On Mar 8, 1:27 am, Dave wrote:
Owen Duffy wrote:

SNIPPED

The question is can the plate (or the whole transmitter for that matter)
be accurately replaced by an equivalent series circuit of a fixed voltage
generator and fixed equivalent series resistance (independent of load).

SNIPPED

The answer is NO!!

Power Amplifiers are not linear devices! [Regardless of manufacturer's claims].

My AL-80B puts out ~850 watts with ~1300 watts input. IF a conjugate match
existed the output would be ~650 watts. The Zo of the 3-500 varies depending on
the phase of the pulse signal. The amplifier provides a pulse of energy into the
tuned circuit, tank circuit, tuner, antenna, where the reactances maintain the
current/voltage under resonant conditions.

My understanding is that reflected energy is also coupled into the tuned
circuits. The active device, power amplifier, may be cutoff, saturated, or
somewhere on the active load line. The energy in the tuned circuit will increase
the Vmax and/or Imax depending on the circuit QL. This increase in stored energy
provides the extra stress on the active device. If the QL 10, nominal design
value, then 90% of the reflected energy is re-reflected back towards the load.
The missing 10% produces heat in the tuned circuit.

Devices that operate from saturation to cutoff are by definition NON-LINEAR.

The tuned circuits store both forward and reflected energy. Ultimately all the
power is radiated, either as a rf field or as heat.

Sorry Dave, the statements in your above post indicates a common
misunderstanding of the operation of an RF power amplifier.

With the possibility that you will consider what I'm about to say is
in the 'he said she said' category, I'd still like for you to review
some of my writings, consider them seriously, and then we'll have
another conversation on the subject. Perhaps I can convince you that
some of your statements are just plain wrong--if not, then we both
simply go our separate ways and believe what we want.

One paper I'd like you to review is Chapter 19 in Reflections 2, also
published in QEX. (I'm now in a hotel in Jax, FL, awaiting spinal
surgery, so I'm not at home where I can obtain the references for
you.) Then I'd also like for you to review Chapter 19A that will
appear in Reflections 3. However, you can find these chapters on my
web page at www.w2du.com. Chapter 19 is found by clicking on 'Review
Chapters from Reflections 2', and Chapter 19A is found by clicking on
'Preview Chapters from Reflections 3'.

I would like to hear from you after reviewing these two papers. I hope
this will help you understand the reason why some of your statements
are incorrect. If you believe I'm wrong, so be it.

Walt, W2DU

So would you please give me both Denny's and Owen's email addresses.

Walt

It appears neither Denny nor Owen reveal their email here, so the only
alternative is for this appeal.

73's
Richard Clark, KB7QHC

Uuuhhhh, Walt... Certainly my email in not a state secret - especially
since every person in Nigeria seems to know it!



Is ther anything I can do to help?

denny / k8do

On Mar 8, 2:19 pm, "Denny" wrote:
So would you please give me both Denny's and Owen's email addresses.

Walt

It appears neither Denny nor Owen reveal their email here, so the only
alternative is for this appeal.

73's
Richard Clark, KB7QHC

Uuuhhhh, Walt... Certainly my email in not a state secret - especially
since every person in Nigeria seems to know it!



Is ther anything I can do to help?

denny / k8do

OK, the magic munchkin tried to protect me by truncating said email
address

ad4hk2004 at yahoo com

denny

Owen,

Just returned from five days in Jacksonville, FL for spinal surgery that didn't
occur. I had cataract surgery on Feb 20, and the spinal surgeon said I needed
six weeks of recovery from the earlier surgery before he'd perform the spinal,
for fear of damaging the yet unhealed eye. So now I can get back to business as
usual for a while.

On Wed, 07 Mar 2007 23:22:28 GMT, Owen Duffy wrote:

"walt" wrote in
oups.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.

I'm familiar with the Maximum Power Transfer Theorem that appears in Everitt's
'Communication Engineering', but not with Jacobi's. Is there a difference in
their definitions?

I still believe that the 1400 ohms appearing in my paper you reviewed is the
average of the dynamic resistance of the source, because the maximum power
available for the given drive level, i.e., the 'available' power, was being
delivered when the input resistance of the pi-network was 1400 ohms, while less
than the available power was delivered when the input resistance of the network
was either greater or less than 1400 ohms. This condition conforms to the
Maximum Power Transfer Theorem as I understand it.

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.

Owen, you wouldn't believe the sensitivity of these measurements unless you
tried them.

First, measuring voltages v1 and v2 with an analog voltmeter just won't cut it.
A VM with digital readout is essential, and it must be precise to 0.1 v. Because
the delta current in the denominator is so small, even an error of 0.2 v skews
the result.

