Plot the Maximum Power Transfer Theorem involving the Impedance Module and Phase ZLC

I would like to be able to visualize y plot the Maximum Power Transfer Theorem involving the Impedance Module and Phase ZLC. I have the following questions, that I would greatly appreciate could you guide me to solve: 1.- I would like to know in a graph, the Module and Phase of the impedances ZLCsource and ZLCload, to relate their variation with the Maximum Power Transfer Theorem. 2.- I would like to be able to use DC Sweep, to be able to graph Power in an impedance ZLCsource, or ZLCload in function of Rl_load, as a changing parameter.

It will be appreciated that because the impedances are equal, the dissipated powers are equal in both impedances ZLCsource and ZLCload. If we change any parameter, and uncouple them, the power delivered to the load decreases.

Thank you very much!

by luis_presso
August 30, 2020


As far as I know CL does not offer phasor diagrams (Modulus and Phase/Argument). I have been experimenting and arranged a schematic (below) to show z as (a + bj), for ZLCsource. ZLCload will be the same for default values. The plots for z are shown with a Frequency-Domain simulation. Perhaps this will help.


I was not able to make the DC sweep work in respect of frequency-dependent power. Instead, I used the Frequency-domain simulation and used Rl_load (50,100,150) as parameters. In the schematic I have plotted the power in ZLCload and the power in Rl_load.

Apart from frequency range DC-100Hz I have no intuition about what might happen, so no idea as to correctness...

by EF82
September 01, 2020

Dear @EF82, Your work has been very helpful so that I can have a new analysis tool in Circuit Lab. At point 1 of your answer, it is possible to clearly see how the Impedance Z varies in the frequency domain, with enough detail for analysis. In point 2 of your answer, it is possible to study the behavior of the power delivered by the source vs the power in the resistive part of the Zload. Again, I am very grateful for your valuable contributions. Best regards.

by luis_presso
September 01, 2020

I have made additional simulation plots for the two circuits: using the REAL() expression for two of the currents. I hope this will clarify the difference between Apparent and True power.

The difference to the results is very subtle in this context, but in other applications e.g. power transformers, the differences can be very significant.

I'm sure this will all be explained much better in Chapter 4 of the textbook "Alternatiing Currrent (AC)", when it is published.

by EF82
September 02, 2020

Dear @EF82, I share a circuit that I think can be used to study the following:

Impedance module under study: (V (V_LOAD.nA) / I (I_LOAD.nA))

Phase, in degrees, of the Current flowing over said Impedance

Phase, in degrees, of the Voltage applied to said Impedance

Best regards!

by luis_presso
September 03, 2020

Thanks for that - looks like you have some clear diagrams for analysis, EF82

by EF82
September 05, 2020

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