On Jun 3, 10:39*am, Richard Clark wrote:
On Thu, 3 Jun 2010 04:59:24 -0700 (PDT), Keith Dysart

wrote:
But what exactly do you mean by 'real'?
R=V/I?
R=deltaV/deltaI?
Heat is dissipated?

Hi Keith,

As demonstrated by Walt's data.

73's
Richard Clark, KB7QHC

Richard, you ask me where to begin. Well, I begin with Terman, where I
quote him in Chapter 19, Sec 19.3, in Reflections 2. Since attachments
are prohibited in this forum I'm going to try to copy Sec 19.3 here,
which explains in detail why plate resistance Rpd is dissipative,
while Rp is non-dissipative--it explains the difference between the
two. In addition, I don't believe the diode is a correct model for
describing the operation of a Class B or C amplifier. Now the quote:

Sec 19.3 Analysis of the Class C Amplifier

The following discussion of the Class C amplifier, which reveals
why the portion of the source resistance related to the
characteristics of the load line is non-dissipative, is based on
statements appearing in Terman’s Radio Engineers Handbook, 1943 ed.,
Page 445, and on Terman’s example of Class C amplifier design data
appearing on Page 449. Because the arguments presented in Terman’s
statements are vital to understanding the concept under discussion, I
quote them here for convenience: (Parentheses and emphasis mine)

1. The average of the pulses of current flowing to an
electrode represents the direct current drawn by that electrode.
2. The power input to the plate electrode of the tube at any
instant is the product of plate-supply voltage and instantaneous plate
current.
3. The corresponding power (Pd) lost at the plate is the product
of instantaneous plate-cathode voltage and instantaneous plate
current.
4. The difference between the two quantities obtained from items
2 and 3 represents the useful output at the moment.
5. The average input, output, and loss are obtained by averaging
the instantaneous powers.
6. The efficiency is the ratio of average output to average
input and is commonly of the order of 60 to 80 percent.
7. The efficiency is high in a Class C amplifier because
current is permitted to flow only when most of the plate-supply
voltage is used as voltage drop across the tuned load circuit RL, and
only a small fraction is wasted as voltage drop (across Rpd) at the
plate electrode of the tube.

Based on these statements the discussion and the data in
Terman’s example that follow explain why the amplifier can deliver
power with efficiencies greater than 50 percent while conjugately
matched to its load, a condition that is widely disputed because of
the incorrect assumptions concerning Class B and C amplifier operation
as noted above. The terminology and data in the example are Terman’s,
but I have added one calculation to Terman’s data to emphasize a
parameter that is vital to understanding how a conjugate match can
exist when the efficiency is greater than 50 percent. That parameter
is dissipative plate resistance Rpd. (As stated earlier, dissipative
resistance Rpd should not be confused with non-dissipative plate
resistance Rp of amplifiers operating in Class A, derived from the
expression Rp = delta Ep/delta Ip.)
It is evident from Terman that the power supplied to the
amplifier by the DC power supply goes to only two places, the RF power
delivered to load resistance RL at the input of the pi-network, and
the power dissipated as heat in dissipative plate resistance Rpd
(again, not plate resistance Rp, which is totally irrelevant to
obtaining a conjugate match at the output of Class B and C
amplifiers). In other words, the output power equals the DC input
power minus the power dissipated in resistance Rpd. We will now show
why this two-way division of power occurs. First we calculate the
value of Rpd from Terman’s data, as seen in line (9) in the example
below. It is evident that when the DC input power minus the power
dissipated in Rpd equals the power delivered to resistance RL at the
input of the pi-network, there can be no significant dissipative
resistance in the amplifier other than Rpd. The antenna effect from
the tank circuit is so insignificant that dissipation due to radiation
can be disregarded. If there were any significant dissipative
resistance in addition to Rpd, the power delivered to the load plus
the power dissipated in Rpd would be less than the DC input power, due
to the power that would be dissipated in the additional resistance.
This is an impossibility, confirmed by the data in Terman’s example,
which is in accordance with the Law of Conservation of Energy.
Therefore, we shall observe that the example confirms the total power
taken from the power supply goes only to 1) the RF power delivered to
the load RL, and 2) to the power dissipated as heat in Rpd, thus,
proving there is no significant dissipative resistance in the Class C
amplifier other than Rpd.

