The power explanation
"walt" wrote in
ups.com:
Walt,
....
First, let me say that although the average source resistance at the
plates appears to be 1400 ohms in the case I described, and IMHO I
believe it is, I'm not in the position of stating that is as a fact.
Ok, I think we are agreed that the measurements haven't directly
supported that belief.
What I do claim as a fact is that when the transmitter is loaded to
deliver all available power to its load, the OUTPUT source resistance
(or impedance) at the output terminals is the conjugate of its load.
If it were a linear source and you delivered *maximum* (as opposed to
*all*) to the load, I agree that the load impedance is the complex
conjugate of the source impedance. That is essentially the Jacobi Maximum
Power Transfer Theoram.
The question is whether it is a sufficiently linear source to use that
model.
I'm differentiating between the conditions at the input of the pi-
network and those at the output, because the energy storage effect of
the network Q isolates the output from the input, such that the
conditions at the output can be represented by an equivalent Thevenin
generator. At the output terminals the conditions appearing at the
input are irrelevant, such as the shape and duration of the voltage
applied to the pi-network, as long as the energy storage Q is
sufficient to support a constant voltage-current relationship (linear)
at the output for whatever load is absorbing all the available power
from the network.
Thus, when all available power is delivered into a 50-ohm load the
source resistance at the output terminals is 50 ohms. Please also
review the later portion of Chapter 19, also available on my web page.
On those pages I report the results of measurements using the load-
variation method, which also shows the output source resistance to
equal the load resistance when the amp is delivering all its available
power.
Walt, I have just re-read that section and note your measurements which
explored the delta V and delta I for small load variation (delta R) where
delta R is always negative, and calculated results.
Your results are interesting.
I have seen others report quite different results, and have found
differently myself on rough measurements, but I note your comments on the
sensitivity of the calculated Rs to tuning/matching which might reveal
why other tests disagree.
(It only takes one sound repeatable experiment that shows that the source
impedance is not the conjugate of the load to disprove the generality.)
On a practical note, the sensitivity discussed above does mean that if
your assertion about matching is true, it is unlikely that transmitters
are exactly matched.
My measurements have been on transistor PAs with broadband transformer
coupling to the load. The transmitters have had a lowpass filter with a
break point well above operating frequency between the transistors and
load. It is a different configuration, and although my measurements were
rough, they indicated different apparent source impedance at different
drive levels which questions the linear model for large signal operation,
especially for modes with varying amplitude such as SSB telephony.
Owen
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