Blair is right that a 40+j10 ohm load has an impedance magnitude is
41.23 ohms, but it has a vector angle of 14 degrees. The SWR is only
the simple ratio of the impedances when the vector angle is 0
degrees, i.e. the impedance is purely resistive.
With normal RF transmission lines, you can never have a 1:1 SWR when
the load Z is reactive. No kidding.
The formulas for the calculation when the load Z is reactive are a
pain due to the imaginary numbers involved.
This page explains it all: http://www.microwaves101.com/encyclopedia/vswr.cfm
(The good stuff is at the bottom.)
However, it's much simpler to use one of the programs like ARRL's TLW
by N6BV or this online calculator from W9CF:
73, Terry N6RY
At 11:05 AM 2008-11-13, Blair S Balden wrote:
>I guess this is something I'm not clear on. By my calculations, an
>antenna having an impedance of 40+j10 or 40-j10 would have 41.23 ohms.
>If SWR is the ratio of the two impedances (coax and load), then 50
>ohms / 41.23 ohms would give an SWR of 1.21. It would take 30 ohms
>of reactance combined with 40 ohms of resistance (40+j30 or 40-j30)
>to give 50 ohms. So, it would seem to me that the
>40-ohms-at-resonance antenna would need to have 30 ohms of reactance
>combined with it in order to achieve an SWR of 1.
>At least, that is what I would expect. Am I missing something in my thinking?
>----- Original Message -----
>Date: Thursday, November 13, 2008 12:33 pm
>Subject: Re: [TowerTalk] wire antenna question
> > Blair, that is not quite right. Using a 50 ohm swr indicator, the
> > lowest swr
> > is shown when the reactance is zero.
> > Using a transmission line program, 40 ohm load 40+j0; swr=1.25.
> > 40+j10=1.37;
> > 40-j10=1.37.
> > So, when you tweak your dipole for the lowest vswr at a given
> > frequency, you
> > are in essence resonating the antenna at that frequency.
> > 73,
> > Gerald K5GW
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