Second, reading the voltage at each load requires a few seconds for the voltage
and current to stabilize, and then the readings must be taken while the voltage
and current are stabile for at least two to three seconds. You'd be surprised
how unstable the voltage is at the 0.1 v measurement level. Even so, many
readings must be taken, first the reference, then the load, then average out the
readings.

Third, consider the breadth of the slope of the power vs load resistance curve
at the peak power point--it is broad! For example, a load resistance of +/- 10%
of the source resistance, say 55 or 45 ohms, yields a 1.11111 mismatch to the
source, for a reflection coefficient of 0.053, for a power loss of only 0.012
dB. When trying to adjust the amp loading for maximum delivery of power using an
analog meter, it's impossible to observe a change of 0.01 dB, thus when one
appears to have loaded for maximum, the source resistance can be anywhere
between 45 and 55 ohms and you'd never know just what it is. Thus, it's
practically impossible to achieve a perfect conjugate match in practice, but you
could. On the other hand, though not a perfect conjugate match, you'll have a
practical conjugate match, because the difference in power delivered is
insignificant. What I'm trying to convey is that a conjugate match is possible,
though difficult to achieve when loading the xmtr.

Consequently, I can appreciate why others have obtained results different from
mine, unless they have taken the necessary steps to overcome the sensitivity
problem of the small current number in the denominator of the load-variation
equation.

(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.

See my above comment.

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

I should have mentioned above that all of my measurements that determined a
particular source resistance were taken with constant drive level, If
source-resistance measurements are taken at any one drive level, the observed
source resistance will be equal to the load resistance if all available power
was delivered during the measurements. But if the drive level is changed without
readjusting the loading, the source resistance will also have changed. However,
I have found that for any given drive level, the measured source resistance will
equal the load resistance if the loading is adjusted so that all the power
available for that drive level is being delivered.

Just to be sure we're on the same page, let me define my understanding of
'maximum' power and 'available' power. For any given drive level there is a
maximum of power that can be delivered. I call that the 'available' power. I
consider 'maximum' power to be that which can be obtained by overloading a tube
with excessive voltage or current relative to the manufacturer's ratings.

Walt, W2DU

On Wed, 7 Mar 2007 12:08:53 -0600, (Richard Harrison) wrote:

Owen Duffy wrote:
"Breaking out of the previous thread to explore the "power explanation"
in a steady state situation:"

All OK as I see it.

Bird tells us that if you have significant standing waves, reflected
power is 10% or more of the forward power, and the ratio of reflected
power to forward power is then easily determined on the Bird Thruline
Wattmeter. Ratio of the reflected power to forward power is easily
converted to VSWR.

Bird supplies, charts, slide rules, and a formula for this conversion.

Bird confirms: "Power delivered to and dissipated in a load is given by:

Watts into load = Watts forward - Watts reflected."

Owen Duffy told us 100W is developed in 70 ohm load and the DC input
power of the transmitter is 200W.

Obviously 100W is dissipated in the transmitter and the efficiency is
50%.

Best regards, Richard Harrison, KB5WZI

Much has been said in this thread concerning whether reflected power does or does not enter the power
amplifier and cause heating of the plate. In describing below the experimental procedure that I have performed
many times in my RF Lab, I am offering proof here that such heating does not occur.

The following material from Chapter 19A of Reflections 3 is presented to show why reflected power
does not enter the amplifier and cause heating of the tube plate.

"We’ll now examine the experimental data that resulted from measurements performed
subsequent to those reported in Chapter 19, new data that provides additional evidence that a
conjugate match exists at the output terminals of an RF power amplifier when all of its
available power is delivered into its load, however complex the load impedance. According to
the definition of the conjugate match as explained earlier, if this condition prevails there is a
conjugate match. In addition, the data presented below also provides further evidence that the
output source resistance of the RF amplifier is non-dissipative. CONSEQUENTLY, THIS EVIDENCE
PROVES THAT REFLECTED POWER DOES NOT CAUSE HEATING OF THE PLATE. The following steps describe
the experimental procedure I employed and the results obtained:

1. Using a Kenwood TS-830S transceiver as the RF source, the tuning and loading of the pi-
network are adjusted to deliver all the available power into a 50 + j0-ohm load with the grid
drive adjusted to deliver the maximum of 100 watts at 4 MHz, thus establishing the area of
the RF power window at the input of the pi-network, resistance RLP at the plate, and the
slope of the load line. The output source resistance of the amplifier in this condition will
later be shown to be 50 ohms. In this condition the DC plate voltage is 800 v and plate
current is 260 ma. DC input power is therefore 800 v x 0.26 a = 208 w. Readings on the
Bird 43 wattmeter indicate 100 watts forward and zero watts reflected. (100 watts is the
maximum RF output power available at this drive level.) From here on the grid drive is left
undisturbed, and the pi-network controls are left undisturbed until Step 10.

