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

On Apr 1, 2:38 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.

....

I have a lot of trouble with that one, especially the "must therefore"
part. What is "optimum operation"? Is it delivering the most power
to the load, or is it delivering the RATED power to the load, at some
particular efficiency and level of distortion? I'd claim it's the
latter.

There are lots of examples of "optimum" load NOT being "conjugate-
matched" load. A typical stereo amplifier has an output impedance
that's a fraction of an ohm, but the amplifier is optimized to deliver
power to loads in the vicinity of 4 to 8 ohms, most often. The power
lines delivering power to a home show a source impedance that's a tiny
fraction of an ohm, but with everything in the house turned on, the
net load might be as low an an ohm--in rare cases a bit less than an
ohm. The load placed on a typical battery is similarly many times the
battery's internal resistance, except in the case of a heavy load on a
battery near the end of its charge. And lest you think that all
sources are optimized for load resistances higher than the source
resistance, I can change the feedback on that stereo amplifier without
changing the power output stage design, so the amplifier is still best
at delivering power to loads in the 4-8 ohm range, but now the output
impedance with new feedback is around 100 ohms.

So WHY should we expect a transmitter to represent a source impedance
particularly close to the load impedance, or to its complex conjugate?

I've gone through analyses similar to what you what you reported in
the remainder of your posting, with an output network whose Q I varied
(in the analysis), and come to similar conclusions. Just as you say,
Owen, when I do that, it's all clear and not magical at all. And the
source resistance can be made to be what I want through feedback, if I
wish. In some of the work I do, it's important to have a virtual ZERO
impedance at a particular node, but that's generally done using an AGC
loop, so the very short term dynamic impedance at that node may be
something considerably different from zero. But if you do power
measurements with varying loads, it will appear that the impedance
there is very close to zero. (Then you can put a 50 ohm resistor from
that node to a precision 50 ohm line, and have a very good 50 ohm
source; you can put another 50 ohm resistor from that node to another
line and have two matched sources, for testing other circuits...part
of a vector network analyzer.)

Cheers,
Tom

"K7ITM" wrote in news:1175469074.999185.17760
@d57g2000hsg.googlegroups.com:

On Apr 1, 2:38 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.

...

I have a lot of trouble with that one, especially the "must therefore"
part. What is "optimum operation"? Is it delivering the most power
to the load, or is it delivering the RATED power to the load, at some
particular efficiency and level of distortion? I'd claim it's the
latter.

Tom, I chose the word optimum for a reason, and I agree with you.

The design process does not find a drop dead maximum power in the way
that loading a source with a variable impedance finds a maximum power.
The rated power of an amplifier is a compromise, and dependent on the
available voltage and current, required linearity / IMD, active device
characteristics (eg saturation effects), dissipation limits (anode,
control grid etc), harmonic output, efficiency to name just a few. To
complicate crude experiments to determine maximum power output, the valve
is usually operated close to saturation, so small load changed result in
severly non-linear behavior. Further, apparent output impedance is
affected by the regulation of the DC supply, which is many transmitters
is better for short term current demands than sustained load.

For example, I have a Ameritron AL811H amplifier with 4 x 811A. The
operating point for SSB telephony is different to AM due to anode
dissipation limits. Some would suggest that when optimised for each of
the SSB telephony and AM operating points (ie different anode load
resistances) into a 50 ohm load, that the equivalent source impedance
*must* be 50 ohms, and that it happens without specific design
provisions.

Owen

Owen Duffy wrote in
:

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 last sentence should read:

Essentially, the value calculated for a class B amplifier will be about
half the inverse of the slope of the constant grid voltage line.

Owen

Owen Duffy wrote:
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.

Does that take into account the step-down transformation?
The "source load" that results in the "source load line",
is not the physical load in the system. It is the physical
load in the system transformed by the transmission
line, the filters, the tank circuits, and the transformers.
In short, it is the transformed load seen directly
*by the source - at the source*.

For instance, a source may have a dynamic source
resistance of 1000 ohms. A 20:1 tank circuit
transformation takes it to 50 ohms. The load line
for that amp has a slope of 1000, not 50.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote in
t:

Owen Duffy wrote:
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.

Does that take into account the step-down transformation?

Cecil,

The two previous paragraphs that you have omitted in your quote provide
the context for the paragraphs that you did quote. The context is in the
anode circuit of the PA being discussed.

The "source load" that results in the "source load line",

I don't really understand the concepts of a "source load" or "source load
line". Perhaps your meaning is the load in the anode circuit of the PA, I
will read on with that interpretation.

is not the physical load in the system. It is the physical
load in the system transformed by the transmission
line, the filters, the tank circuits, and the transformers.
In short, it is the transformed load seen directly
*by the source - at the source*.

