On Sat, 14 Jun 2008 09:40:26 -0700 (PDT),
wrote:

On Jun 14, 8:46*am, "Walter Maxwell" wrote:

I don't understand how my statement in the email above indicates that I^2*R and
V*R could be zero. The simple ratio of E/I is not zero, yet it defines a
resistance that is non-dissipative because a ratio cannot dissipate power.

Walt

Hi Walt -

If E and I are not zero, then E*I is not zero. But you are correct
that the equations themselves do not dissipate power. :-) Resistors
do, however. If there isn't an actual resistor located where you make
your measurement, then of course there's no power being dissipated
there.

Hi All,

It has taken considerable restraint not to ask some pointed questions:

1. Is a metal wire wound resistor NOT a resistance because it is not
carbon?

2. Is a carbon resistor NOT a resistance because it is not metal
wire-wound?

3. Is a Tube NOT a resistance because it contains no metal?

4. Is a Tube NOT a resistance because it contains no carbon?

5. Is a cathode resistor NOT a resistance when the tube conduction is
zero?

6. Is that same cathode resistor NOT a resistance because it conducts
non-linearly for some speciously constrained (and myopically chosen)
incomplete cycle of time?

finally, and possibly the only compelling logic that seems to flow
from this thread:

7. Is a Tube NOT a resistance simply because it lacks the familiar
shape of an axial lead resistor? (Or, rather, that a familiar axial
lead resistor cannot be found soldered between cathode and plate
within the vacuum?)

I have offered a spectrum of questions guaranteed to be accessible to
the buffet style of responding to cosmetic issues instead of
substance.

As this is all Rhetoric, I will take the author's prerogative to
short-cut the anticipated sputterings of denial, condemnation,
damnation, and outrage.

1. 2. 3. and 4. Carbon is a metal.

3. and 4. Plate dissipation bears scant relation to Ohmic Loss. And
yet there is heat there that is correlatably and causally related to
match, loss, and drive - from any "source."

4. there are many power tubes with Graphite (carbon) plates. The
original 813B comes to mind. Some power tubes have their screen grids
graphite (carbon) coated too! (Ohm's law still does not appreciably
account for plate dissipation.)

5. and 6. are sucker bait for those who would prove the world is
non-linear because of the discontinuity at the time of the big-bang
(or creation, take your pick).

7. Is, as I intimated, the implicit populist choice (masked as a
question) for those who cannot say what the source resistance IS, but
are over fulsome by half to say what it is NOT.

Describing what source resistance is NOT is like moving the stacks of
brass disks between the Towers of Hanoi. You can do that forever
without really coming to any conclusion. Given the length of many
threads that imitate this behavior, its popularity marks its less than
stupendous insights. But lest I interrupt the modern interpretation
of that game as it is played here, I would point out that parsing
"ratio" is even more funny. It sure beats Brett dragging the cesspool
for newspaper reports of cures for cancer.

-Phew-

73's
Richard Clark, KB7QHC

"Walter Maxwell" wrote in
:


"Owen Duffy" wrote in message
...
(Richard Harrison) wrote in news:23000-
:

Jim Lux wrote:
"in a linear system"

It produces no significant harmonics, so the system is linear.

That is a new / unconventional definition of 'linear'.

The term is usually used in this context to mean a linear transfer
characteristic, ie PowerOut vs PowerIn is linear.

Considering a typical valve Class C RF amplifier with a resonant
load:

Conduction angle will typically be around 120°, and to achieve that,
the grid bias would be around twice the cutoff voltage.

If you attempted to pass a signal such as SSB though a Class C
amplifier that was biased to twice the cutoff value, there would be
no output signal when the peak input was less than about 50% max
drive voltage, or about 25% power, and for greater drive voltage
there would be output. How could such a transfer characteristic be
argued to be linear?

Owen

Owen, 'linear transfer characteristic' isn't the only context for the
use of the word 'linear'. Even though the input circuit of a Class C
amplifier is non-linear, the output is linear due to the energy
storage of the tank circuit that isolates the input from the output,
therefore, the output is linear. Proof of this is that the output
signal is a sine wave. In addition, the voltage and current at the
output terminals of the pi-network are in phase. Furthermore, the
ratio E/I = R appearing at the network output indicates that the
output source resistance R is non-dissipative, because a ratio cannot
dissipate power. This resistance R is not a resistor.

Hi Walt,

A few issues....

