Cecil Moore wrote:
wrote:

R is by definition a physical "property of conductors which depends on
dimensions, material, and temperature".


That's only one definition. From "The IEEE Dictionary",
the above is definition (A). Definition (B) is simply
"the real part of impedance" with the following Note:
"Definitions (A) and (B) are not equivalent but are
supplementary. In any case where confusion may arise,
specify definition being used."

Definition (B) covers Walt's non-dissipative resistance.
A common example is the characteristic impedance of
transmission line. In an ideal matched system V^2/Z0, I^2*Z0,
or V*I is the power being transferred under non-dissipative
conditions.

Yes. I agree with that, Cecil. But that's not the claim to which I
responded.

73, ac6xg

Owen Duffy wrote:
"Richard stated "It produces no significant harmonics, so the system is
linear." It is that with which I disagree."

A clear statement. Congratulations. Too bad it is wrong.

Terman wrote:
"Amplitude distortion exists when the modulation envelope contains
frequency components not present in the modulating signal."

It is also true that absence of of harmonics is proof of linearity, as
in my microwave monitoring system alarm. No alarm, a linear system. An
alarm, a nonlinear system. I agree with Terman.

I challenge you to prove a mistake in Terman`s writings.

Best regards, Richard Harrison, KB5WZI

(Richard Harrison) wrote in news:20731-
:

Owen Duffy wrote:
"Richard stated "It produces no significant harmonics, so the system is
linear." It is that with which I disagree."

A clear statement. Congratulations. Too bad it is wrong.

Terman wrote:
"Amplitude distortion exists when the modulation envelope contains
frequency components not present in the modulating signal."

Fine.

It is also true that absence of of harmonics is proof of linearity,

That is not a logical implication of your quote from Terman, it is
entirely your statement, and without splitting hairs over the absolute
meaning of 'absence', it is wrong when applied to a Class C amplifier
with pure sine wave excitation and a resonant load.

The converse is not logically equivalent to the original.

...
I challenge you to prove a mistake in Terman`s writings.

I have no problems with the statement you attribute to Terman and haven't
said anything contrary to that during the discussion.

Richard, I accept that you are committed to your view, lets leave it at
that. I don't think your statements on the matter support Walt's
proposition, rather since they are in my view flawed, I think they weaken
the body of evidence.

Owen

"Owen Duffy" wrote in message
...
(Richard Harrison) wrote in news:20731-
:

Owen Duffy wrote:
"Richard stated "It produces no significant harmonics, so the system is
linear." It is that with which I disagree."

A clear statement. Congratulations. Too bad it is wrong.

Terman wrote:
"Amplitude distortion exists when the modulation envelope contains
frequency components not present in the modulating signal."

Fine.

It is also true that absence of of harmonics is proof of linearity,

That is not a logical implication of your quote from Terman, it is
entirely your statement, and without splitting hairs over the absolute
meaning of 'absence', it is wrong when applied to a Class C amplifier
with pure sine wave excitation and a resonant load.

The converse is not logically equivalent to the original.

...
I challenge you to prove a mistake in Terman`s writings.

I have no problems with the statement you attribute to Terman and haven't
said anything contrary to that during the discussion.

Richard, I accept that you are committed to your view, lets leave it at
that. I don't think your statements on the matter support Walt's
proposition, rather since they are in my view flawed, I think they weaken
the body of evidence.

Owen

Owen, as I view your last paragraph above it seems apparent that you do not
believe Richard's and my position that the output of a Class C amplifier can be
linear. We're talking about at the 'output', not the 'thruput'. How can you
refute the evidence of a nearly pure sine wave at the output terminals of the
pi-network?

Walt, W2DU

"Owen Duffy" wrote in message
...
(Richard Harrison) wrote in news:20731-
:

Owen Duffy wrote:
"Richard stated "It produces no significant harmonics, so the system is
linear." It is that with which I disagree."

A clear statement. Congratulations. Too bad it is wrong.

Terman wrote:
"Amplitude distortion exists when the modulation envelope contains
frequency components not present in the modulating signal."

Fine.

It is also true that absence of of harmonics is proof of linearity,

That is not a logical implication of your quote from Terman, it is
entirely your statement, and without splitting hairs over the absolute
meaning of 'absence', it is wrong when applied to a Class C amplifier
with pure sine wave excitation and a resonant load.

The converse is not logically equivalent to the original.

...
I challenge you to prove a mistake in Terman`s writings.

I have no problems with the statement you attribute to Terman and haven't
said anything contrary to that during the discussion.

