Determining Zo for coax cable
 

Some of us may already know this; for those that don't, it could well be useful for you.

If you have test equipment for measuring inductance and capacitance and you need to know the characteristic impedance of a length of coax (which, for the procedure below, should be at least 3m. long or more), you can use the fundamental equation:

Zo = √(L/C) ohms,
where C is in farads and L in henries.

Procedure.
1. Make sure test equipment has warmed up, etc.
2. With one end of the cable open-circuit, measure the capacitance of the cable at the other end: call it C.
3. With one end of the cable short-circuit (can be same O/C end as in step 2), measure the inductance of the cable at the other end: call it L.
4. Then use the equation above.

Example.
Today, in my workshop store room, I found about 40 feet of cable of unknown Zo.
The above procedure produced C = 1800 pF; L = 10 µH.
Calculation result: Zo = 74.5 Ω.
To me, that's Zo = 75 Ω. (Experimental error, etc.)

And finally, yes: I do know that there are several other methods for determining cable Zo. I might discuss them in another thread, which I - or maybe another member - may choose to open.

Al.

Re: Determining Zo for coax cable
 

Good quality 75 Ohm coax (E.G. Suhner) has a tolerance spec of around +/- 1.5 Ohms

David

Re: Determining Zo for coax cable
 

For this method to work the cable needs to be long enough to put the C and L within the range of your LC meter, and short enough that it is still a small fraction of a wavelength at whatever frequency the meter uses.

Re: Determining Zo for coax cable
 

Provided that you know the relative permeability of the dielectric (εr), you can calculate the characteristic impedance (Zo) by measuring the centre conductor diameter (d) and the internal diameter of the screen (D).

The formula is: Zo = (138 x log(D/d))/√εr

For a foamed polyethylene or semi air-spaced dielectric, I doubt the relative permeability will be much above that for air which, of course, is 1 but it might be interesting to try the formula out with some known cable samples to find out.

Getting an accurate internal diameter for a braided outer will, of course, be impossible but it will be the same as the outside diameter of the dielectric.

Re: Determining Zo for coax cable
 

Re: post 3.

For the measurements, I customarily use an HP 4332A LCR meter. It uses two freqs., depending on the range selected (L or C). Highest is 100 kHz; lowest is 1 kHz.
For capacitance, I can also use an R & S capacitance meter (KARU 510). Highest freq. is 175 kHz; lowest is 5 kHz.
Of those two instruments, the shortest wavelength is 1700 m. (≈ 175 kHz).
Any cables that I will ever be likely to measure the Zo of will a lot shorter that 1700 m. ! 8-\

Al.

Re: Determining Zo for coax cable
 

Foamed or semi-air-spaced may be around 1.5, solid poly around 2.

If you measure a known length of coax then you can find out. Speed of propagation is sqrt(1/LC), where L and C are per metre. Compare this with speed of light in vacuum.

Re: Determining Zo for coax cable
 

Of course, the classic method is to use a TDR (time domain reflectometer). IIRC, procedure is as follows. Terminate one end of the cable with a known, calibrated resistance, send a short pulse down the cable and look for (or better still, measure) the magnitude of any return pulse. If zero return, the Zo = that terminating resistance.

Without thinking too deeply about that, it may be possible to build a relatively simple piece of test gear to do that. Any ideas, anyone? :shrug:

Al.

Re: Determining Zo for coax cable
 

I think Alan, W2AEW has several youtube videos showing various homebrew TDR setups where he measures the Zo of a cable. The downside with the TDR method is that it generally requires a fairly long piece of transmission line unless you start using exotic means. It makes a great demo and it's very intuitive but I'm not sure how useful it would be for real world applications unless you have piles of unknown coax cable lying about. Usually the cable type is stamped on it anyway and if it isn't it probably isn't good quality cable.

I rarely 'need' to measure coax Zo but sometimes I need to measure/prove the Zo of twisted pair lines and usually this means measuring something maybe 20-50cm long. The wire would normally go in a wideband transformer, eg 1:1 or maybe a 4:1 and it helps to be able to optimise the Zo to suit the transformer. There are several ways to measure the twisted pair line but it would be tricky to do it with a TDR setup because the line is so short and the line is balanced.

Re: Determining Zo for coax cable
 

We used to use the reverse property at work, where we'd DC-charge a transmission line then discharge it through a switch into a load matched to the line impedance. It's a good way of getting a reasonably square pulse of half the DC-charge voltage and lasting as long as the line's round-trip time, with relatively little happening after the pulse is over.

Cheers,

GJ

Re: Determining Zo for coax cable
 

You can send a square edged pulse down the line with a pot on the end and adjust for the cleanest pulse with scope and a t-piece.
It helps but it's not vital if the sending end has roughly the same impedance as the pot setting. Use a nice low value cermet trimmer.

Ging

Re: Determining Zo for coax cable
 

I'd use a TDR and a terminated length of coax of known-impedance.

Join the unknown and known coaxes in series, then run a TDR. If you can see the transition then the two coaxes are of different impedance.

Though I've always got near-enough by measuring inner/outer diameter ratios. Oddities like RG62A/U [93 Ohm, used for IBM '3270' display-screens] are usually revealed by their construction before you bother to reach for any testgear.

Re: Determining Zo for coax cable
 

Yes, I've done exactly this too. I used a nice 1k log pot that I found in a drawer at work, and put it in a small diecast box with a BNC socket - it lives at work and students use it during practicals.

Why 1k log?

It means that 50 ohms and 75 ohms are easy to adjust, but by turning it fully clockwise, you can easily and quickly get to what is close enough to an open-circuit for the purposes of demonstrating strong reflections to students. Of course, if you use a lin pot, then 50 and 75 ohms will be cramped down near the CCW end stop.

Having adjusted the pot (I suppose I should say "rheostat") for zero reflections, a DC resistance measurement of the pot with a DMM gives a value that is within an ohm or two of the cable spec, which is more than good enough for determining what type of cable it is.

I've tried the inductance/capacitance method plenty of times before, and find the variable resistance box gives more accurate answers more quickly. My difficulty is that I have 3 ways to measure inductance and capacitance at the sorts of values we're talking about. However, all 3 methods give slightly different answers! This, of course, is the classic problem with having more than one meter ;) By contrast, the variable resistance method feels more "direct", simply because by killing all of the reflected pulse, you've - by definition - correctly terminated the cable. Job done :thumbsup:

The source impedance doesn't really make much difference. If the pulse is fully absorbed in the load, then there is nothing coming back needing to be terminated by the source impedance. There are plenty of instances where the source impedance is not the same as the transmission line and termination - the classic examples being transmitters, where losing power in Zout would not be welcome.

Only caveat: don't use a wirewound pot. I'm sure that's stating the obvious for 99.99% of us :thumbsup:

I have thought about building a simple resistance meter into the box - perhaps operated via a changeover switch, or indeed by using a dual-gang pot (assuming the tracking is good enough) to give a live value update. Suitable panel-mount DVM modules are cheap enough from the usual sources. But KISS wins every time - especially when teaching.

Re: Determining Zo for coax cable
 

I have a very simple TDR (actually a telephone line tester, 'Tester 301B'). I found it quite interesting that if I connected 1000 feet of twisted pair (a full reel of ethernet cable) to it I got the expected reflection. Shorting the free end turned the reflection over (if you see what I mean). And when I connected a resistance box to the free end, the reflection disappeared at 100 ohms or so. Said resistance box was not designed for high frequency work either (but I suspect the resistance coils are non-inductively wound).

Nothing like seeing it in practice (on the little CRT of the Tester 301B) to get it to stick in your mind.

Re: Determining Zo for coax cable
 

Isn't because a 180° phase-change has occurred?

Al.

Re: Determining Zo for coax cable
 

Yes Dave. I took Webro's data for WF100 - centre conductor 1mm, inner dielectric diameter 4.8mm, so D/d = 4.8, took the log and multiplied by 138 then divided by 75 and squared the result which was 1.57.

Strange that you don't seem to be able to find the relative permeability figure for foamed PE in any table (well, any that I could find) but solid PE is usually stated at around 2.2.

Re: Determining Zo for coax cable
 

The problem is that the question would immediately be "how foamed ?". There's a compromise between putting as many air bubbles in as possible, in which case the beneficial dielectric properties of the air (particularly low dispersion and low high-frequency attenuation) predominate, and leaving plenty of polythene, in which case the beneficial electrical and mechanical properties of polythene (high breakdown strength, good rigidity to keep the inner centred, and good crush resistance to allow relatively tight bend radii) are retained. Since the wavelength of the RF signals will always be much much greater than the dimesnions of the foam structure the material will look simply like a weighted average of the permittivities of the two materials. You don't need to worry about the permeability by the way. All plastics and air are very close to being non-magnetic (relative permeability of 1).

Cheers,

GJ

Re: Determining Zo for coax cable
 

I was up a ladder at the front of the house, and found I could demonstrate the mechanical equivalent of this to my kids by giving our phone line a big thump and watching the out-of-phase reflection come back from the pole. Well, that dealt with the high-Z termination case. I'll have to creep out at night to the pole and think about how to characteristically terminate it. And the low-Z case will annoy the missus when she wants to use the internet :)

Re: Determining Zo for coax cable
 

Wrap the end in squidgy foam?

Re: Determining Zo for coax cable
 

I’d usually read the value off the insulation.

Sorry, I couldn’t resist.... ;D

Re: Determining Zo for coax cable
 

Hey Al,

I'm scratching my head here.

If the characteristic impedance of some coax is 75 Ohms, (or 50ohms, for that matter), why should I need to measure it?

I don't understand the rationale.

I know from many of your posts that you like to know exactly what you have to hand and often do theoretical calculations, but in this case, I'm left wondering why you wouldn't trust the manufacturer's spec?

I do know how characteristic impedance is theoretically determined and I also note David's reassuring comment on tolerance in post no 2. of the thread.