Yes, I understand the context in which you mean linear (though I have
issues with your proposition)... but my comment was referring to the
assertion that 'no harmonics' relates to linear operation which seems to
me to refer to the transfer characteristic linearity context.

I do have issue with your stated 'proof'. Firstly, I must qualify that we
are talking steady state... the mention of resonant loads means we are in
the frequency domain. Whilst it might seem that the tank circuit / pi
coupler / whatever is just a network of passive parts and they are all
linear, the energy that is supplied to that circuit in each cycle depends
on the resonant load impedance and traditional PA design methods suggest
that that Eout/Iout relationship is not linear for changes in load Z,
although it might be approximately linear over a small range.

I recognise a distinction between resistance (the ratio of E/I) and a
resistor (one type of component that exhibits resistance)... but I would
not claim that resistance is just a 'ratio' because it implies it is a
dimensionless ratio.

Owen

Walter Maxwell wrote:
"Alan Peake" wrote in message

Alan, I disagree with you when you say that 'voltage to current' is not a ratio.
IMHO, your are definine 'ratio' to narrowly. Below is a quote from Google:
.............

Well, someone has redefined "ratio" since I went to school. My old maths
text book says "The term ratio is used when we wish to compare the size
ofr magnitude of two quantities (or numbers) of the same kind, i.e.,
expressed in the same units, and is measured by a fraction"
All my dictionaries say much the same thing. There is no mention of
comparing quantities of different units. That to me would be like
comparing apples with oranges.

Alan

Richard Harrison wrote:

Some people are persuaded that resistance = loss. Not so at all.
Resistance is just a name given to the ratio of voltage to current.

If you define resistance as simply V/I with no regard to phase, then
what you say is true but if V and I aren't in phase then you have
impedance consisting of real and imaginary components - resistance AND
reactance.

Free-space has a lossless Zo of 120 pi (or 377 ohms) according to page
326 of Saveskie`s "Radio Propagation Handbook". This is a ratio which is
related to volts and amps but is actually the ratio of the electric
field strength to the magnetic field strength in an EM wave. The volts
and amps are in phase so it has the units of a pure resistance.

I suppose you could also say that a real resistor is also lossless as
the heat due to I*I*R is radiated into space and thus is not lost
Alan

I found a note I intended to post but don`t see it so I suppose it was
lost in cyberspace somewhere. I was responding to Owen Duffy.

Owen wrote:
"How could such a transfer characteristic be argued to be linear?"

I responded:
Conditioning.

Class C amplifiers are used lawfully in great abundance. That is proof
enough that they are relatively free from distortion. Pulses in plate
current don`t prevent the output of the Class C amplifier from becoming
a pure sinusoid. Just as an internal combustion engine uses an almost
endless string of exlosions in its cylinders to produce a smooth uniform
rotation of its crankshaft and flywheel, the Class C amplifier uses an
almost endless series of pulses to produce a smooth sinusoid.

I will quote B. Whitfield Griffith, Jr., Principal Engineer (retired) at
Continental Electronics, Dallas Texas, builder of many of the world`s
most powerful radio transmitters. Griffith says on page 500 of
"Radio-Electronic Transmission Fundamentals", that it is important where
you couple the load to the Class C amplifier:
"Figure 56-2 shows how the class C amplifier might look in a typical
arrangement. Many refinements of the circuit, which are necessary for
practical reasons, are omitted here, since we are concerned only with
the fundamental principles of its operation at this time. The plate load
impedance consists of a tank circuit of a type similar ro that of Fig.
15-5; the difference is that the load resistor is in series with the
inductance rather than the capacitance. This is the preferred
arrangement, because the harmonic components of the plate current all
have frequencies higher than the fundamental and quite naturally tend to
follow the capacitive branch of the circuit. By extracting power from
the inductive branch, therefore we can expect to find less harmonic
energy in the output than would be present if we loaded the capacitive
branch. This load resistance may be an actual resistor, if we wish to
feed the output of this amplifier into a dummy load for measurement
purposes, or it may be the input resistance presented by some type of
impedance-matching network so arranged that the loading of the amplifier
can readily be varied. Another common method is to couple resistance
effectively into the tank inductance by means of the mutual inductance
between the tank and a secondary coil which is coupled to it
magnetically, where resistive loads appear in the secondary circuit.

