Topband: How to determine impedance

[John Kaufmann]

Here's another method that's based on the engineering textbook transmission
line equation and use of an impedance analyzer to make an impedance
measurement.

You can look up the transmission line equation on Wikipedia:
https://en.wikipedia.org/wiki/Transmission_line.  Scroll down the page to
the paragraph with the title "Input impedance of lossless transmission
line".    This equation gives the impedance Zin looking into a transmission
line in terms of the line's characteristic impedance (Zo), the load
impedance (ZL) at the far end, and the electrical length of the transmission
line.

If electrical length of the line is 1/8-wavelength (lambda/8), you terminate
the line in a short circuit (ZL=0), and you solve for Zin, you find:  
Zin=jZo or Zo=-jZin.  Everything drops out of the transmission line equation
except for the characteristic impedance Zo that you are trying to find!
(Homework assignment for you mathematicians:   Terminate the line in an open
circuit (ZL=infinity) and solve for Zin in terms of Zo for the same 1/8-wave
line).

Now you need to set up a measurement with your analyzer that duplicates
these conditions.

Terminating the line in a short circuit is the easy part.  Next you have to
determine the frequency where the line is 1/8-wave long.  How do you do
this?  First use your impedance analyzer to find the frequency where the
line is a 1/4-wave long (if the line is terminated in an open circuit at the
far end, the input impedance goes to zero at the lowest frequency where the
line is a 1/4-wave long).   Divide that frequency by 2 and you have the
frequency where the line is 1/8-wave long.  Now tune your analyzer to that
frequency and measure the input impedance Zin to the line.  In general
Zin=R+jX.  For an ideal line, that impedance is purely imaginary, i.e. R=0
and X is some finite number.  If your analyzer gives you some small R value
that is not zero, ignore it and work with the just the X value.  You now
have Zo=-X as derived above.  You're done.

73, John W1FV

-----Original Message-----
From: Topband [mailto:topband-bounces at contesting.com] On Behalf Of Martin
Sent: Wednesday, January 24, 2018 6:28 AM
To: topBand List
Subject: Topband: How to determine impedance

Topbanders,
for the construction of the beverage ( a 2 wire reversible beverage, that
is) from my post a few days ago i wanted to know how to measure or determine
the impedance of the open wire. I stumbled across a very simple method some
of of you might know , some might not. Anyway, here is the method. It works
for coaxial cable or open wire.
You need no fancy measurement gear-  rule, pocket calculator and LC meter
will do. For really long runs you might need the help of a tape rule or even
google maps.

Measure the length of the unknown coaxial cable or open wire (DUT Device
under test) in meters m.

With both ends open, measure capacitance C of DUT, divide it by it's length
( C' = C/m) .

Shorten one end, measure inductance of DUT, divide it by length ( L' =
L/m) .

Now calculate

Z= 1000 * squareroot(L'/C')

Voila.

It may also help to determine if and where your cable or 2 wire beverage has
an intermittance when you already know it's impedance it had before the
failure. Transform the formula accordingly.
I think it should also help to determine the impedance of the beverage (
single wire or 2 wire) measured against ground(?).


-- 

Ohne CW ist es nur CB..

73, Martin DM4iM
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