On Wed, 02 Jun 2004 08:37:30 -0500, Cecil Moore wrote:

Walter Maxwell wrote:

wrote:
Steve at first said the energy in the canceled waves continues to flow toward the
source without a voltage and current and that interference was not involved. He later
changed his mind. All that should be archived on r.r.a.a on Google for the summer
of 2001. Here's an excerpt. Steve said: "The total forward power increases as a direct
result of the vector superposition of forward voltage and current. This DOES NOT
require a corresponding destructive interference process ..." thus contradicting Hecht
in _Optics_ who says any constructive interference process must be accompanied by
an equal magnitude of destructive interference.

Superposition of forward voltage and current?

I'm sure he meant "superposition of forward voltages and superposition of
forward currents."

I don't recall Steve ever mentioning current.

I think you are right re his article. The above quote is from an
r.r.a.a. posting circa Summer 2001.

What Steve apparently doesn't understand is how the
energy direction is reversed when the rearward voltages and currents go to zero.

"How" is not explained in any of the physics references. The closest
physics reference that explains it is _Optics_, by Hecht where he says
something like, at a point some distance from a source, constructive
interference must be balanced by an equal magnitude of destructive interference.
In a matched system, there is "complete destructive interference" toward the
source side of the match point and "complete constructive interference" toward
the load side of the match point. Energy is always displaced from the "complete
destructive interference" event to the "complete constructive interference"
event. (That's what you call a "virtual short" or "virtual open" capable of
re-reflecting the reflected energy.)

Cecil, I explained the 'how', both in Reflections and in QEX. My explantion of
'how' is what Steve is continually stating is incorrect, especially in his last
3-part QEX article. Statements in that article prove he doesn't understand the
wave mechanism that reverses the direction of the reflected energy. Evidence of
this is that by simply saying the voltages cancel is insufficient description of
how the energies reverse direction. In fact, in his Oct 99 ComQuart article he
specifically states that both voltages and power cancel. This tell me that he
doesn't understand the wave action he's attempting to teach.

MIT's Slater and Harvard's Alford both explain it brilliantly, but Steve rejects
those references as 'irrelevant', and says I mistakenly used them as references
in Reflections.

What is really perplexing to me is that several posters on this subject said
that Steve's 3-parter is the best and most illuminating article they ever read
on the subject. How can they have missed some of the most egregious errors
appearing in that paper is unbelievable!

In s-parameter terms, b1 is the reflected voltage from port 1 toward the source.
Port 1 is the input to a matched tuner (transmatch). The equation is:

rearward-traveling voltage reflected toward the source b1 = s11(a1) + s12(a2)

For b1 to be zero, i.e. zero reflections toward the source, s11(a1) must be equal
in magnitude and opposite in phase to s12(a2). That is "complete destructive
interference". Since there are only two directions, "complete constructive interference"
must occur in the direction of b2 = s21(a1) + s22(a2) toward the load which is the
opposite direction from b1.

Cecil, if s11(a1) is equal in magnitude but in opposite phase with s12(a2) this
constitutes a short circuit. Assume two generators delivering harmonically
related output voltages equal to the two 's' voltages. When the generators are
connected with their output terminals reversed, causing their voltages to be 180
degrees out of phase--this configuration is a SHORT CIRCUIT. What I've been
trying to say is that this is the same condition as when the reflected waves of
voltage and current from a mismatched termination are of equal magnitude and
opposite phase with the voltage and current waves reflected by a matching device
such as a stub, the opposing voltages in those two sets of waves constitute a
short circuit the same as the voltages delivered by the two opposing
generators.

s11 is the port 1 reflection coefficient. a1 is the port 1 incident voltage.
s21 is the port 2 to port 1 transmission coefficient. a2 is the voltage
reflected from the load that is incident upon port 2.

Match-Point
Port1 Port2
Source------Z01--------x------------Z02------------load
a1-- --a2
--b1 b2--

The only dissipative resistance in the amp is that which heats
the plate. That dissipation is the only dissipation in the source--the other
dissipation is only in the load.

Why isn't the source impedance a negative resistance, i.e. a source
of power Vs a positive resistance, a sink of power?

Cecil, the source impedance is often correctly referred to as a negative
resistance. But it must be remembered that the source resistance of Class B and
C amps is non-dissipative, and thus totally re-reflect incident reflected power.
By this I mean that the dissipative resistance that heats the plate is entirely
separate from the output resistance represented by the load line. Remember, the
DC power goes to only two places: that which is dissipated as heat, and that
which is delivered to the load. The reflected power incident on the output
terminals of the tank has no effect on the power dissipated as heat.

Here's an example. First, adjust an amp to deliver 100 watts into a 50-ohm
resistive load. Second, change the load to a reactive 50 + j50 load and readjust
the pi-network to again deliver 100 watts into the new load. The plate current
will be exactly as in the first case, and the heat dissipated will be the same.
The difference is that in the first case the output impedance of the amp was 50
+ j0, while in the second case the output impedance is 50 - j50, due to
readjusting the reactive components in the pi-network to match the 50 + j50-ohm
load. Whether one likes it or not, this constitutes a conjugate match.

As for the plate temperature remaining the same in both cases, first, the
readjustment of the pi-network returned the input resistance of the network to
the same value as in the first case. Thus the plates saw no different condition
between the two cases. And second, Eric Nichols, KL7AJ, has measured
calorimetrically the temperature of the water cooling the tubes of megawatt
transmitters with greatly differing values of reflected power incident on the
xmtr. He has shown that the water temperature remains constant whatever the
value of the reflected power.

Since you mentioned earlier that some posters would like my opinion on the
nature of the source resistance in rf amps I'll put a paragraph or two together
with measurement data to support my opinion.

Walt