On Apr 1, 3:38 pm, Owen Duffy wrote:
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


(Yes, I was well aware that you were taking issue with the usually
assumed use of "optimal." Sorry if my previous posting might have
suggested you agreed with it.)

More on how things reflect through a pi network: consider a pi
network at 5MHz designed to present a 1400 ohm load to the plates of
an amplifier, given a 50 ohm output load. One such network is 215pF
at the plates (including plate capacitance), 5.397uH, and 950pF at the
output. If the plate resistance--the net resistance you see looking
back into the plates, excluding the capacitance at that node (since
it's included in the pi network), is 2000 ohms, the impedance seen
looking back into the pi output terminals is 50+j18: the resistive
change at one end resulted in an almost purely reactive change at the
other. If Rplate = 4000 ohms, the impedance looking back into the pi
output is about 36+j45. Rplate = 6000 ohms --- 26+j53.

At least in theory, it's possible to use a 1/4 wave transmission line
to match the 50 ohm load so it presents 1400 ohms to the plates: a
264.57 ohm line will do the trick. But then plate resistances of
2000, 4000 and 6000 ohms reflect pure source resistances of 35, 17.5
and 11-2/3 ohms, respectively.

You can make a lower Q matching network that still has good
attenuation of harmonics by using more L-C sections. If you simply
add an inductor to the output of a pi network, you can again match a
50 ohm load so it presents 1400 ohms to the plates, by using (still at
5MHz) 3.1uH to the output, 258pF shunt to ground, 16.74uH in series to
the plates, and net 50pF from plates to ground. Now plate resistances
of 2000, 4000 and 6000 ohms reflect the following source impedances at
the output which is designed to be loaded with 50 ohms: 43.32+j15.33,
26.19+j31.88 and 18.16+j35.73.

Adding another L-C "L" section to the output (3 inductors in series,
three capacitors shunt to ground) you can end up with a network that
yields, with the same 1400 ohm load to the plates with a 50 ohm output
load, and the same 2000, 4000 and 6000 ohm plate resistances,
65.18+j13.81, 85.88+j62.5 and 82.11+j96.58 ohms source impedance.

In summary, the output network can -- does -- have a big effect on
exactly what a given effective plate resistance will reflect to the
output port. There's a huge variety of possible output matching
networks, and an infinite set of part values, that will yield the
"proper" plate (or collector or drain...) load, for good power output
with reasonable efficiency and reasonably low distortion. There
usually isn't much reason to CARE what the source impedance is,
looking back into the output port, but if you do care, make sure that
you understand what your output network is doing to transform the
plate impedance as seen at the output port.

Cheers,
Tom