteristic on the responses of active rc filters

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Abstract
This paper first deals briefly with negative impedance converters and with the methods of active network synthesis devised by Linvill and Yanagisawa. The greater part of the paper treats the effects of small errors in the element values and in the transfer characteristic of the negative impedance converter on the response of low-pass Maximally Flat Magnitude (Butterworth) and Equal Ripple (Chebyshev) filters of secondorder. Butterworth and Chebyshev filters of the fourth-order are also considered. Curves are given showing the way in which the errors distort the response characteristics; the importance is pointed out of the proximity to the negative impedance converter of a circuit element having an error in its value. A symmetry between the effects of error in circuit elements on either side of the converter is also noted. The method of display of the sensitivity of circuits to errors used in this paper is believed to be unique for active networks in that the effect on the response curve is shown directly. In other work on the subject, reviewed in this paper, equations are given showing the sensitivity of the poles of the network function to changes in element values and converter sensitivity. The pole shifts are, of course, a measure of the effect on the response of the filter but the effect is shown more clearly when a change in the response curve is given.

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