There is also shown in Fig. 56-2 the r-f waveform of voltage and current
which we would expect to find at various points in the amplifier
circuit. No allowance is made in these illustrations for the differences
in potentials of various portions of the circuit; these diagrams are
merely representative of the behavior of the r-f potentials and
currents. Notice particularly that the r-f plate voltage is 180 degrees
out of phase with the r-f grid voltage. The reason for this is easily
understood. When the grid is its at its most positive potential, the
plate current is at its maximum. As the plate current is drawn through
the load impedance, the increase in plate current causes a corresponding
reduction in plate voltage. The plate voltage therefore swings downward
at the moment the grid voltage swings upward. We also see that the
current in the load resistor is lagging the r-f plate voltage by an
angle of a little less than 90 degrees. Correct operation of the tank
circuit requires that the resistance of this load resistor be much
smaller than the reactance of the coil."

Best regards, Richard Harrison, KB5WZI

"Richard Harrison" wrote in message
...
I found a note I intended to post but don`t see it so I suppose it was
lost in cyberspace somewhere. I was responding to Owen Duffy.

Owen wrote:
"How could such a transfer characteristic be argued to be linear?"

I responded:
Conditioning.

Class C amplifiers are used lawfully in great abundance. That is proof
enough that they are relatively free from distortion. Pulses in plate
current don`t prevent the output of the Class C amplifier from becoming
a pure sinusoid. Just as an internal combustion engine uses an almost
endless string of exlosions in its cylinders to produce a smooth uniform
rotation of its crankshaft and flywheel, the Class C amplifier uses an
almost endless series of pulses to produce a smooth sinusoid.

I will quote B. Whitfield Griffith, Jr., Principal Engineer (retired) at
Continental Electronics, Dallas Texas, builder of many of the world`s
most powerful radio transmitters. Griffith says on page 500 of
"Radio-Electronic Transmission Fundamentals", that it is important where
you couple the load to the Class C amplifier:
"Figure 56-2 shows how the class C amplifier might look in a typical
arrangement. Many refinements of the circuit, which are necessary for
practical reasons, are omitted here, since we are concerned only with
the fundamental principles of its operation at this time. The plate load
impedance consists of a tank circuit of a type similar ro that of Fig.
15-5; the difference is that the load resistor is in series with the
inductance rather than the capacitance. This is the preferred
arrangement, because the harmonic components of the plate current all
have frequencies higher than the fundamental and quite naturally tend to
follow the capacitive branch of the circuit. By extracting power from
the inductive branch, therefore we can expect to find less harmonic
energy in the output than would be present if we loaded the capacitive
branch. This load resistance may be an actual resistor, if we wish to
feed the output of this amplifier into a dummy load for measurement
purposes, or it may be the input resistance presented by some type of
impedance-matching network so arranged that the loading of the amplifier
can readily be varied. Another common method is to couple resistance
effectively into the tank inductance by means of the mutual inductance
between the tank and a secondary coil which is coupled to it
magnetically, where resistive loads appear in the secondary circuit.

There is also shown in Fig. 56-2 the r-f waveform of voltage and current
which we would expect to find at various points in the amplifier
circuit. No allowance is made in these illustrations for the differences
in potentials of various portions of the circuit; these diagrams are
merely representative of the behavior of the r-f potentials and
currents. Notice particularly that the r-f plate voltage is 180 degrees
out of phase with the r-f grid voltage. The reason for this is easily
understood. When the grid is its at its most positive potential, the
plate current is at its maximum. As the plate current is drawn through
the load impedance, the increase in plate current causes a corresponding
reduction in plate voltage. The plate voltage therefore swings downward
at the moment the grid voltage swings upward. We also see that the
current in the load resistor is lagging the r-f plate voltage by an
angle of a little less than 90 degrees. Correct operation of the tank
circuit requires that the resistance of this load resistor be much
smaller than the reactance of the coil."

Best regards, Richard Harrison, KB5WZI

Richard, I thoroughly enjoyed reading your post above on the analogy between the
action of the energy storage of the tank circuit and that of a automobile
engine, so I'd like you to read a portion of Chapter 19 from Reflections 2 to
see how I approached the same analogy for the book that I quote below:

Therefore, the pi-network must be designed to provide the equivalent
optimum resistance RL looking into the input for whatever load terminates the
output. The current pulses flowing into the network deliver bursts of electrical
energy to the network periodically, in the same manner as the spring-loaded
escapement mechanism in the pendulum clock delivers mechanical energy
periodically to the swing of the pendulum. In a similar manner, after each plate
current pulse enters the pi-network tank curcuit, the flywheel effect of the
resonant tank circuit stores the electromagnetic energy delivered by the current
pulse, and thus maintains a continuous sinusoidal flow of current throughout the
tank, in the same manner as the pendulum swings continuously and periodically
after each thrust from the escapement mechanism. The continuous swing of the
pendulum results from the inertia of the weight at the end of the pendulum, due
to the energy stored in the weight. The path inscribed by the motion of the
pendulum is a sine wave, the same as at the output of the amplifier. We will
continue the discussion of the flywheel effect in the tank circuit with a more
in-depth examination later.

