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Re: [Amps] close to off topic - how to read antenna R + jX ??

To: Dan Sawyer <dansawyer@earthlink.net>
Subject: Re: [Amps] close to off topic - how to read antenna R + jX ??
From: David Kirkby <david.kirkby@onetel.net>
Date: Sat, 26 Feb 2005 22:42:45 +0000
List-post: <mailto:amps@contesting.com>
Dan Sawyer wrote:

>All,
>
>I have become interested in leaning more about what is actually going on 
>at the antenna. I have a vertical and would like to measure it.
>
>First I have an Autek RF-1. It measures swr, Z, L, and C at a preset f. 
>I am not certain what the L and C are reading. When I measure a 50 Ohm 
>terminator at 7.2 MHz it actually reads a Z of 50 and an SWR of 1.0. 
>However the L and C readings are of 2 uH and 2500 pf.  What are these 
>actually measuring? The values are very close to those from the antenna. 
>

I'd look at the manual.  This does not make much sense to me, and I have 
quite a good understanding of transmission lines. The instrument is 
either faulty, or the manufacturer has decided to give you some odd 
information, that I can't determine.

Since you are attaching a 50 Ohm terminator, and the system indicates a 
VSWR of 1.0, it is reasonable to assume this instrument indicates the 
VSWR in a 50 Ohm system. That is common practice, but there is no 
theoretical reason one could not use 1 Ohm or a million Ohms. Just 50 is 
a standard (It was chosen as a compromise between minium loss and 
maximum breakdown voltage on coax).

Since the VSWR is 1.0, there can be no L or C. This implies a purley 
real impedance of 50 Ohms. I thought of two things these 2 uH and 2500 
pF might be trying to indicate, both of which are a bit silly, but 
neither workout out anyway.

1) It could be saying a capacitance of 2500pf/m and inductance of 2 uH/m 
on a cable would give the same real impedance. But that is not true, as 
it gives 28.5 Ohms. But there are an infinite set of values of 
inductance per metre and capacitance per metre that would give 50 Ohms, 
so it would be a bit silly.

2) It's implying a 2 uH inducator would have a reactance of 50 Ohms. 
That would again be silly too, but again it does not work out, as 7.2 
MHz, it would give a reactance of j90.8 Ohms.

3) It thinks your load has 2500pF capacitance and 2 uH inductance. That 
would be a pretty alful load, and not give anywhere near a VSWR of 1.

I'd look at a book and understand what R+jX is theoretically before 
worry about what this bit of kit is indicating, as I think it will only 
confuse you.

Bascially an impedance Z consists of a real part R and an imaginary part 
X. In a purely resistive system (like an ideal dummy load), R is some 
non-zero value (usually 50 for a dummy load) and X=0.  A pure capactor 
would give an impedance of 0 -jX and a pure inductor of 0+jX. Where X is 
in each case given by

For a capacitor
X = 1/(2 * pi  * f *c)
(where f is in Hz, and C in Farads)

For an inductor
X = 2 * pi * f * L
(where f is in Hz and L in Henrys).

You really need to read a book on AC theory to get to grips with this, 
and understand how to calculate with complex numbers to really 
understand it fully.

But I would not take too much notice of an instrument which indicates 
significant values for C or L when connected to a 50 Ohm load, whilst 
indicating a VSWR of 1.0  None of that makes sense.

>How can I actually measure the L and or C component of the antenna? If I 
>use an impedance bridge at the frequency will it measure L (or C)?
>
At a single frequency (other than DC), you can't measure capacitance, 
since any inductance will mess up your computation. Likewise you can't 
actually measure inductance, since any capacitance will mess up your 
values. Instruments that do this at a specific frequency can either

1) Compute L, assuming C to be zero (which is fine if measuring perfect 
inductors)
2) Compute C, assuming L to be zero (which is fine if measuring perfect 
capacitors)
3) Compute an impedance R + jX, and leave you to determine what part of 
X is due to inductance and capacitance.

You need to read a book on this - it is not trivual unless you have a 
reasonable grash of maths.

-- 
Dr. David Kirkby, 
G8WRB

Please check out http://www.g8wrb.org/ 
of if you live in Essex http://www.southminster-branch-line.org.uk/



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