From: gary@ke4zv.uucp (Gary Coffman)
Newsgroups: rec.radio.cb,rec.radio.amateur.misc
Subject: Re: But wait! There's More!!!
Date: 17 Aug 92 14:23:27 GMT
Reply-To: gary@ke4zv.UUCP (Gary Coffman)
Organization: Gannett Technologies Group

In article <hg06390@pro-haven.cts.com> phantom@pro-haven.cts.com (Tiffany Bloxom) writes:
>Oh....
>        
>        Hey....just a strange little question here.
>        
>        If you have your coax in multiples of your fundamental wavelength
>(i.e. 102"....), won't that Also make your coax Resonant?????????
>        If so, then this is not good....
>        Pl. Enlighten me, Ok?

If the coax is properly matched, it doesn't matter what it's length is.
There's no magic to quarterwave sections. If the line has a VSWR of other
than 1:1, then *any* transmission line segment will act as a transmission
line transformer. It happens that a quarterwave transmission line segment
has a particularly useful transformation ratio, but it's not unique in
acting as a transformer. In the mismatched case, the antenna load presents
an impedance R+jX to the coax. This is transformed down the length of the
coax to another value R'+jX'. Now it may be that a particular line length
will, in a particular case, transform the R of the antenna to an R more
to the liking of the radio at the other end. This can be useful. *But*,
the jX will also change and this must be dealt with. If the radio has
a variable output network, the reactance can be absorbed into the network
and effectively "tuned out". Thus radio and antenna are happy and maximum
power is transferred. But if the radio has a fixed tuned output network,
the reactance will change the *tuning* of the output network in such a
manner that the R value that the radio wishes to see will be different
than 50 ohms. This can be bad or good. With the proper combination of complex
load impedance and line length, it's possible that the reactance presented
to the fix tuned network will be just the right amount and sign to *retune*
the network to properly match the R' presented to the radio resulting in
maximum power transfer. In this case *only* does line length matter. In
all other cases, the jX just makes the match worse.

Note in case it isn't clear that the output network of a transmitter is
itself a transformer made up of inductors and capacitors. It's job is to 
transform a nominal 50 ohm load impedance to the output impedance of the 
final amplifier's active device.  In the case of a transistor final, this 
is usually only a few ohms, or even a fractional ohm in higher powered 
amplifiers. In the case of tube amplifiers, the active device output 
impedance is usually a few thousand ohms. The output network transforms 
this impedance to an idealized 50 ohms. 50 ohms is chosen because it's a 
convienent value of impedance for a coaxial cable. There's nothing magic 
about this number. Another impedance could equally well have been chosen.

An idealized quarterwave vertical antenna has a base impedance of 37.5
ohms. This isn't a match for 50 ohm cable either. So a matching network
is part of the antenna to allow the impedance to be transformed to 50
ohms. Now either matching network, at the antenna or at the transmitter,
can be tuned to match a different impedance by the addition of reactance
of one sign or the other. When the transmission line is not matched, IE
it has a VSWR of other than 1:1, it will present a value of reactance
at the other end that depends on the length of the cable, the degree
of mismatch, and the sign of the mismatch. This reactance will *retune*
the matching network terminating the line to a different transformation
ratio. 

The interactions of the *system* can become quite complex. In the
end, the only transformation that matters is the one from transmitter
active device to antenna radiating element. That is, Rg must match Rr.
If there are mismatches in between on the transmission line, they don't 
matter. They just become a part of the total transformer system. So
it makes no difference if the VSWR on the transmission line is 1:1
or 7.38:1 or any other reasonable value, as long as the radiating load's
impedance ultimately is transformed to the active device's impedance, 
either by happenstance of transmission line length or deliberate adjustment
of matching component values.

Transmission line VSWR is particularly easy to measure, so you see a
lot of these meters. But it's not necessarily the most important
measurement of system performance. A distant field strength indicator
is the most reliable indicator of good system performance. You shouldn't
care what the transmission line VSWR is as long as you are putting the
maximum possible field strength reading on the distant meter. *One*
case where this will be true is when the antenna matching network transforms
Rr to 50 ohms and the transmitter output network transforms this 50 ohms
to the output impedance of the active device. In this case *only* will
a VSWR of 1:1 coincide with maximum radiated signal. In other cases, a
VSWR other than 1:1 may be *necessary* in order to achieve maximum
power transfer.

Gary KE4ZV