.....

We now return to conduct a close examination of the vitally important
flywheel effect of the tank circuit. The energy storage (Q) in the tank produces
the flywheel effect that isolates the nonlinear pulsed energy entering the tank
at the input from the smoothed energy delivered at the output. As a result of
this isolation the energy delivered at the output is a smooth sine wave, with
linear voltage/current characteristics that support the theorems generally
restricted to linear operation. We know that the widely varying voltage/current
relationship at the tank input results in widely varying impedances, which
precludes the possibility of a conjugate match at the input of the tank circuit.
However, the energy stored in the tank provides constant impedance at the output
that supports both the Conjugate Matching and the Maximum Power-transfer
Theorems.1

The acceptance by many engineers and amateurs of the notion that the output
of the RF tank is nonlinear is a reason some readers will have difficulty in
appreciating that the output of the RF tank circuit is linear, and can thus
support the conjugate match. Valid analogies between different disciplines are
often helpful in clarifying difficulties in appreciating certain aspects of a
particular discipline. Fortunately, energy storage in the mechanical discipline
has a valid and rigorous analogous relationship with energy storage in LC
circuitry that makes it appropriate to draw upon a mechanical example to clarify
the effect of energy storage in the RF tank circuit. (A further convincing
analogy involving water appears later in the Chapter, in which the origin of the
term 'tank circuit' is revealed.)

The smoothing action of the RF energy stored in the tank circuit is
rigorously analogous to the smoothing action of the energy stored in the
flywheel in the automobile engine. In the automobile engine the flywheel smooths
the pulses of energy delivered to the crankshaft by the thrust of the pistons.
As in the tank circuit of the amplifier, the automobile flywheel is an energy
storage device, and the smoothing of the energy pulses from the pistons is
achieved by the energy stored in the flywheel. In effect, it is the flywheel
that delivers the energy to the transmission. The energy storage capacity
required of the flywheel to deliver smooth energy to the transmission is
determined by the number of piston pulses per revolution of the crankshaft. The
greater the number of pistons, the less storage capacity is required to achieve
a specified level of smoothness in the energy delivered by the flywheel. The
storage capacity of the flywheel is determined by its moment of inertia, and the
storage capacity of the tank circuit in the RF amplifier is determined by its Q.

(Richard Harrison) wrote in news:26406-
:

....
Class C amplifiers are used lawfully in great abundance. That is proof
enough that they are relatively free from distortion. Pulses in plate
current don`t prevent the output of the Class C amplifier from becoming
a pure sinusoid.

.... a very long dissertation on Class C amplifiers snipped.

Richard, analysis of the Class C amplifier excited with a constant
amplitude single frequency sine wave is revealing about their transfer
linearity.

I do not disagree that a Class C amplifier excited with a constant
amplitude single frequency sine wave driving a resonant load produces a
low distortion constant amplitude single frequency sine wave output.

But the absence of harmonic distortion in such an amplifier is not
evidence that the amplifier transfer characteristic is linear. You may be
able to use harmonic distortion to detect non-linearity in, for example,
audio amplifiers... but not in RF amplifiers with a resonant load... for
the reasons set out in your quotation.

A Class C amplifier is unsuited to amplfying SSB telephony because it is
manifestly non-linear. In fact, a Class C amplifier is so non-linear that
it is well suited to use as a relatively efficient harmonic multiplier.

Class B and AB RF amplifiers are extremely sensitive to non-linearity in
the region near cut-off and must have sufficient idle current in every
active device (which means conduction ange is 180°) so that distortion
products are sufficiently low. This means that the theoretical conduction
angle of 180° for Class B is just not realisable because of distortion,
much less 120°.

Owen

"Owen Duffy" wrote in message
...
(Richard Harrison) wrote in news:26406-
:

...
Class C amplifiers are used lawfully in great abundance. That is proof
enough that they are relatively free from distortion. Pulses in plate
current don`t prevent the output of the Class C amplifier from becoming
a pure sinusoid.

