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measure the characteristic impedance of a line
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Good morning
I am trying to measure the characteristic impedance of various transmission lines, especially in order to build line transformers. I submit to you the case of a coaxial cable insulated with tfleon of 2 mm in diameter. I have other measurements for two-wire lines but the case of 50 ohm coaxial is more trivial. I attach you - My report explaining why and how - My Excel file supporting the calculation Please - Could you explain to me what I see? - Am I making a reasoning error in the measure? -- F1AMM Fran?ois |
The current version of Nanovna-H firmware includes a feature for this:Yes, but I have an NanoVNA-F and I take the measurements using nanaovan-saver. Do you know the algorithm (method) used in the -H to calculate this characteristic impedance? I measured with a 50 ohm cable from 1m Radial source. The result is clearer but I don't understand the discontinuity near the 1/4 wave (48.439 MHz). -- F1AMM Fran?ois -----Message d'origine-----De la part de DougVL Envoyé : mercredi 10 mai 2023 13:38 |
Hi, I am not sure but something with the velocity factor. 50 MHz, 6 meter multiplied bijThe 1/4 wave (48.439 MHz) is for |Z| is infinite (read on the graph of nanovna-saver), the line being short-circuited. This frequency is identified on the value of Zc in attachment; it is shifted on the pattern. This brings a doubt on the formula, especially since then the value of Zc goes from 50+4 ? to 50-4 ?. - What does -H say in this case? - Does it use the same formula? -- F1AMM Fran?ois -----Message d'origine-----De la part de alex Envoyé : mercredi 10 mai 2023 14:01 |
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Hello Francois,
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You do not mention if the cable is open or shorted in your attachment "Cable 50 - 1m - dia5mm" but I believe what you are seeing is the phase change as the cable "looks" alternately Capacitive then Inductive every 1/4 wavelength. Overlay the Smith Chart and Phase traces on the NanoVNA-F screen and you will see it. It becomes obvious as you move a marker across either linear trace. You will also notice the Smith trace tends to spiral inwards indicating increasing cable loss as the frequency increases. HTH...Bob VK2ZRE On 10/05/2023 9:52 pm, Fran?ois wrote:
The current version of Nanovna-H firmware includes a feature for this:Yes, but I have an NanoVNA-F and I take the measurements using nanaovan-saver. |
You do not mention if the cable is open or shorted in your attachmentOk. This graph is the result of a calculation in Excel. There are *2 measures of the S11* : - Coax line being open - Coax line being short-circuited I attach the file "50 Ohms 5 mm.xlsx" which corresponds to this cable of 5 mm length 1 m. Graphs are visible in the .xlsx file and you can see how they are calculated. - In the sheet "Calculations (Open)" it is the S11 in open circuit which is used - In the sheet "Calculations (Close)" it is the S11 in short circuit which is used - In the sheet "Zc" we perform the calculation of Zc 73 -- F1AMM Fran?ois -----Message d'origine-----De la part de Bob Ecclestone VK2ZRE Envoyé : mercredi 10 mai 2023 15:54 |
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Hi Fran?ois,
I suggest that you go back to the very basics, and do this: 1.- Calibrate your NanoVNA 2.- Connect a piece of that coax cable, with very clean, short, direct contacts to the same points at which you calibrated the NanoVNA. 3.- With the other end of the coax cable open, but not stripped (that is, clean-cut), measure the capacitance, in a range from the lowest frequency your NanoVNA covers, to about 1MHz or so. You will see a curve, that gets noisy towards the low end of frequency. Mentally draw that curve cleanly to zero frequency. That's the capacitance of your cable sample. 4.- Now short the far end of the cable, with a very direct, clean short. Measure the inductance of the cable, in the same way you measured the capacitance in the previous step. 5.- Divide the inductance by the capacitance, using base units (henry and farad), and take the square root of the result. That's the cable's impedance. |
You have to know the velocity in the cable for this measurement. (So you already assume toNo, I agree with Manfred Mornhinweg, it is not necessary to know the velocity coefficient. Open line closed etc. that's what I do. Nevertheless : --------------- 1/ The characteristic impedance at low frequency is not the same as at high frequency because at low frequency the linear resistance becomes significant compared to the linear choke. It can be seen very well when measuring L and C with an BF bridge (1 kHz, 10 kHz 100kHz). 2/ The characteristic impedance is not purely real as soon as there are losses. In wired telephony, to terminate a telephone line correctly, a trellis network is used as a load. 3/ The formula that I use, and of which I am not sure, but that one finds in the literature and that I exposed in the document Please-en.pdf makes it possible to generalize the measurement of the characteristic impedance and , in particular, its variations as a function of frequency. 4/ When we use the /3 formula, then we see that there is a problem when we arrive at the quarter wave and that, before and after the quarter wave, the value of Zc is not the same. Why this apparent limitation to "the formula" For what : ----------- I study Ruthroff transformers where the characteristic impedance of the lines strongly characterizes the bandwidth. -- F1AMM Fran?ois -----Message d'origine-----De la part de Flam Boom Envoyé : mercredi 10 mai 2023 18:56 |
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Hello Manfred,
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I purchased a nanoVNA-H4 about a month ago and use it mainly to measure my 80-10M antenna SWR, low pass filter response, and toroidal inductor inductance.? Thank you for the very concise description of how to measure coaxial cable inpedance.? I'll give that a try at some point. Best Regards, SteveH N0GWC On 5/10/23 11:40 AM, Manfred Mornhinweg wrote:
