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On the Form of the Phase Response Curve for a Single Real Pole or Zero

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The mathematical description of the phase response of a single real pole or zero on a logarithmic frequency basis is shown not to be "the familiar arctangent curve," but of the form y=arctan ¿x or, by shift of ordinate, Y=arctan tanh x/2. The difference between the arctangent and these functions on a normalized basis is found to be in excess of 15 percent. The best straight-line approximation for phase shift is determined as intersecting the 0° and 90° values at 0.0970 and 10.315 times the corner frequency, so that the often used "one-tenth and ten-times" straight-line approximation is confirmed as being extremely good for practical purposes.

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IEEE Transactions on Education  (Volume:8 ,  Issue: 4 )