2. The amplifier is now powered down and the load resistance RL is measured across the input
terminals of the resonant pi-network tank circuit (from plate to ground) with an HP-4815
Vector Impedance Meter. The resistance is found to be approximately 1400 ohms. Because
the amplifier was adjusted to deliver the maximum available power of 100 watts prior to the
resistance measurement, the average of the dynamic resistance RLP looking into the plate
(upstream from the network terminals) is also approximately 1400 ohms. Accordingly, a
non-reactive 1400-ohm resistor is now connected across the input terminals of the pi-network
tank circuit and output source resistance Ros is measured looking rearward into the output
terminals of the network. Resistance Ros was found to be 50 ohms.

3. Three 50-ohm dummy loads (a 1500w Bird and two Heathkit Cantennas) are now connected
in parallel to provide a purely resistive load of 16.67 ohms, and used to terminate a coax of
13.5° length at 4 MHz.

4. The impedance ZIN appearing at the input of the 13.5° length of coax at 4 MHz terminated
by the 16.67-ohm resistor of Step 3 is measured with the Vector Impedance Meter, and
found to be 20 ohms at +26°. Converting from polar to rectangular notation, Zin = 17.98 +
j8.77 ohms. (Zin = Zload from the earlier paragraphs.) This impedance is used in Steps 5
and 6 to provide the alternate load impedance in the load-variation method for determining
the complex output impedance of the amplifier, and for proving that the conjugate match
exists.

5. With respect to 50 ohms, Zin from Step 4 yields a 2.88:1 mismatch and a voltage reflection
coefficient (rho) 0.484. Therefore, power reflection coefficient (rho squared) 0.235, transmission
coefficient (1 - 0.235) = 0.766, and forward power increase factor 1/(1- 0.235) = 1/0.766 = 1.306.

6. Leaving pi-network and drive level adjustments undisturbed, the 50-ohm load is now
replaced with the coax terminated with the 16.67-ohm load from Step 4, thus changing the
load impedance from 50 ohms to 17.98 + j8.77 ohms, the input impedance Zin of the coax.

7. Due to the 2.88:1 mismatch at the load, neglecting network losses and the small change in
plate current resulting from the mismatch, approximately the same mismatch appears
between RLP and ZL at the input of the pi-network. Consequently, the change in load
impedance changed the network input resistance RL from 1400 ohms to complex ZL = 800 -
j1000 ohms, measured with the Vector Impedance Meter using the method described in Step
2. To verify the impedance measurement of ZL the phase delay of the network was
measured using an HP-8405 Vector Voltmeter and found to be 127°. Using this value of
phase delay the input impedance ZL was calculated using two different methods; one
yielding 792 - j1003 ohms, the other yielding 794.6 - j961.3 ohms, thus verifying the
accuracy of the measurement. However, because grid voltage Ec, grid drive Eg, and plate
voltage Eb are left unchanged, the average dynamic resistance RLP at the plate has remained
at approximately 1400 ohms, leaving a mismatch between RLP and ZL at the input of the pi-network.
As stated above, this value of ZL yields the substantially the same mismatch to plate resistance
RLP as that between the output impedance of the pi-network and the 17.98 + j8.77-ohm load, i.e.,
2.88:1. This mismatch at the network input results in less power delivered into the network,
and thus to the load, a decrease in the area of the RF window at the network input, and a
change in the slope of the loadline. (It must be remembered that the input and output
mismatches contribute only to mismatch loss, which does not result in power delivered and
then lost somewhere in dissipation. As we will see in Step 8, the mismatch at the input of
the pi-network results only in a reduced delivery of source power proportional to the
degree of mismatch.)

8. Readings on a Bird 43 power meter now indicate 95w forward and 20w reflected, meaning
only 75 watts are now delivered by the source and absorbed in the mismatched load. The
20w reflected power remains in the coax, and adds to the 75 watts delivered by the source to
establish the total forward power of 95w.

9. We now compare the measured power delivered with the calculated power, using the power
transmission coefficient, (1 - 0.235). The calculated power delivered is: 100w x (1 - 0.235) = 76.6w,
compared to the 75w indicated by the Bird wattmeter. However, because the new load
impedance is less than the original 50 ohms, and also reactive, the amplifier is now
overloaded and the pi-network is detuned from resonance. Consequently, the plate current
has increased from 260 to 290 ma, plate voltage has dropped to 760 v, and DC input power
has increased from 208 w to 220.4 w.

