I am intrigued that many people have attempted to measure the equivalent
source impedance of a transmitter with such varying results.

On the one hand is the assertion that a transmitter adjusted for optimum
operation is comparable with a linear source, and the source impedance
must therefore be the conjugate of the load.

On the other hand is the analysis usually used to engineer a PA that
should reveal the sensitivity of output power to small changes in load
impedance and therefore an equivalent dynamic source impedance.

Taking a valve amplifier as an example for discussion...

On first glance, the change in peak anode voltage and current is
indicated on the anode I/V characteristics by laying an incrementally
different load line on the chart and observing the change with peak grid
voltage held constant. The deltas then could be used to calculate a
dynamic source resistance at the anode. Essentially, the value calculated
will be the inverse of the slope of the constant grid voltage line.

The required anode load resistance is the resistance calculated from the
fundamental anode RMS voltage divided by the fundament anode RMS current.

These are not necessarily the same value. In fact, the dynamic source
resistance is usually much higher than the required load resistance, and
the ratio is usually higher for a pentode or tetrode than for a triode
operating at the same voltage and current.

So, immediately, there is an apparent conflict with the proposition that
the dynamic source resistance and the load resistance are the same.

Many of the experiments to try to prove that the PA is "conjugate
matched" have used a valve transmitter with a PI coupler, so let us
examine the behaviour of a PI coupler.

I have designed PI couplers for a 7MHz transmitter using the formulas
given in Eimac's "Care and Feeding of Power Tubes". The formulas seem to
assume that the intrinsic Q of the components is infinite, ie that the
components themselves are lossless. This assumption introduces error, but
my supposition is that for very small changes in load resistance, the
assumption that Qi is very large will not seriously impact the models.

Models were constructed with loaded Q ranging from 8 to 21, and for a
range of anode load impedances, the the sensitivity of the impedance
presented to the anode to small changes in the nominal 50 ohm external
load.

The interesting observation is that a very small decrease in the nominal
50 ohms load can result in a different relative change in the anode load,
indeed, it can result in an increase in anode load impedance, and the
sensitivity depends on loaded Q and the required anode load resistance.

For example:
-if Ql is 10 and Ra is 1400 ohms, a 1% decrease in the extenal 50 ohm
load results in a 0.26% decrease in the anode load impedance; and
-if Ql is 12 and Ra is 1400 ohms, a 1% decrease in the extenal 50 ohm
load results in a 0.48% decrease in the anode load impedance.

For this very small change in operating Q, the effect of a small change
in external load resistance is quite different on the anode load
impedance.

A further set of examples:
-if Ql is 10 and Ra is 1260 ohms, a 1% decrease in the extenal 50 ohm
load results in a 0.32% decrease in the anode load impedance; and
-if Ql is 12 and Ra is 1260 ohms, a 1% decrease in the extenal 50 ohm
load results in a 0.52% decrease in the anode load impedance.

So, if the PA is "tuned up" to deliver a slightly different anode load
resistance (in this case 10% lower), the sensitivity of anode load
impedance to small changes in the external 50 ohm load is different.

The modelling suggests that conventional circuit theory can explain some
of the experimental results that are otherwise ascribed to some magical
behaviour of the PI network.

Owen