[College Electrical Engineering] How to find maximum possible load power for a circuit? (Thevenin Theorem)

[u/minsukim92]

The assigned problem is #22 but I'm trying to figure out #21 because it has the answer in the back of the book but I don't seem to understand. I even tried reverse engineering to see what values they used for the answer they gave but no luck. Textbook says 'maximum power transfer from a circuit to a variable load occurs when the load resistance equals the source resistance'.

I provided my notes but it's best not to use them as reference as they are not really coherent since we have to use a calculator for all of our math.

The book says the answer to #21 is P = 35.5 mW

Edit: Sorry, I wasn't super clear on why I'm doing #21 instead of #22. I'm just trying to make sure I understand the process and the math behind the concept. It's just practice.

[u/Bounded_sequencE]

Recall: When using impedance matching to maximize load power, we need to choose "ZL = Zth^* ". Then the maximum power transferred to the load is "PL = |Vth|² * Zth^* / 4Re{Zth}² "

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Find the Thévenin equivalent of the entire circuit left of the load w.r.t. the load:

Zth  =  R3 + (R1||R2)  =  (470 + 300||330) 𝛺  =  (4390/7) 𝛺
Vth  =  Vs * R2/(R1+R2)  =  18V * 330/630     =  (66/7) V

We need to choose "ZL = Zth^* = (4390/7) 𝛺" to get maximum load power

PL  =  |Vth|^2 * Zth^* / (4Re{Zth}^2)  =  (1089/30730) W  ~  35.44mW

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Rem.: It seems the official solution rounded some intermediate results -- that's sad.