> >> > The length of 50 Ohm coax is not relevant if the antenna is truly 50
> >> > Ohms.
> >> >
> >> > I've never met a 1/4 wave mobile antenna that is 50 ohms.  In fact, I
> >> > think you'll find it is about 37.5 Ohms.  In this case, the length of
> >> > the coax does make a difference as this *IS* the matching network.
> >> >
> >> > However many antennas, mobile or otherwise, are engineered to present
> >> > exactly 50 Ohms at the feedpoint.
> >
> >But the length of the coax does not change the swr. That is strictly a
> >function of the match between the coax and the antenna feed point. If
> >the feed point is 37 ohms and the coax is 50 ohms you have mismatch and
> >the length does not change that.
>
> Not true. set your SWR meter on a mismatch system (37ohms) and keep adding
> pieces to the coax about one foot at a time. You will see your SWR meter go
> up and down. If the impedance of the mismatch is higher than 50 ohms the coax
> starts to become capacitely reactive and if the mismatch is lower than 50
> ohms the coax starts to become inductive. The longer the coax the more the
> reactive component and that has an effect on the SWR. Just try it.

MYTH: "The longer the coax the more the reactive component and that
has an effect on the SWR."

FACT: The SWR does not change by changing the length of the
transmission line.

PROOF: The ratio of the voltage that is reflected by the load is
given by the reflection coefficient, p.  (Actually, this is a Greek
letter).  Let me give you an example to show my point that the
length of the transmission line does not affect p, and therefore
does not affect the SWR or the SWR reading:

Consider an antenna (termination) with an impedance 100 ohms that
is used in a standard 50 ohm system.  I'm sure that we all agree
that this is an SWR of 2:1.  If you connect a 1/4 wavelength coax
to this antenna, the input impedance of the coax will be 25 ohms
(this can be shown on a Smith chart or with appropriate software).
What the SWR with a 25 ohm load?  Answer: 2:1, the same thing!
Even though this is not the same impedance as seen with zero length
coax (at the antenna), the SWR has not changed.

I have illustrated that you do not have to see the same
impedance at the input to the coax as seen at the antenna
input to get the same SWR reading but I am not done.

Here is the formula for reflection coefficient:

p = sqrt(((Ra-Ro)^2 + Xa^2) / ((Ra+Ro)^2 + Xa^2))

where Ro = line impedance (50 ohms)
      Ra = input resistance
      Xa = input reactance

Here is the formula for SWR:

SWR = (1 + p)/(1 - p)

If you calculate the reflection coefficient and SWR for these
impedances, you will get:
for line length = 0 (at the antenna)
    Ra = 100
    Xa = 0
    p = 0.333
    SWR = 2:1

for line length = 1/4 wave
    Ra = 25
    Xa = 0
    p = 0.333
    SWR = 2:1

I chose those arbitrary values because one can easily calculate
the SWR for those in his head.  But I will go one step further.
If the coax length were 1/8 wave (or any other length), the
imput impedance would be some complex value but the SWR would
still be 2:1.  I will show this next.

If the coax length were 1/8 wave, you can find this on a Smith
chart:
    Ra = 40
    Xa = -30
    p = 0.333
    SWR = 2:1

Even with the crazy impedance of 40-j30 ohms seen 1/8 wavelength
away from the antenna, the SWR is still 2:1 !!!
It can be shown (I will leave it to you) that every point along
the transmission has the same 2:1 SWR.

Intelligent responses welcome.

George Warner
warnergt@loveboat.com