10. With the 17.98 + j8.77-ohm load still connected, the pi-network loading and tuning are
now re-adjusted to again deliver all available power with drive level setting still left
undisturbed. The readjustment of the plate tuning capacitor has increased the capacitive
reactance in the pi-network by -8.77 ohms, canceling the +8.77 ohms of inductive reactance
in the load, returning the system to resonance. The readjustment of the loading control
capacitor has decreased the output capacitive reactance, thus reducing the output resistance
from 50 to 17.98 ohms. Thus the network readjustments have decreased the output
impedance from 50 + j0 to 17.98 - j 8.77 ohms, the conjugate of the load impedance,
17.98 + j8.77 ohms. The readjustments have also returned the network input impedance ZL
to 1400 + j0 ohms (again equal to RLP), have returned the original area of the RF window at
the network input, and have returned the slope of the loadline to its original value. For
verification of the 1400-ohm network input resistance after the readjustment, ZL was again
measured using the method described in Step 2, and found it to have returned to 1400 + j0
ohms.

11. Bird 43 power meter readings following the readjustment procedure now indicate 130w
forward and 29.5w reflected, indicating 100.5w delivered to the mismatched load.

12. For comparison, the calculated power values a Forward power = 100 x 1.306 = 130.6w,
reflected power = 30.6w, and delivered power = 130.6w - 30.6w = 100w showing
substantial agreement with the measured values. (1.306 is the forward power increase factor
determined in Step 5.) Plate current has returned to its original value, 260 ma, and likewise,
plate voltage has also returned to the original value, 800 v. Consequently, the DC input
power has also returned to its original value, 208 w.

13. It is thus evident that the amplifier has returned to delivering the original power, 100 watts
into the previously mismatched complex-impedance load, now conjugately matched, the
same as when it was delivering 100 watts into the 50-ohm non-reactive load. But the
reflected power, 30.6 watts, remains in the coax, adding to the 100 watts delivered by the
amplifier to establish the 130.6 watts of forward power, proving that it does not enter the
amplifier to dissipate and heat the network or the tube.

It must be kept in mind that impedance Zin appearing at the input of the 13° line connecting
the 16.7-ohm termination to the output of the amplifier is the result of reflected waves of both
voltage and current, and thus reflected power is returning to the input of the line, and becomes
incident on the output of the amplifier.
The significance of these measurement data is that for the amplifier to deliver all of its
available power (100w) into the mismatched load impedance Zin = 17.98 + j8.77 ohms, the
readjustment of the tuning and loading of the pi-network simply changed the output
impedance of the network from 50 + j0 ohms to 17.98 - j8.77 ohms, the conjugate of the
load impedance, thus matching the output impedance of the network to the input impedance
of the coax. Consequently, there IS a conjugate match between the output of the transceiver
and its complex load. QED. The readjustments of the pi-network simply changed its
impedance transformation ratio from 50:1400 to (17.98 - j8.77):1400, returning the input
resistance RL of the pi-network to 1400 ohms, the value of RLP. Thus the plates of the amplifier
tubes are unaware of the change in external load impedance.

14. We’ll now make an additional indirect measurement of Ros that proves the conjugate
match statement above is true. Leaving the pi-network adjustments undisturbed from the
conditions in Step 10, with the amplifier powered down we again connect a 1400-ohm non-
reactive resistor across the input terminals of the pi-network tank circuit and measure the output source
impedance Zos looking rearward into the output terminals of the network. The impedance was
found to be Zos = 18 - j8 ohms.

From a practical viewpoint, measured impedance Zos = 18 - j8 ohms is the conjugate of
load impedance Zload = 17.98 + j8.77, proving that the amplifier is conjugately matched to
the load, and also proving the validity of the indirect method in determining that the source
impedance of the amplifier is the conjugate of the load impedance when all available power is
being delivered to the load.
Thus the data obtained in performing Steps 1 through 14 above proves the following four
conditions to be true:

No reflected power incident on the output of the amplifier is absorbed or dissipated in
the amplifier, because:

1. The total DC input power is the same whether the amplifier is loaded to match the resistive
Z0 load of 50 + j0 ohms, with no reflected power, or to match the complex load of 17.98 -
j8.77 ohms with 30.6 watts of reflected power, while 100 w is delivered to either the Z0 load or
the re-matched complex load.

2. All the 100 watts of power delivered by the transmitter is absorbed in both the Z0 load and
the re-matched complex load cases, with the same DC input power in both cases.