Richard, I accept that you are committed to your view, lets leave it at
that. I don't think your statements on the matter support Walt's
proposition, rather since they are in my view flawed, I think they weaken
the body of evidence.

Owen

Owen, as I view your last paragraph above it seems apparent that you do not
believe Richard's and my position that the output of a Class C amplifier can be
linear. We're talking about at the 'output', not the 'thruput'. How can you
refute the evidence of a nearly pure sine wave at the output terminals of the
pi-network?

Walt, W2DU

"Walter Maxwell" wrote in
:
....
Owen, as I view your last paragraph above it seems apparent that you
do not believe Richard's and my position that the output of a Class C
amplifier can be linear. We're talking about at the 'output', not the
'thruput'. How can you refute the evidence of a nearly pure sine wave
at the output terminals of the pi-network?

Walt, you have posted this twice.

There are subtle word shifts here, you are saying "a Class C
amplifier can be linear" rather than is (always) linear.

It is true that a Class C amplifier with resonant load and a constant
amplitude sine wave drive may appear linear when comparing Vout to Vin.

But, as I explained earlier, if you vary the drive amplitude, it is
clearly not linear... in typical cases output will cease below about 25%
of the drive level required for maximum output.

Further, if you drive it with a complex waveform, it is clearly non
linear at any drive level.

Richard's solution to detecting RF PA distortion by monitoring harmonics
is an interesting one, because it suffers the disadvantage of output
filtering masking the harmonics (unless the monitor point was prior to
filtering).

The most widely accepted test for linearity (Vout/Vin) of an RF PA is the
'two tone test', where the drive is a complex waveform (the sum of two
equal amplitude sine waves quite close in frequency) and at least some of
the distortion products due to third order and fifth order etc transfer
terms appears in-band in the output after all output filtering, and where
they can be reliably compared in amplitude to the desired signals. A
Class C RF PA will not appear to be linear under such a test at any drive
level.

I suspect that the issue of transfer linearity is a red herring to your
proposition about the Thevenin equivalent of an RF PA, but if you do
depend on arguing that the transfer characteristic of a Class C RF PA is
linear, I think you are on shaky ground.

Owen

"Owen Duffy" wrote in message
...
"Walter Maxwell" wrote in
:
...
Owen, as I view your last paragraph above it seems apparent that you
do not believe Richard's and my position that the output of a Class C
amplifier can be linear. We're talking about at the 'output', not the
'thruput'. How can you refute the evidence of a nearly pure sine wave
at the output terminals of the pi-network?

Walt, you have posted this twice.

There are subtle word shifts here, you are saying "a Class C
amplifier can be linear" rather than is (always) linear.

It is true that a Class C amplifier with resonant load and a constant
amplitude sine wave drive may appear linear when comparing Vout to Vin.

Owen, with a Class C amplifier biased beyond cutoff the grid is never going to
see a constant amplitude sine wave, even if the constant amplitude sine wave
were impressed on the grid. How then can the transfer linearity ever occur under
these conditions? I maintain that it cannot.

But, as I explained earlier, if you vary the drive amplitude, it is
clearly not linear... in typical cases output will cease below about 25%
of the drive level required for maximum output.

Further, if you drive it with a complex waveform, it is clearly non
linear at any drive level.

Richard's solution to detecting RF PA distortion by monitoring harmonics
is an interesting one, because it suffers the disadvantage of output
filtering masking the harmonics (unless the monitor point was prior to
filtering).

The most widely accepted test for linearity (Vout/Vin) of an RF PA is the
'two tone test', where the drive is a complex waveform (the sum of two
equal amplitude sine waves quite close in frequency) and at least some of
the distortion products due to third order and fifth order etc transfer
terms appears in-band in the output after all output filtering, and where
they can be reliably compared in amplitude to the desired signals. A
Class C RF PA will not appear to be linear under such a test at any drive
level.

I suspect that the issue of transfer linearity is a red herring to your
proposition about the Thevenin equivalent of an RF PA, but if you do
depend on arguing that the transfer characteristic of a Class C RF PA is
linear, I think you are on shaky ground.

Owen

Owen, you are either twisting my words, or you're not listening. I've made it
very clear that I'm NOT talking about 'transfer linearity', and never have. My
position is only that the OUTPUT of the pi-network is linear. The linearity at
the output is irrelevant to the waveform at the input of the tank circuit in
Class C amplifiers. I don't even understand why the discussion concerning
'transfer linearity' with respect to Class C amplifiers should have come up.

Walt, W2DU

PS--I didn't send two identical emails--something must have happened at the
server to have caused it.