Hi Fran?ois, |
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I have what? hope to be a quick question. Here lately I have the need to find the resonance of antennas. Mainly 75 Ohm CATV headend antennas. I have been using the Nano VNA Saver app to do this. I have calibrated the VNA by open and short at the end of the 75 ohm jumper cable I connect to the antenna. The odd thing is while not changing anything and repeating the test I may get different readings each time. Also when I go to the analysis tab on occasion it won't open and the entire Nano VNA Saver program will terminate.? Is the a more reliable way to find resonance of an antenna?? The reason behind this is to find a close as possible match to the digital frequencies as these are older antennas optimized for analog. I'm running WIN 10 Pro 64 on a Toughbook laptop and 0.5.5 VNA Saver. Thanks for any assistance I'm just getting started with this machine and read the tutorials several times LOL
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Wt On 5/10/2023 1:41 PM, SteveH wrote:
Hello Manfred, |
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Be careful about this. The capacitance will vary little with frequency, but the inductance will drop off from its zero frequency value with increasing frequency, becoming asymptotic to some constant value at high frequencies. That's why the expression sqrt(L / C) is constant and indicative of the characteristic impedance over a wide range of frequencies.
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At zero frequency, the total inductance of a coaxial cable includes both internal and external inductance, that is, internal to the center conductor and external to it. The internal inductance at zero frequency can be shown to be independent of the diameter of the conductor and is Lidc = 0.05 uH / meter (Ref. 1, equation 6.5, page 72) The external inductance is not independent of the diameter of the center conductor and is shown to be proportional to the natural log of the ratio of the radius of the interior of the coax to the radius of the center conductor. At zero frequency, and at low to medium frequencies, both internal and external inductance are contributors to the total inductance of the coax. At high frequencies, skin effect reduces the internal inductance to an insignificant value and it may usually be ignored. Chipman (Ref. 1, example 6.4 on page 96) works out the characteristic impedance of a typical coaxial transmission line assuming that the internal inductance is negligible and is therefore ignored. He gets a characteristic impedance of 52.4 ohms. I reworked the problem, using Zo = sqrt(L / C) with both internal and external inductance included, as would be the case if I measured the inductance at zero frequency and I get Zo = 57.3 ohms. Not much error here, but it depends on what sort of accuracy you are after. Ref. 1: Robert A. Chipman, "Schaum's Outline Series, Theory and Problems of Transmission Lines," McGraw-Hill, 1968 73, Maynard W6PAP On 5/10/23 09:40, Manfred Mornhinweg wrote:
Hi Fran?ois, |
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Hi Francois,
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We have all been side tracked here. That is what happens when I try to think clearly at midnight:-) The simple answer to your noted low impedance is because your sample test cable is an electrical quarter wave open circuit stub at around 48MHz. At an electrical quarter wave (taking account of Velocity Factor), an OPEN circuit cable looks like a SHORT circuit. This repeats every ODD quarter wave frequency. On a Z Smith chart, the marker will be near the far left hand side. Similarly, a SHORT circuit cable will look like a very high impedance (OPEN circuit) at ODD 1/4 wave frequencies. On a Z Smith chart, the marker will be near the far right hand side. These characteristics are what are used in repeater cavity duplexers for example. A cavity is only a length of transmission line. At the EVEN quarter wave (1/2 wave and multiple) frequencies, the impedance repeats the cable termination. That is, a SHORT looks like a SHORT and an OPEN looks like an OPEN. The Smith chart (Z or Y) will do a full 360 degree rotation. You can demonstrate this quite simply to yourself. Set up an open circuit cable and sweep through the 1/4 wave frequency. I suggest you display the Z, Phase and Smith traces on the NanoVNA screen and set a marker at the 1/4 wave frequency. While still sweeping, short circuit the open end of the cable. I use the Short from the Calibration SOLT kit when demonstrating this effect. You will see the 3 traces "swap" between Open and Short. HTH...Bob VK2ZRE On 11/05/2023 12:21 am, Fran?ois wrote:
You do not mention if the cable is open or shorted in your attachmentOk. |
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On Wed, May 10, 2023 at 07:52 AM, Fran?ois wrote:
Sorry, but that wasn't clear. Do you know the algorithm (method) used in the -H to calculate thisThe source code for the App is openly available, at the same web site as the program download. -- Doug, K8RFT |
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Francois is exactly right about telephone cable pairs. In radio work, we are used to the expression sqrt(L / C) which yields a real value, representative of the characteristic impedance across a wide range of frequencies for which wL >> R and wC >> G where w is the radian frequency. At lower frequencies R >> wL and G isn't significant for most cable pairs, so the characteristic impedance may be approximated by sqrt(R / jwC). Note that this expression yields an angle of -45 degrees so the real and imaginary parts of the characteristic impedance are equal in magnitude. That's why listings of Zo for voice frequency telephone cable pairs have negative angles of nearly 45 degrees.
