From: gary@ke4zv.uucp (Gary Coffman)
Subject: Re: SWR Tuning and PLL
Reply-To: gary@ke4zv.UUCP (Gary Coffman)
Organization: Destructive Testing Systems
Date: Tue, 5 Jan 1993 18:13:18 GMT

In article <93Jan04.222725.18274@acs.ucalgary.ca> ming@enel.ucalgary.ca (Yang Ming) writes:
>In article <1993Jan1.162457.24424@ke4zv.uucp> gary@ke4zv.UUCP (Gary Coffman) writes:
>
>[deleted ...]
>
>>
>>The reflected wave can combine vectorially with the dynamic voltage
>>present at the output of the amplifier. This changes the *slope*
>
>If you are talking about a linear amplifier, the question is how the
>vectorial combination of the two voltages can *change* the slope?

The loadline slope is defined as E/I where E and I are the dynamic
voltages and currents at the output of the active device. Since
the reflected wave's voltage adds vectorially to the voltage
being generated by the active device, E changes. Therefore E/I
changes, and thus the output impedance changes.

>>of the load line which changes the *output* impedance of the 
>>amplifier since the output impedance *is* the slope of the load
>>line. This changes the operating characteristic of the amplifier,
>>usually shifting it off most efficient operation, *and* changes
>>the *virtual* impedance seen looking into the output port through the
>>matching network to a virtual short circuit. This is similar in
>>principle to the "virtual" ground at the input of an opamp. This 
>>*conjugate mirror* causes the reverse wave to be re-reflected 
>>totally from the transmitter output because it appears as a 
>^^^^^^^^
>>completely unmatched termination to the line.
>>
>
>What you are trying to say is that the reflected wave changes the 
>operating point and causes the amplifier to *totally* reflecte the power
>back to antenna. This is a good thing if you can have all the power
>*eventually* sent to tha antenna, why complain?  However, please note
>
>a)	Nobody can build a amplifier with a pure 
>	imaginary output impedance;

The output impedance isn't imaginary in the sense of 0+jX, it's
a *virtual* value that's a combination of the dynamic voltages and
currents being generated by the active device with the voltages and
currents in the reflected wave. This is similar in concept to the
virtual ground at the input of an opamp. It's not a real ground,
nor is it an imaginary ground in the sense of 0+jX, it's a *virtual*
ground caused by the summing of voltages in a node.

Let me give a crude analogy to illustrate what happens when a
reflected wave enters an operating amplifier's output port, think
of it as trying to piss into the nozzle of a operating firehose. 
It all gets reflected back to you. The conjugate mirror effect is 
what causes total re-reflection of the wave.

>b)	Linear circuts' operating points do NOT change with the
>	amplitude of the signal (even it is a combination of whatever
>	waves). This is the *definition* of linearity;

No, you're confusing different things again. Linear circuit operating
points do not change with varying *input* signals. That's true. But
the reflected wave isn't an *input* signal going into the *input*
port of the device. Instead it's a rogue *output* signal that's trying
to squeeze back into the *output* port of the device. As I noted above,
the vector sum of the reflected wave and the forward wave from the
active device changes the loadline seen by the active device. An
amplifier is a 4 port, not a 2 port, network.

>c) 	The best efficiency is obtained when the 
>	load impedance is the conjugate of the output impedance of
>	the amplifier. If you have a non-zero real part for your
>	load impedance, the best efficiency is that you have the same
>	non-zero real part and an imaginary part with opposite sign,
>	which can be obtained with the help of matching network.

Sure. That's another thing matching networks can be used for, cancelling
reactance. But it's totally unrelated to what we've been discussing, it
just happens to be done by a different adjustment of the same LC components.

>>See chapter four of Walt Maxwell's classic "Reflections" for
>>a through mathematical treatment of this subject. Walt was
>>chief designer for RCA for many years and is *the* recognized
>>expert authority on this subject.
>>
>
>I do not have access to this classic book. My university library does not
>have it. All the books I have say that you have a complex output impedance
>and you should try by using matching network to have conjugate match to 
>get the maxmum power dilevery. It is the following equation:
>
>		R_s  =  R_l and X_s = -X_l
>
>If you have pure imaginary output impedance, how can you match it?

Since that's a strawman, it's a moot point. The impedance isn't imaginary,
it's *virtual*. A totally different thing. Your book equation is fine for
analyzing arbitrary passive 4 port networks, but doesn't include the 
effects of an active conjugate matched source interacting with the 
reflected wave.

I want to clear up something else before it arises yet again. Most
college lab experiments use a signal generator as a source. This
is a constant voltage generator in series with a real physical fixed
resistance.  It does not behave like a conjugate matched transmitter 
which is not a constant voltage generator and is not in series with 
a physical resistor. The virtual resistance, the load line, the *output* 
impedance, all the same thing in a transmitter, changes dynamically under 
conditions of reflected waves and varying load. This makes the book equation 
too simple to describe the real behavior of transmitters. There are non-linear
dependent variables in the equation describing the output behavior of a
transmitter. The only valid solutions require complex vector calculus.
I don't have the symbols for that on this terminal, look harder for
Maxwell's book, it's ISBN 0-87259-299-5.

Gary
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