Topband: How to determine impedance

[Grant Saviers]

What I used for data transmission line Z finding was a pulse gen, scope 
and variable resistor (non inductive).  A fast risetime pulse reflects 
very clearly on the scope at the source.  When the terminating resistor 
equals line Z the reflection disappears, usually a shelf up or down on 
the "sent" pulse if it is a few cable lengths in time.  Measure with the 
VOM.  No calcs.  Works for short lengths with fast scopes/gen since 
propagation is about 1nsec/ft or with slower instruments on longer 
cables.  We didn't have fancy stuff like network analyzers or RF 
impedance analyzers laying around the computer labs.

Grant KZ1W

On 1/26/2018 9:34 AM, John Kaufmann wrote:
> 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(?).
>
>