3. All the 30 watts of reflected power has been shown to add to the source power, establishing
the total 130 watts of forward power in the case involving the re-matched complex load.

4. All the reflected power is added to the source power by re-reflection from the non-
dissipative output source resistance Ros of the amplifier. Had the output source resistance of
the amplifier been dissipative the reflected power would have been dissipated there to heat,
instead of being re-reflected back into the line and adding to the source power. In addition, the
Bird 43 power meter would have indicated 75 watts of forward power, not 95. This proves that
reflected power incident on the output of the amplifier does not cause heating of the tube.

It should also be noted, an accepted alternative to the load-variation method for measuring
the output impedance of a source of RF power is the indirect method demonstrated above. As
performed during the measurements described above, the procedure for this method is to first
make the necessary loading adjustments of the output network to ensure that all of the
available power is being delivered to the load. Next, the input impedance of the load is
measured. It then follows that, as proven above, the source impedance is the conjugate of the
input impedance measured at the input of the load, because when all available power is being
delivered to the load, this condition conforms to the Conjugate Matching and the Maximum
Power-transfer Theorems.
Additionally, I previously performed this same measurement procedure using a HeathKit
HW-100 transceiver, using several different lengths of coax between the 16.7-ohm load and
the output of the transceiver in each of several measurements. The different lengths of coax
provided different complex load impedances for the transceiver during each measurement. The
same performance as described above resulted with each different load impedance, providing
further evidence that a conjugate match exists when the amplifier is delivering all of its
available power into its load. These results also prove that the single test with the Kenwood
transceiver is not simply a coincidence.

More recent experimental evidence has been presented since that of Chapter 19, adding
further proof that a conjugate match can exist when the source is an RF power amplifier, and
that the output source resistance of the amplifier is non-dissipative. It was also shown that
the average dynamic resistance RLP looking toward the plate from the network input equals
resistance RL appearing at the input of the pi-network when a conjugate match is obtained,
while contrary to Bruene’s claim, there is no requirement that RL = RS to obtain a conjugate match,
thus proving Bruene’s definition of the conjugate match appearing in his November 1991 QST
article 142 invalid.

Walt, W2DU

I wrote:
"Obviously 100W is dissipated inthe transmitter and efficiency is 50%."

This is a Class A amplifier limit but not for other classes of
amplifiers. Terman tells us on page 450 of his 1955 opus:
"The high efficiency of the Class C amplifier is a result of the fact
that plate current is not allowed to flow except when the instantaneous
voltage drop across the tube is low; i.e., Eb supplies energy to the
amplifier only when the largest portion of this energy will be absorbed
by the tuned circuit.

"Transmission Lines, Antennas, and Wave Guides" by King, Mimno, and Wing
is an excellent reference, and like Terman, the authors agree with
Walter Maxwell. On page 43 is found:
"Principal of Conjugates in Impedance Matching - If a dissipationless
network is inserted between a constant-voltage generator of impedance Zg
and a load of impedance ZR such that maximum power is delivered to the
load, at every pair of terminals the impedance looking in opposite
directions are conjugates of each other."

The real world is full of imperfections which by no means preclude
practical work.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

"Transmission Lines, Antennas, and Wave Guides" by King, Mimno, and Wing
is an excellent reference, and like Terman, the authors agree with
Walter Maxwell. On page 43 is found:
"Principal of Conjugates in Impedance Matching - If a dissipationless
network is inserted between a constant-voltage generator of impedance Zg
and a load of impedance ZR such that maximum power is delivered to the
load, at every pair of terminals the impedance looking in opposite
directions are conjugates of each other."

And can be seen clearly by looking at the reflection of a smith chart
upside down.

Best, Dan.

Dan Bloomquist wrote:
"And can be seen clearly by looking at the reflection of a Smith chart
upside down."

Clever idea! Standing on my head, peering at a Smith chart from that
perspective, did not much change my view of the R/Zo and jX/Zo circles.

I agree the Smith Chart is a marvelous way to visualize what is
happening on a transmission line.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

Dan Bloomquist wrote:
"And can be seen clearly by looking at the reflection of a Smith chart
upside down."

Clever idea! Standing on my head, peering at a Smith chart from that
perspective, did not much change my view of the R/Zo and jX/Zo circles.

You need to stand on your head _and_ use a mirror!

Otherwise, just flip the page over, top to bottom, and look at it
through the back side.

I agree the Smith Chart is a marvelous way to visualize what is
happening on a transmission line.

And a great engineering tool too.

Best regards, Richard Harrison, KB5WZI

Best, Dan, KJ6FI