This won't matter for most of our radio work, but when making measurements or calculations at frequencies of a few hundred kHz or below, be careful as sqrt(L / C) may not be very accurate for some cables at some frequencies. 73, Maynard W6PAP |
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Let's take the problem from another angle.
Doug, K8RFT told us: ----"----- The current version of Nanovna-H firmware includes a feature for this: Look at the "NanoVNA Menu Structure Map" and find Measure>Cable(S11) That is a wonderful new feature that I find to be VERY useful. ----"----- If anyone knows how to read the firmware code can you tell us how the characteristic impedance is calculated and displayed. measure.c ? I did C so I know a little but I can't find anything about the characteristic impadance Perhaps a screenshot of this functionality, applied to a length of coax, would be a good start. On Measuring cables, the initial frequency - minimum, final - must be such that the cable length is more than 1/4 of the wavelength, automatically measures the length, characteristic impedance, loss at the point of the active marker. The measuring range is chosen so that the Smith is rotated clockwise 180 degrees, the most important point for this measurement is at marker 1. The shorter the cable, the higher the maximum frequency. Can you explain to me how this measure is implemented? One of the questions is whether my formula Square root (Zcc * Zopen) is legit - Zcc is the *complex* impedance measured with the end of the line being short-circuited - Zopen is the *complex* impedance measured with the end of the line being open The calculation is done in Excel in the form =COMPLEX.ROOT(COMPLEX.PRODUCT(B30;C30)) -- F1AMM Fran?ois |
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On 5/11/23 7:09 AM, Fran?ois wrote:
Let's take the problem from another angle. The transmission line equation is: Zin = Z0 * (Zload*cosh(gamma) + Z0*sinh(gamma))/ (Zload*sinh(gamma)+Z0*cosh(gamma)) gamma is the propagation constant alpha + j beta, where alpha is in nepers and beta is in radians. For a *lossless* line, 1/4 wavelength cosh(gamma) =0 and sinh(gamma) = 1, so that simplifies a lot. The tricky part here is that short is easy = Zload = 0, so Zin = Z0 * ( Z0 * sinh(gamma))/(Z0*cosh(gamma) = Z0 * sinh(gamma)/cosh(gamma) But when Zload is infinite, you need to flip it around and use the admittance form: Yin = Y0 * (Yload*cosh(gamma)+Y0*sinh(gamma))/(Y0*cosh(gamma)+Yload*sinh(gamma)) Y0 is 1/Z0 And now, Yload = 0, so: Yin = 1/Z0 * sinh(gamma)/cosh(gamma) Then invert again to get back to Z Zin = 1/(sinh(gamma)/(Z0*cosh(gamma)) = Z0*cosh(gamma)/sinh(gamma) Now you have a Zopen = Z0 * sinh(gamma)/cosh(gamma) and Zshort = Z0 * cosh(gamma)/sinh(gamma). Some algebra would get you to something useful, if you expand cosh and sinh. After all, in your test, gamma is constant (if unknown) the square root of the product works, but only for certain lengths (i.e. 1/4 wavelength) More info in the attachment. |
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Hi Francois,
Not sure if this helps answer your question, but where you see the large deviations from the nominal expected value of approximately 50 ohms in your plots I believe those large deviations are happening when you are making measurements where the NanoVNA is least accurate as I believe the impedance is either close to 0 ohms or close to infinite where you are seeing those large deviations (not exactly 0 and not exactly infinite due to losses in the coax). I believe The NanoVNA uses a 50 ohm resistive bridge design and most accurate measurements are made when you are measuring impedances close to the 50 ohm design of the bridge. As impedances being measured get further from the 50 ohm design the accuracy in measurement starts to degrade and I suspect that's the biggest factor why you are seeing what you are seeing (I think it's just inaccuracy due to operating the NanoVNA in a range where it's least accurate). Just my opinion based on a quick read of your posting. Don wd8dsb |
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