Ideal Gyrator Circuit

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: