# [AMPS] Conjugate Matching and Efficiency

Tom Rauch W8JI@contesting.com
Mon, 28 May 2001 18:16:52 -0400

```> >Therefore, since Norton and Thevenin sources are equivalent, the concept
> >of calculating system efficiency based on them is flawed.
> >
> Exactly! Basic circuit theory says that Norton and Thevenin sources are
> equivalent - that is, in any case where they *can* be applied correctly.
> We can take that as a hard fact. The other hard fact is that they give
> nonsense results when trying to calculate PA efficiency (with the unique
> exception of 50%). Logically, Captain, that is all you need to prove that
> those two theorems can *not* be applied to this problem.

These theorems can never be used to explain what happens inside
a source. That fact is very clear.

They can be used to describe the way a source "looks" to a load.
That is also well documented and easy to measure.

This makes it very easy to sort out who has looked at the problem, and who is just giving off-the-cuff answers. When someone uses a Thevenin model to explain why a conjugate match only produces 50% efficiency in a source, it is clear he doesn't understand the problem.

> >The reason WHY this is the case is something I've not been able to fully
> >grasp nor have I seen good reason from anyone else.  The best I can come
> >up with is that once you start to calculate efficiency you are starting
> >to go inside the model of the source and using it for things it was not
> >intended. You can't use the model to model itself.  It's weak, but so far
> >I lack better answers.

You can't go inside a source because these models, like all
models, have limits. Models are shortcuts that intentionally remove
or ignore all unnecessary information from whatever problem we are
solving. They allow us to represent complex systems in a very
simple form.

In this case we have a black box that looks like something to the
load, and that behaves like some very simple thing under a given
set of conditions. The only problem occurs when people start to
think the model is the actual circuit.

It doesn't matter if the source is a transistor PA, a tube PA, a
transmission line, or whatever. We can still represent it as either a
Thevenin or Norton model when looking at impedance matching for
maximum available power, and we can never tell by that model
what the source looks like inside the black box.

If we make a careful measurement of load power and make a very
small change in load impedance, we will see the resulting power
change is equal to the source looking like some "resistance".
Nothing says the apparent resistance of the source has to be
dissipating power, or the efficiency is 50% if that apparent
resistance matches the load resistance.

The reason this argument continues is because many like to think
the model we use to "black-box" the source is actually what the
source looks like inside.
73, Tom W8JI
W8JI@contesting.com

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