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Impedance transformation software

# Impedance Transforming L-Networks

Author: R.J.Edwards G4FGQ © 3rd October 2001
`       o-----////////-----o---o       o---o-----////////-----o               jXs        ¦               ¦       jXs                          ¦               ¦  From Generator.         \$               \$          To Load ---->  Zin = Rin +jXin     jXp \$               \$ jXp      ZL = RL + jXL           ---->          \$               \$                          ¦               ¦             Network A    ¦               ¦    Network B       o------------------o---o       o---o------------------o`

Both networks A and B transform the load impedance RL + jXL to Rin + jRin. If RL > Rin then network A applies. If Rin > RL then network B applies. Series reactances Xs and parallel reactances Xp can be either coils or capacitors. Sometimes both components in a network may be of the same L or C type.

Both A and B have two alternative versions - L's and C's being interchanged.

Given ZL, Zin and frequency, the program calculates values of L uH and C pF.

Further Notes
The L-network is defined in this program as an impedance transformer. It transforms a terminating (load) impedance RL + jXL to the network's input impedance Rin + jXin. An equipment designer usually has the choice of a low-pass or high-pass filter configuration and so a network may have a dual purpose.

The physical construction of a component may influence choice of circuit configuration. This can happen when one or both components are variable.

A network, of course, can be used to match a load to a generator such that maximum available power is delivered to the load, this being a very frequent application. To match a load to a purely resistive generator it is necessary only to set Rin equal to the generator resistance and set Xin to zero.

When the generator has a complex internal impedance Zgen for maximum power transfer the network input impedance must be set equal to the CONJUGATE of Zgen.

The conjugate of Rgen + jXgen is Rgen - jXgen. In other words, the conjugate is obtained simply by reversing the sign of the reactance. The magnitude of the impedance remains as it was. This may seem a trivial operation but, when the reactance to resistance ratio is high, circuit behaviour is profoundly changed.