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So I know this is going to seem like a very simple question, but my book provides no definition. If the power P_in is defined as the power the goes from the source into the load in a transmission line, what is the source power in terms of the generator voltage, generator internal resistance, and any other relevant constants.

I've seen elsewhere the book that $$P = \frac{1}{2} Re\{VI^*\}$$. In the case of a generator with some internal impedance (resistance in the simple case) Z_G and some voltage source V_G what is the power it can deliver $$\frac{V_G^2}{Z_G}$$ or $$\frac{1}{2} \frac{V_G^2}{Z_G}$$ and why?

I'm just not fundamentally understanding all our different power definitions for these problems, and it would be very helpful if someone could provide a concise summary of what I need to know to tell what's going on. Thanks.

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  • \$\begingroup\$ electronics.stackexchange.com/questions/29496/s-vi-2-derivation ? \$\endgroup\$ – C. Lange Sep 11 '19 at 4:35
  • \$\begingroup\$ I don't know the canonical answer to your question, but I wouldn't consider the power consumed by the generator's internal impedance to be "delivered". So my answer would be different from either of your proposed answers. \$\endgroup\$ – The Photon Sep 11 '19 at 4:55
  • \$\begingroup\$ an RF 'transmission line', 50 ohms, is a very different context to a power 'transmission line', 132kV, which do you mean? While the physics meaning of 'power' is well defined, there will be nominal or rated powers that might be defined slightly differently depending on context, 'source power' is one such power in the RF context. \$\endgroup\$ – Neil_UK Sep 11 '19 at 5:09
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While the physics of computing power remains the same for all situations, the context may require that you choose particular values for impedance or voltage, for particular power definitions.

In the context of RF, the 'source power' of a generator will usually be defined as the power it actually delivers into its defined system impedance, which is usually 50 or 75 ohms. This remains the definition whether the generator has an output impedance of nominally the system impedance, or very different from it. If it's different, then this is not the maximum power that can be got from the generator.

If you load a generator with a load other than the system impedance, then it will produce a different power. This new power can be computed in terms of the defined source power, and corrections to it based on source and load matching to the system impedance. This is one of the benefits of referring all measurements to the system impedance, it allows the details of source and load match to be handled systematically, and allows small corrections to be ignored.

When comparing different formulae for power, take care to understand where the voltage is being measured, so whether at the physical port from the generator, or at the theoretical voltage source that drives the theoretical output impedance before the port.

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