# Ideal Gyrator Circuit

Submitted by admin on Tue, 11/25/2008 - 07:13

A gyrator is a two port which realizes the following port equations:

i1 = g2 * v2 i2 = -g1 * v1

The currents are defined as into the two port.

Consider putting an impedance Z at port 2. Then v2/i2 = -Z. Using this to substitute gives:

i1 = g2 * v2 = g2 * i2 * (-Z) = g2 * (-g1 * v1) * (-Z) = g1 * g2 * v1 * Z

The impedance at port 1 is therefore

z1 = v1/i1 = 1/(g1 * g2 * Z)

If a capacitor (z = 1/SC) is placed across port 2 the impedance at port 1 is that of an inductor (z = SL).

CCICAP can model a gyrator with two cross coupled VCC (voltage to current) elements.

.title Gyrator ' define a frequency of interest .par fo 1.kHz ' get results in Real and Imaginary form .opt r&i ' sweep frequency from fo/10 to fo*10 .ac 20 10 { fo 10 / } { fo 10 X } ' define the impedance at port 1 as v1/i1 .calc z1 { v1 i1 / } ' plot real and imaginary parts of z1 .plot ac png z1 .plot ac png z1 > .ckt v v1 1 1a 1. am i1 0 1a ' load capacitance c z 2 0 1.ufd vcc g1 1 0 2 0 1. ' reverse polarity for g2 vcc g2 0 2 1 0 1. .end .go .stop

In this example the impedance at port 1 is that of a 1 uH inductor. At 1 KHz the impedance is 0.0 + j*0.0063. The resulting plots are:

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