Owen Duffy wrote:
"Richard, I accept that you are committed to your view. Let`s leave it
at that."

Owen is "throwing in the towel' but not admitting error.

I have no allegiance to a particular view. I am happy to view things
from another`s perspective. Owen mught do the same.

Owen Duffy also wrote:
"I understand your position to be that the behavior of a tank circuit is
independent of the transfer linearity of the active device...but
asserting that things are linear because there are no harmonics is wrong
and saying so is no support for your argument."

Owen has it wrong. The final amplifier is linear because its output is
an exact replica of its input except for amplitude, or close enough so.

When the waveshape of the output signal from an amplifier varies in any
respect other than amplitude from the waveshape of the signal feeding
the amplifier, the amplifier is distorting the signal.

Sinewave a-c is considered the perfect waveform. It consists of a single
frequency. Any other waveform consists of more than one frequency, So
the presence or absence of harmonics in addition to the fundamental is a
clear indication of distortion. Anyone can confirm waveform using an
oscilloscope.

Best regards, Richard Harrison, KB5WZI

Owen Duffy wrote:


The most widely accepted test for linearity (Vout/Vin) of an RF PA is the
'two tone test', where the drive is a complex waveform (the sum of two
equal amplitude sine waves quite close in frequency) and at least some of
the distortion products due to third order and fifth order etc transfer
terms appears in-band in the output after all output filtering, and where
they can be reliably compared in amplitude to the desired signals. A
Class C RF PA will not appear to be linear under such a test at any drive
level.

Actually, in modern systems with very complex signals, there are more
meaningful tests like noise power ratio with a notch that look for
spectral regrowth. The two tone test has the advantage of being
moderately easy to perform for middling performance amplifiers/devices.
But if you're looking for very high performance, such things as
generating the two tones without one generator interfering with the
other get to be challenging.



I suspect that the issue of transfer linearity is a red herring to your
proposition about the Thevenin equivalent of an RF PA, but if you do
depend on arguing that the transfer characteristic of a Class C RF PA is
linear, I think you are on shaky ground.

I don't know that the concept of a Thevenin equivalent (a linear circuit
theory concept) really has applicability to "box level" models, except
over a very restricted range, where one can wave one's hands and ignore
the nonlinearities as irrelevant to the question at issue. Sure, over a
restricted dynamic range and bandwidth and restricted class of input
signals, a Class C (or class E or Class F or E/F1, or a fancy EER
system) can be adequately modeled as a linear ideal amplifier.


The real question is what is the value of that model. If the model
provides conceptual understanding of some underlying problem, great. For
instance, it might help with a link budget. If the model helps design a
better amplifier, great. The model might allow prediction of behavior;
so that you can, for instance, detect a fault by the difference between
model and actual observation, as Richard mentioned with the harmonic
energy detector.




Owen

On Tue, 17 Jun 2008 17:08:12 -0500, (Richard
Harrison) wrote:

Owen has it wrong. The final amplifier is linear because its output is
an exact replica of its input except for amplitude, or close enough so.

Hi Richard,

This is a presumption that is either not in evidence, or it is forced
by the necessity of your argument. Consider:

When the waveshape of the output signal from an amplifier varies in any
respect other than amplitude from the waveshape of the signal feeding
the amplifier, the amplifier is distorting the signal.

The presumption (forced, or otherwise) is that the input is
sinusoidal. In fact, the cathode current of the amplifier proves
quite positively that only a pulse in, 120 degrees of the sinewave, or
even less, is sufficient to generate a remarkably clean sinewave at
the final's output.

Simply put, a pulse with a 33% duty cycle, and having sufficient
amplitude (and steep skirts) would present an output that was wholly
non-linear in relation to the pulse excitation. Looking only at the
output, you couldn't possibly say if the input was a complete 360
degrees of sine wave, or 33% DC of a rectangular wave. Not unless new
constraints are added that push the argument away from current issues.

To extend an analogy, the circular motion of the car's wheels prove
there is a non-linear relationship to the explosion of the gas mixture
in the compression cylinder.

Or to further decimate the argument, an oscillator produces as pure a
signal to no input at all (barring the excitation of noise that
engenders a selectively reinforced oscillation).

But the debate over linearity is window dressing to answering the
practical question:
What is the source resistance of any power amplifier?

I am not interested in the values that are NOT the source resistance.
I am content that those who have not responded to this specific and
observable characteristic don't know. However, given the thrashing of
this topic, someone (besides me) should.

73's
Richard Clark, KB7QHC