The Design of a Constant-Angle or Power-Law Magnitude Impedance

A passive driving point impedance can be built from RL or RC elements to vary in magnitude nearly as and to have a nearly constant angle at over an arbitrarily wide frequency range, . Except at the extreme ends, the successive positions of the network poles (along the negative frequency axis) are taken in the ratio , in which in the range 6 to 25 determines an approximation error in the range 1 per cent to 10 per cent. The zeros of an arbitrarily wide-band network lie between poles, in the ratio from a pole. A series string of parallel RL or RC pairs can be used to realize the impedance, according to whether is positive or negative. The R/L or 1/RC of successive pairs are in the ratio , and the resistors of successive pairs are in the ratio . One pair "at" each band edge, the "corrector" or "compensation" impedance, is specified by different ratios, so as to account for band-edge effects. An experimental admittance constructed with five capacitors and five resistors approximated an admittance at a constant 45° angle to within the measurement accuracy of 1 per cent in magnitude and 1° in phase over the frequency range 50 cps to 10,000 cps.