Calculate the Terminating Impedance of L-Matching NetworksAuthor: R.J.Edwards G4FGQ © 15th August 2005
A n RF generator is connected to the left-hand terminals. A resistive termination is connected to the right-hand terminals. Computed values of Rt and Xt are those which cause a network's input impedance to match the generator's internal resistance. When terminated with Zt there is a conjugate match at a network's output terminals and maximum available power is dissipated in Rt.
Before making use of computed results always carefully check component input values. It is very easy to make mistakes. Also check that the correct network number from Net.1 to Net.4 has been selected.
This program operates in the reverse manner to program L_TUNER which computes the values of coil and capacitor of L-matching networks for given input and terminating impedances, and frequency.
It is occasionally useful to know the value of the terminating impedance that causes the generator to be correctly loaded for maximum power output into the termination. The termination often is the input impedance of a transmission line feeding an antenna. Various factors can be deduced from the line input impedance.
All that needs to be known are the values of the network's coil and capacitor and the network's configuration. These often can be estimated with sufficient accuracy from a visual inspection of an L-tuner. Component settings will have been adjusted by means of the Transmitter Loading Indicator (TLI) (sometimes misnamed an SWR meter).
For educational and entertainment purposes one can use L_TUNER to find values of inductance and capacitance of matching networks and then insert them in this program to return to the original terminating impedances. It is interesting to use impedances similar to those at the input of antenna feedlines while setting the generator impedance in L-TUNER to be purely resistive such as 50+j0. The range of impedances that can be covered by coil and capacitor settings in an L-Network then can be estimated by varying the values of inductance and capacitance and observing the computed data.
The efficiency of L-match networks in transmitting applications is somewhat greater than the more popular T-match. This is because the working Q of a T- network is higher at some settings. The disadvantage of an L-match is that it requires complicated re-configuring to cover the full range of possible load impedances. It also may have larger values of L or C for the same values of terminating impedance.
The program disregards the intrinsic Q's of coils and capacitors.
The working network Q equals the component reactance/generator-resistance when the generator is in series with one of the L or C components in the various network configurations. The network working Q equals the generator resistance/component-reactance when the generator is in parallel with a component. The network Q can be varied by varying the generator resistance.
The computed characteristic-resistance = Squareroot(L/C) which may be of interest to experts in network analysis. The natural resonant-frequency of L and C also is computed and displayed.
It will be seen that all four networks constitute LCR tuned-circuits. The generator resistance becomes the sum of the series loss-resistances of L and C with Net 1 and Net 2 and the generator resistance completes a series tuned-circuit.
Net 3 and Net 4 become parallel tuned circuits with the generator being an equivalent high-value shunt loss-resistance with their output terminals short-circuit.
The Q's of all four network circuits are displayed.
If the natural resonant frequency of L and C is entered as the test frequency it will be seen that the series loss resistance (the generator) is transformed to the high value, purely resistive shunt-loss resistance (the terminating resistance). It is best to use Net 1 or 2 in this case. Set the generator resistance to a few ohms as it is now the loss resistance of the coil or capacitor. Finely adjust the test frequency to reduce series reactance to a negligible value.
It is apparent that an L-match network is just an application of an ordinary tuned-circuit.
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