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Author Topic: Measuring Impedance...?  (Read 1944 times)

Posts: 1125

« on: March 15, 2012, 10:34:29 AM »

I am planning to develop a mathematical model (using Mathematica) that models my transmission line system.  This model will assume either 300 ohm or 450 ohm ladder (window) line, a balun (one of the DX Engineering and one of the Comtek baluns), and the COAX feed to the transceiver.  In order to do this I need the complex impedance (R+jX) for each component (ladder line, coax, and balun).  I have found on the Internet, sources for complex impedance of various COAX products (i.e. LMR-400, RG-8X, etc.) but so far not for baluns or ladder line.

So, if anyone has pointers to this information I would appreciate it.  But, I also plan to measure these.  This is what I would like to learn here on this forum if my measurement approach is sound.  I have an MFJ-259 to use (which I have calibrated and seems to be pretty good, at least for R values in test).  So, the plan is this:

(1)  To measure the impedance (at the SO-239 connector of balun) I plan to put a resistor (either 450 ohm or 300 ohm depending on my tests) across the balanced line input to the balun.  Then, using my MFJ-259 I would measure the R+jX (yes, I know the sign for X is missing but I can figure that out) at the coax input to Balun.  Are there any gotcha's to this process?

(2)  I would like to measure the ladder line using a similar approach that includes the balun itself.  Maybe a stretch of 40 to 50 feet of ladder line stretched across my yard, about 6 feet above ground (or whatever I can easily achieve) with the far end shorted by 300 or 450 ohm resistor depending on the ladder line nominal impedance.  This one is sure to be more affected by stray affects but I am not sure to what extent.

73, phil, K7PEH

P.S. The major part of this exercise is to play with Mathematica which is another hobby of mine so comments suggesting alternative programs would be interesting but not particularly what I am looking for.

Posts: 861

« Reply #1 on: March 15, 2012, 01:56:31 PM »

You won't for baluns because the value changes with the frequency. It is also different for every ferrite core, construction method and co-ax used in construction.

Posts: 5908

« Reply #2 on: March 15, 2012, 04:13:50 PM »

You can't use a simple two element LC model for a long t-line. But you can use many LC sections. Use 20 or more sections per wavelength.

Here is how to calculate the L and C of a t-line.



 t is the time of flight through the length of t-line. Zo is the characteristic impedance.

Example: We have a 450 ohm ladder line having a velocity factor (VF) of 0.95. The velocity of light a medium having a VF of 1 is 300,000,000 meters per second. For a VF of 0.95  is it 285,000,000 meters per second. Let's say we want to know the L and C for a 1 meter section of our 450 ohm ladder line.

C = (1/285,000,000)/450 = 7.8 pF

L = (1/285,000,000)(450) = 1.6 uH.

Check: Z = (L/C)^0.5 = (1.6uH/7.8pF)^0.5 = 453 ohms.

Now, what if you want to measure the characteristic impedance of a t-line rather than rely on the specified Zo? An open 90 degree line presents a short. An open 45 degree line presents a capacitive reactance equal to the Zo.

Dial the MFJ until you find the lowest frequency for which the open line presents a short. This is where it is 90 degrees. Now dial the MFJ to half this frequency, read the X and that is the Zo.

Posts: 1125

« Reply #3 on: March 15, 2012, 05:15:19 PM »

wx7g ---

Thanks for your comments and your L and C computation example.  With regard to your first comment about 20 or more sections per wavelength, I plan to use many more in solving the differential equation (Telegrapher's equation).  I was not going to use a simple circuit model.  Just the differential models for transmission line (both coaxial and parallel).  I might find myself asking you some follow up question though when I think thru this a little more.

Your call sign is familiar though and I am wondering if we have ever had a QSO, I am 90 percent CW or so.  I should check my log book but I have to get off my couch here with my Macbook Pro in my lap and walk over to my iMac where I have my log book app and I am too lazy to do that right now.

Posts: 5419

« Reply #4 on: March 16, 2012, 08:23:14 AM »

You might have a slight problem here.  The MFJ259B covers 0 to about 600 ohms resistance and reactance, plus or minus.  But open wire/ladder line is not used in it's "characteristic impedance", so the impedance will vary along the transmission line.  You can probably expect up to about 10:1 VSWR at times, so the measurements will be outside the limits of the MFJ tester.
This just means your testing ability will be limited.  But a simple 2:1 SWR with 450 ohm line will range between 225 ohms and 900 ohms.  And the MFJ will not measure reactance below 10 ohms accurately, or above 650 ohms.
It is still a nice meter to have in the field when trying to get an antenna functioning!

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