"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.