# General Impedance Converter.

Cuthbert Nyack

Laddder filters can require large inductors if designed for low frequencies. These inductors are not only inconvenient, their
resistance can also have an adverse effect on the frequency response of the filter. The circuit of a general impedance converter is shown above along with the value of the
impedance seen looking into the Vin terminal.

To simulate an inductor, impedance Z_{4} is a capacitor and the other impedances are resistors, the
impedance of the circuit is

Z = (sCR_{1}R_{3}R_{5}/R_{2})

This is equivalent to an inductor L = (CR_{1}R_{3}R_{5}/R_{2})

This configuration is used to simulate large grounded inductors in ladder networks.

To simulate a FDNR or D element Z_{1} and Z_{3} are capacitors
while the other
impedances are resistors. The impedance is

Z = R_{5}/(s^{2}C^{2}R_{2}R_{4})

with D = (C^{2}R_{2}R_{4})/R_{5}

If a ladder network has grounded capacitors then the components can be multiplied
by 1/s, resistors become capacitors,
inductors become resistors and capacitors become D elements. The
resulting grounded D elements can then be simulated by the GIC.

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COPYRIGHT © 1996 Cuthbert A. Nyack.