Data from Terman’s example on Page 449 of Radio Engineers Handbook:

(1) Eb = DC Source Voltage = 1000 v.
(2) Emin = Eb - EL = 1000 - 850 = 150 v. [See Terman, Figs 76(a) &
76(b)]
(3) Idc = DC Plate Current = 75.l ma. 0.0751a.
(4) EL = Eb - Emin = 1000 -150 = 850 v. = Peak Fundamental AC Plate
Voltage
(5) I1 = Peak Fundamental AC Plate Current = 132.7 ma. 0.1327 a.
(6) Pin = Eb x Idc = DC lnput Power = l000 x O.0751 = 75.l w.
(7) Pout (Eb - Emin)/2 = ELI1/2 = Output Power Delivered to RL =
[(1000 -150) x 0.1327]/2 = 56.4 w.
(8) Pd = Pin - Pout = Power Dissipated in Dissipative Plate Resistance
Rpd = 18.7 w,
(9) Rpd = 18.7W/0.0751^2 = Dissipative Plate Resistance Rpd = 3315.6
ohms
(10) RL = (Eb - Emin)/I1 = EL/I1 = Load Resistance = 850/0.137 = 6405
Ohms (6400 in Terman)
(11) Plate Efficiency = Pout x 100/Pin = 56.4 x 100/75.1 =
75.1%

Note that Terman doesn't even mention non-dissipative plate
resistance Rp, and therefore it cannot be considered the source
resistance.
Note also in line (10) that RL is determined simply by the ratio
of the fundamental RF AC voltage EL divided by the fundamental RF AC
current I1, and therefore does not involve dissipation of any power.
Thus RL is a non-dissipative resistance. (For more on non-dissipative
resistance see Appendix 10.)
Referring to the data in the example, observe again from line
(10) that load resistance RL at the input of the pi-network tank
circuit is determined by the ratio EL/I1. This is the Terman equation
which, prior to the more-precise Chaffee Fourier Analysis, was used
universally to determine the approximate value of the optimum load
resistance RL. (When the Chaffee Analysis is used to determine RL.
from a selected load line the value of plate current I1 is more
precise than that obtained when using Terman’s equation, consequently
requiring fewer empirical adjustments of the amplifier’s parameters to
obtain the optimum value of RL.) Load resistance RL is proportional to
the slope of the operating load line that allows all of the available
integrated energy contained in the plate-current pulses to be
transferred into the pi-network tank circuit. (For additional
information concerning the load line see Sec 19.3a 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.
Let us now consider the dissipative plate resistance Rpd, which
provides the evidence that the DC input power to the Class C amplifier
goes only to the load RL and to dissipation as heat in Rpd (Again, not
Rp.) With this evidence we will show how a conjugate match can exist
at the output of the pi-network with efficiencies greater than 50
percent. In accordance with the Conjugate Matching Theorem and the
Maximum Power-transfer Theorem, it is well understood that a conjugate
match exists whenever all available power from a linear source is
being delivered to the load. Further, by definition, RL is the load
resistance at the tank input determined by the characteristics of the
load line that permits delivery of all the available power from the
source into the tank. This is why RL is called the optimum load
resistance. Thus, from the data in Terman’s example, which shows that
after accounting for the power dissipated in Rpd, all the power
remaining is the available power, which is delivered to RL and thence
to the load at the output of the pi-network. Therefore, because all
available deliverable power is being delivered to the load, we have a
conjugate match by definition. In the following Sec 4 we will show
how efficiencies greater than 50 percent are achieved in Class C
amplifiers operating into the conjugate match.

Walt, W2DU