... a very long dissertation on Class C amplifiers snipped.

Richard, analysis of the Class C amplifier excited with a constant
amplitude single frequency sine wave is revealing about their transfer
linearity.

I do not disagree that a Class C amplifier excited with a constant
amplitude single frequency sine wave driving a resonant load produces a
low distortion constant amplitude single frequency sine wave output.

But the absence of harmonic distortion in such an amplifier is not
evidence that the amplifier transfer characteristic is linear. You may be
able to use harmonic distortion to detect non-linearity in, for example,
audio amplifiers... but not in RF amplifiers with a resonant load... for
the reasons set out in your quotation.

A Class C amplifier is unsuited to amplfying SSB telephony because it is
manifestly non-linear. In fact, a Class C amplifier is so non-linear that
it is well suited to use as a relatively efficient harmonic multiplier.

Class B and AB RF amplifiers are extremely sensitive to non-linearity in
the region near cut-off and must have sufficient idle current in every
active device (which means conduction ange is 180°) so that distortion
products are sufficiently low. This means that the theoretical conduction
angle of 180° for Class B is just not realisable because of distortion,
much less 120°.

Owen

Sorry about the 'long dissertation on Class C amps', Owen, but I thought it
appropriate to include it in view of Richard's similar discussion on the
automotive engine analogy to the RF tank circuit. I'll try to keep my comments
shorter from now on.

Walt, W2DU

"Owen Duffy" wrote in message
...
(Richard Harrison) wrote in news:26406-
:

...
Class C amplifiers are used lawfully in great abundance. That is proof
enough that they are relatively free from distortion. Pulses in plate
current don`t prevent the output of the Class C amplifier from becoming
a pure sinusoid.

... a very long dissertation on Class C amplifiers snipped.

Richard, analysis of the Class C amplifier excited with a constant
amplitude single frequency sine wave is revealing about their transfer
linearity.

I do not disagree that a Class C amplifier excited with a constant
amplitude single frequency sine wave driving a resonant load produces a
low distortion constant amplitude single frequency sine wave output.

But the absence of harmonic distortion in such an amplifier is not
evidence that the amplifier transfer characteristic is linear. You may be
able to use harmonic distortion to detect non-linearity in, for example,
audio amplifiers... but not in RF amplifiers with a resonant load... for
the reasons set out in your quotation.

A Class C amplifier is unsuited to amplfying SSB telephony because it is
manifestly non-linear. In fact, a Class C amplifier is so non-linear that
it is well suited to use as a relatively efficient harmonic multiplier.

Class B and AB RF amplifiers are extremely sensitive to non-linearity in
the region near cut-off and must have sufficient idle current in every
active device (which means conduction ange is 180°) so that distortion
products are sufficiently low. This means that the theoretical conduction
angle of 180° for Class B is just not realisable because of distortion,
much less 120°.

Owen

Sorry about the 'long dissertation on Class C amps', Owen, but I thought it
appropriate to include it in view of Richard's similar discussion on the
automotive engine analogy to the RF tank circuit. I'll try to keep my comments
shorter from now on.

Walt, W2DU

"Walter Maxwell" wrote in
:

Sorry about the 'long dissertation on Class C amps', Owen, but I
thought it appropriate to include it in view of Richard's similar
discussion on the automotive engine analogy to the RF tank circuit.
I'll try to keep my comments shorter from now on.

Walt, it wasn't so much that it was long, but it was long and for all
that was said, it didn't address the linearity issue.

I understand your position to be that the behaviour of the 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 being so, is no support for your argument.

I am wary of analogies, the switch analogy that was raised is not a good
approximation and I haven't even thought about the car engine.

I am genuinely insterested in your argument. I don't accept it (yet?) as
you know, and I have spent some time over the last 18 months or so
exploring the concept you describe.

Fundamentally, I am trying to reconcile what you say with the techniques
commonly accepted for designing such a PA. Those design techniques give
us a method of predicting power output at different load impedances, and
the E/I characteristic for different loads is not always a straight line
(as it would be if a Thevenin equivalent circuit exists), though it might
appear fairly straight over a narrow domain. Since working from
characteristic curves is so prone to error, my modelling has been based
on an idealised triode transfer characteristic, but with similar
behaviour to an 811A. The analysis is waiting for me to build the
analytical equations for the negative feedback due to cathode
degeneration in a grounded grid configuration. I need to apply more time
to it, and the revived discussion might focus me for a bit!

Owen