Impedance Transforming L-Networks

       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.

Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link L_Tuner then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.