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Measurement of cable impedance - RF Cafe Forums

Because of the high maintenance needed to monitor and filter spammers from the RF Cafe Forums, I decided that it would be best to just archive the pages to make all the good information posted in the past available for review. It is unfortunate that the scumbags of the world ruin an otherwise useful venue for people wanting to exchanged useful ideas and views. It seems that the more formal social media like Facebook pretty much dominate this kind of venue anymore anyway, so if you would like to post something on RF Cafe's Facebook page, please do.

Below are all of the forum threads, including all the responses to the original posts.

 Post subject: Measurement of cable impedance
Posted: Mon Jan 15, 2007 6:23 am 

Joined: Mon Jun 19, 2006 10:27 am
Posts: 13

characteristic impedance of a finite length of line at a given frequency can be derived by taking two impedance measurements, one with the end open circuit and the other with the end short circuited. From these, Zo is calculated as follows:

Z_0 = SQRT ( Z_short * Z_open )

Anyone knows how to derive this equation ?

 Post subject: Measurement of Cable Impedance
Posted: Tue Jan 16, 2007 7:10 am 
User avatar

Joined: Fri Feb 17, 2006 12:07 pm
Posts: 268
Location: London UK
Most standard textbooks on line transmission cover this. It is derived from the T equivalent circuit of the transmission line, having total series impedance of Z1 and shunt impedance z2, correctly terminated in Z0.

Looking from the left end as the input with the right end short circuited, the input impedance is

Zsc = Z1/2 + Z1*Z2/(Z1 + 2*Z2) .............1

Open circuited, the input impedance at left is

Zoc = Z1/2 + Z2 ......................................2

The Characteristic Impedance is given by

Z0 = SQRT( Z1*Z2 + Z1^2/4) ..................3

which needs a separate proof.

If equations 1 and 2 are multiplied together you get

Zoc * Zsc = Z1^2/4 + Z1 * Z2 = Z0^2

Thus Z0 = SQRT (Zsc * Zoc)

My textbook is an ancient Everitt "Communication Engineering" written with a quill pen on parchment. :-)

 Post subject:
Posted: Tue Jan 30, 2007 12:57 pm 
User avatar

Joined: Tue Dec 26, 2006 5:39 pm
Posts: 25
Here is a quick way to test.

Connect to your network analyzer or impedance meter. Find the frequency at which the cable is 1/4 or 1/2 wavelength. Then adjust your network analyzer or impedance meter to a frequency so that your cable is 1/8 wavelength.

Note the reactance when you short or open the far end will be equal and opposite. The magnitude of reactance you measure equals the characteristic impedance. Example, you measure 0.5 +j42 and 0.5 -j42 you now know that the cable Zo is 42.

On a vector network analyzer you can do this really quickly without need to KNOW your frequency. Set the analyzer to 0 Hz sweep and polar display. Keep alternating between shorted and open at the far end and watch the display. Vary the frequency until you see that the capacitive reactance is the same as the inductive reactance (the 'dots' on the CRT will be exactly vertically aligned) as you switch from short to open. Then read the reactance and you have the answer.

For example I have found rolls of RG58 as low as 42 ohm and as high as 62 ohm. It is a lesson to never pay attention to "RG" numbers ever again.

 Post subject:
Posted: Fri Mar 09, 2007 5:34 am 

Joined: Mon Jun 19, 2006 10:27 am
Posts: 13
thank you nubbage and wb9jtk !

Posted  11/12/2012

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