From the previous posting, I can guess who is going to jump all over this.
Keep up the good work.

Tam
"Dave" wrote in message
...
ok, bonzo, i'll bite on the troll bait. but only because its early in the
morning and the normal endless discussion of this stuff hasn't taken over
yet.

"Lord Snooty" wrote in message
nk.net...
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).

wrong. you must transform the R+jX along the transmission line to get
back
to the load seen by the source. you stipulate a low frequency and short
line, so you are close anyway.

2) The classical VSWR is minimised (zero "reflected power") when x = +X,
whatever the value of (r).

doubly wrong. vswr is on a cable and is independent of the source. it
knows nothing of R+jX only the characteristic impedance of the cable. all
following calculations are wrong for this reason alone.


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)

wrong again, the impedance used must be that of the cable not of the
source.
its not worth commenting further until you understand this.

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