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Old May 23rd 04, 09:54 AM
Lord Snooty
 
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Default Conjugate matching and my funky VSWR meter

There has been some discussion in the past months about conjugate matching,
VSWR, and power transfer from source to load.
I've come across a puzzle while noodling on this.
My main issue here is how the heck my VSWR meter is measuring the way it is.

My elementary hook-up is an RF power amp feeding directly into a VSWR meter,
and from there into a load consisting of a carbon resistor and a variable
capacitor rigged in series. The meter connects to the load via about a foot of
50 ohm coax. The frequency is between 1 and 10 MHz.
Model the source impedance as Zs = R + jX, and the load impedance as Zl = r +
jx (or use phasors if you prefer .
The following two statements are true:
1) The power dissipated in the load (r) is maximised when x = -X (so-called
"conjugate matching"), whatever the value of (r).
2) The classical VSWR is minimised (zero "reflected power") when x = +X,
whatever the value of (r).

However, my VSWR meter, whch is a conventional 2-diode bridge and short
transmission line, indicates that minimum indicated VSWR
corresponds to max power dissipated in (r).!! (i.e. at conjugate match, and
NOT when reflected power is zero).

The equation normally used for VSWR is
VSWR = ABS( (1 + |p|) / (1 - |p|) )
where
p = (Zl - Zs) / (Zl + Zs)
and p is a measure of the amount of power reflected back to the source, called
the "voltage reflection coefficient"

I plotted something I call "conjugate VSWR" or VSWR*. which is the same
expression as above, but with p defined as
p = (Zl - Zs*) / (Zl + Zs)
where Zs* indicates the complex conjugate of Zs.
and the behaviour of this VSWR* thingie absolutely matches what I see on my
meter. Aye, there's the rub.

Some points to note
a) Classical VSWR shows NO minimum for all r, when x has the opposite sign to
X
b) VSWR* always has a minimum at the same r-value which causes maximum power
to be dissipated in r, whatever the value of x.

Again, I flat don't understand how my VSWR meter can indicate VSWR* when I
know it should indicate VSWR.

Here are a couple of links to flesh out the theory.

1. Wade through this at your peril - it's you lot fighting abou this issue and
is VERY long
http://www.ibiblio.org/pub/academic/...S/20030831.ant

2. This is much more succint - cut to the chase on p47
http://my.ece.ucsb.edu/yorklab/Usefu...%20AN64-1B.pdf

Best,
Andrew


 
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