[TowerTalk] Measuring cable length using TLW and an antenna analyzer without a TDR function

Sun Jan 12 17:17:32 EST 2020

You don't need an antenna analyzer with a TDR function to accurately 
measure transmission line length.  This method is really simple (more so 
than it looks), and it actually manually mimics a TDR function anyway 
(explanation for that below).

You do need an antenna analyzer that gives you complex impedance 
readings, though, or at least use some method that will give you complex 
values from scalar readings.  I use an FA-VA5, but you can now get 
various versions of the remarkable NanoVNA for less than $50 that will 
give you accuracy at HF that is essentially indistinguishable from lab 
grade equipment.  I would have killed for this kind of capability years ago.

My procedure is:

1.  Connect your analyzer to an available end of the transmission line.

2.  Estimate the maximum length of transmission line under test.

3.  Take complex impedance readings (R  +/-  jX) at a few frequencies 
appropriate for the length of the line you are trying to measure.  Your 
lowest frequency should represent a quarter wavelength shorter than your 
estimate of the maximum transmission line length, and the other (higher) 
frequencies should be within a range that represents some few multiples 
of quarter wavelengths. Try to stay away from frequencies that are 
harmonically related. See my example below.

4.  Load each of the measurements you have taken into TLW, the free 
transmission line application that comes with any ARRL Antenna Book 
published over the last several years.  Be sure to pick the appropriate 
cable type and enter a length greater than you expect the cable to be.

5.  For each measurement enter the frequency, resistance, and reactance 
(don't forget the sign).  Select "Input", "Resist/Reac.", and click on 
"Graph".

6.  You will now see a graph of the transformed impedance as a function 
of the distance from the end of the transmission line that you took the 
readings.  The red line is the resistive portion, and the green line is 
the reactance.  Note that the middle of the reactance scale is zero ... 
not the bottom.

7.  Hover your mouse cursor over the reactance (green) line at the zero 
(middle) point).  Jot down the length for every place the green lines 
crosses zero.

8.  Repeat this for every frequency measurement you have taken.  Be sure 
to re-click "Graph" each time you update the data.

9.  Compare the reactance zero crossing lengths for every frequency.  
There will be only one length that was found for every frequency.

I happened to have a length (rough guess 200 feet long) of LMR-400 coax 
laying on the ground after some work I recently did on my 160m 
Inverted-L, so just now I went out and took the following readings:

2 MHz    58  +  j206
3 MHz    3.7  -  j16.3
4 MHz    24  +  j96
5 MHz    6.7  +  j30.5
6 MHz    10.3  +  j48.5
8 MHz    12.4  +  j43
10 MHz   9.2  +  j13.5

Loading each of those sets of readings into TLW (I set the maximum 
length to be 250 feet) gives the following lengths where the reactance 
line crosses zero.  You can load these same numbers in TLW yourself to 
see how this works.

2 MHz    196
3 MHz    56, 196
4 MHz    89, 194
5 MHz    29, 113, 195
6 MHz    53, 121, 193
8 MHz    39, 91, 144, 195, 248
10 MHz    25, 68, 109, 151, 194, 234

I'd put my money on 194 feet being pretty close to the right length.

In this case, the one measurement at 2 MHz pretty much tells the story, 
but in general you may not have a good guess at the length, especially 
for shorter legnths where you're using higher frequencies. In addition, 
the multiple frequencies tend to average out any jitter for any one 
frequency reading.  In my experience, as few as three well-chosen 
readings does a pretty good job.

This technique actually is very similar to what a TDR does, except the 
one described here is a lot more manual.  A TDR does a frequency sweep 
and takes complex impedance readings at multiple frequencies. It does an 
inverse FFT on that data to get back to the time domain, and then uses 
the propagation factor of the line to convert time to distance.  The 
more hits for any particular impedance as a function of frequency, the 
more bits in the relevant time bucket.  We just did pretty much the same 
thing manually.

Opens and shorts in TLW are pretty obvious, but it would be almost 
impossible to use TLW to find a fixed element network since reactance is 
a function of frequency and would be different for each graph.  So just 
for grins I generated a spreadsheet that takes readings at three 
frequencies, uses the transmission line transformation formula to 
calculate the transformed impedance for every foot on transmission line, 
converts the reactance to inductance or capacitance as the case may be, 
and looks for the place on the line where the fixed element values are 
the same for the three frequencies (within a specified tolerance).  It 
works, although I had to do it in Open Office Calc because my 2010 
version of EXCEL doesn't do inverse trig functions on complex numbers, 
but I have to admit that I can't think of an obvious situation where it 
would be useful.   I only mention it to point out what can be done with 
fairly simple readings.

At this point I'm kind of curious to know if anyone bothered to read all 
of this ... ;)

I'm even more interested to know if anyone has spotted obvious errors in 
any of it.

73,
Dave   AB7E

On 1/12/2020 11:31 AM, Don wrote:
> I'd appreciate your sharing that with those of us casual users with 
> antenna analyzers but who profess to be novices in their use. Have 
> used it for some of the applications but still a learner. Mine happens 
> to be a 269C and I find the instructions to be somewhat lacking.
>
> Don W7WLL
>
> On 1/12/2020 10:24 AM, David Gilbert wrote:
>>
>> If you have an antenna analyzer that can measure complex impedance 
>> (as in R +/- jX) and if you are willing to put a connector on one end 
>> of the cable, I can tell you how to get an accurate length 
>> measurement using TLW, the transmission line application that comes 
>> free with the ARRL Antenna Book.  You don't need an instrument with 
>> TDR capability (Time Delay Reflectometer) to do it.
>>
>> 73,
>> Dave   AB7E
>>
>>
>>
>> On 1/12/2020 3:44 AM, Phil wrote:
>>> I am involved in selling items to benefit the estate of a SK.
>>> One of the items is a unused roll of 400MAX cable that is still
>>> in the plastic cling wrap it was shipped in.  I know there is
>>> at least 100 feet of cable there but I think there is possibly
>>> 50 or even 100 feet more.  I don't want to unroll the cable to
>>> measure it and get it all kinked or dirty.  The roll weighs
>>> 17 pounds.  I've checked the DXE web site but can't find anything
>>> that gives the weight per foot.  The roll is approximately 8 inches
>>> inside diameter, 16 inches outside diameter, and contains 55 to 60
>>> turns.  The packing label on the roll says DXE400MAXDCU200.
>>> Can anyone help me with a good estimate of the length?
>>>
>>> thanks, 73, Phil   W5BVB
>>
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