Ok...


For instance, a source may have a dynamic source
resistance of 1000 ohms. A 20:1 tank circuit
transformation takes it to 50 ohms. The load line
for that amp has a slope of 1000, not 50.

I am not comparing apples with oranges, not comparing impedances on
different sides of the pi network.

To expand the first example with the details:
-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

Rl=50, |Za|=1400.0;
Rl=49.5, |Za|=1396.4, a 0.26% decrease in |Za| for a 1% decrease in Rl.

You cannot think of a PI coupler (and the original post was discussing a
PI coupler) in this application as an idealised symmetric n:1
transformer, whilst this coupler has an apparent ratio of 28:1 (1400/50),
incremental impedance changes are in a quite different ratio.

A PI network is not in the general case symmetric, your example of a 20:1
"tank" circuit (and I would argue that "tank" is usually used to mean a
parallel tuned anode circuit, typically link coupled) is not symmetric
and the point of my post was to say that Zin/Zout is not a straight line,
and general analyses based on a fixed ratio are likely to be flawed.

Owen

Owen Duffy wrote:
Cecil Moore wrote:
Does that take into account the step-down transformation?

The two previous paragraphs that you have omitted in your quote provide
the context for the paragraphs that you did quote. The context is in the
anode circuit of the PA being discussed.

I'm in the process of moving and am having a hard time
keeping up.

If the amplifier were a class-A amp with a 50 ohm
load resistor driving a 50 ohm load, would what
you say still be true?
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote in
t:

Owen Duffy wrote:
Cecil Moore wrote:
Does that take into account the step-down transformation?

The two previous paragraphs that you have omitted in your quote
provide the context for the paragraphs that you did quote. The
context is in the anode circuit of the PA being discussed.

I'm in the process of moving and am having a hard time
keeping up.

If the amplifier were a class-A amp with a 50 ohm
load resistor driving a 50 ohm load, would what
you say still be true?

I don't understand "a 50 ohm load resistor driving a 50 ohm load".

The transformation issue pertains to the PI coupler, you cannot treat a
PI coupler in the general case as an idealised symmetric n:1 transformer.
It certainly isn't in a typical single ended RF linear amplifier.

Owen

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

On Apr 2, 3:03 pm, Owen Duffy wrote:
Cecil Moore wrote . net:

Owen Duffy wrote:
Cecil Moore wrote:
Does that take into account the step-down transformation?

The two previous paragraphs that you have omitted in your quote
provide the context for the paragraphs that you did quote. The
context is in the anode circuit of the PA being discussed.

I'm in the process of moving and am having a hard time
keeping up.

If the amplifier were a class-A amp with a 50 ohm
load resistor driving a 50 ohm load, would what
you say still be true?

I don't understand "a 50 ohm load resistor driving a 50 ohm load".

The transformation issue pertains to the PI coupler, you cannot treat a
PI coupler in the general case as an idealised symmetric n:1 transformer.
It certainly isn't in a typical single ended RF linear amplifier.

Owen


A class A RF amplifier can certainly be fed its DC through an RF
choke, just as is done with other classes. There's no need to limit
the discussion to class A.

If you put a resistance Rshunt in parallel with the plates (or
collectors or drains), at the plates, such that the plate resistance,
Rplate, in parallel with Rshunt equals the load presented by the
output network to the plate circuit, then the source impedance seen at
the output terminals will be the same as the load impedance. That may
be a little confusing...let me put it differently. Consider an output
passive, linear network with two ports, the Plate port and the Load
port. When the Load port is loaded with Zload, the rated load
impedance, the Plate port presents an impedance to the plates, call it
Zpnetwork. If you put an additional load at the plates such that the
Plate port of the network "sees" an impedance equal to Zpnetwork
looking toward the plates, then when the network is connected to the
plates and that additional load, you will "see" a source impedance
equal to the conjugate of Zload looking back into the network's Load
port.

For example, let's say that we have a 6000 ohm plate resistance, and a
4000 ohm resistor we put in parallel with the plates (put it shunt
across the plate DC feed RF choke which is considered to be
essentially infinite impedance). The net resistance looking into that
is 2400 ohms. Assume a load of 50+j50 ohms. Assume an output network
that, when loaded with 50+j50 ohms, transforms that to 2400 ohms,
resistive. Then the impedance looking back into the output port of
the output network will be 50-j50 ohms. It doesn't matter if it's a
pi network, a filter, or a 81.52 degree long piece of 342.73 ohm
"lossless" transmission line.

But if the goal is to deliver as much clean RF power to the external
load as you can, why would you put an RF-dissipating resistor into
your amplifier?

Cheers,
Tom