Nice explanations and derivation of the required formulae. However, in my understanding there is one main flaw which is pretty fundamental: It is stated that the inductance (L') varies with frequency because of the skin-effect. This is correct, however, the phase velocity which is used instead is also frequency specific and not frequency independent! Also, the measured capacitance for a cable also varies with frequency, so the same reason why L' cannot be measured directly (and used to compute Z0) could be applied to C' as well. So the reason why the example measurement turns out to be pretty good is that the lambda-quarter frequency was found at 33 MHz which is a reasonable frequency to measure this cable. I did a quick comparison (with my LiteVNA) between the proposed measuring technique from the video and simply measuring L' and C' directly (at frequencies between 1 - 200 MHz) and found that the error is about the same with both approaches.
The error in low-frequency inductance is much more significant in my experience. I don't have my data, but I believe it was something like measuring 55 Ohms for the characteristic impedance vs 49.5 Ohms after the correct. No measurement is ever going to be perfect, but you can certainly talk sensibly about degrees of error and uncertainty. It is also instructive to realize that the artifact is not a problem with the measurement itself, but a real physical effect within the cable.
Hi, thanks for the video :-) I got a question : As the connector of NanoVNA is an SMA, its impedance is 50 ohm. So if we use a cable with not 50 ohm impedance, there will be mismatch between cable & connector. I would like to know if in this case the calculus you used is still valid for determining the caracteristic impedance of the new cable ? Thanks !
Sir, thank you for this teaching. 2 things that I don't understand, how you came up with Vp=4piL, and speed of light I know as 3x10th8. Thank you for your help.
That beta is supposed to be phase constant. It denotes the change of phase per unit length along the path travelled by the wave. In your experiment, at 33MHz, the change of phase over the length of the cable is pi/2. Which means (pi/2)/L = beta, and hence leads to your equation beta * L = pi/2.
@@jamesnagel2872 No you were not confused - you were good. I was not trying to lecture you, but to point out that you incorrectly mentioned that the beta is the Propagation Constant instead of Phase Constant. And also gave a simpler way to derive your final formula on the first line.
@@tze-venAh, I think I see what you’re saying. You are correct that the terms “propagation constant” and “phase constant” are not the same thing. However, the distinction is subtle. The main difference is when the transmission line has attenuation. In that case, the propagation constant also accounts for attenuation. For lossless lines, however, they simplify into the same thing and are thus interchangeable.
Dear James. I have tried to measure 50 Ohm cable with l=10.07m, 382pF total capacitance and 5,405MHz frequency where on Smith chart is short point. Regarding your calculations I am getting around 121 Ohm. Where I am wrong?
Half way along a Smith chart is 90 degrees isn't it? In other words going from open (right side) to short (left side) takes half a circle or 90 degrees. so the cable's length is half of that or 45 electrical degrees because the signal travels forward & back.
Thanks for the great explanation, quick but clear! One question though, you mention you're not measuring the inductance at low frequency as it varies too much. Does that make the value you now got specific to the 33MHz frequency at which you found the 1/4 wavelength propagation?
There is a "transition" bandwidth where the characteristic inductance varies, but it eventually stabilizes as the frequency gets very large. It happens because the skin depth is decreasing with frequency. Eventually, the skin depth gets so small that the current can be approximated as a thin sheet along the conductor edges, and this is where the inductance stabilizes.
Because when he dialed the marker on the smith chart to the short (closed) position, the first passage over the horizontal line, this is the frequency where the specific piece of cable that is hoked to the NanoVNA acts as a quarter line "stub" for the given frequency, so effectively you used the NanoVNA to find out the what is the frequency where that happens for this cable, where. So now that he knows that at this electrical length, beta*l, the cable is exactly pi/2, a quarter wave.
Hi John, the nanoVNA can't directly measure the characteristic impedance of a feedline. There are numerous ways to determine (or approximate) the characteristic impedance of a feedline using the nanoVNA. There are easier methods using the nanoVNA but James looked at it from a classical transmission line theory approach which was indeed interesting (brought back memories from my college days studying transmission lines and propagation of energy).
The best explanation I've seen how to understand why it is used 50 Ohm impedance cable. Thank you very much.
Nice explanations and derivation of the required formulae. However, in my understanding there is one main flaw which is pretty fundamental: It is stated that the inductance (L') varies with frequency because of the skin-effect. This is correct, however, the phase velocity which is used instead is also frequency specific and not frequency independent! Also, the measured capacitance for a cable also varies with frequency, so the same reason why L' cannot be measured directly (and used to compute Z0) could be applied to C' as well. So the reason why the example measurement turns out to be pretty good is that the lambda-quarter frequency was found at 33 MHz which is a reasonable frequency to measure this cable. I did a quick comparison (with my LiteVNA) between the proposed measuring technique from the video and simply measuring L' and C' directly (at frequencies between 1 - 200 MHz) and found that the error is about the same with both approaches.
The error in low-frequency inductance is much more significant in my experience. I don't have my data, but I believe it was something like measuring 55 Ohms for the characteristic impedance vs 49.5 Ohms after the correct. No measurement is ever going to be perfect, but you can certainly talk sensibly about degrees of error and uncertainty. It is also instructive to realize that the artifact is not a problem with the measurement itself, but a real physical effect within the cable.
Thanks for valuable mathematical insights with total conceptual Clarity on electro-optical Networked vectors transmission line.
I enjoy your videos, please keep posting!
Wow. What a valuable scientific information. It's like put light on darkness.
Zo=Sqrt(Zin_sc x Zin_oc) so simply measure Zin of open circuit and short circuit at any frequency, and you get Zo.
Hi, thanks for the video :-) I got a question : As the connector of NanoVNA is an SMA, its impedance is 50 ohm. So if we use a cable with not 50 ohm impedance, there will be mismatch between cable & connector. I would like to know if in this case the calculus you used is still valid for determining the caracteristic impedance of the new cable ? Thanks !
Sir, thank you for this teaching. 2 things that I don't understand, how you came up with Vp=4piL, and speed of light I know as 3x10th8. Thank you for your help.
Also, what is not stated is that it is vital to properly calibrate the NVA before the measurement!
That beta is supposed to be phase constant. It denotes the change of phase per unit length along the path travelled by the wave. In your experiment, at 33MHz, the change of phase over the length of the cable is pi/2. Which means (pi/2)/L = beta, and hence leads to your equation beta * L = pi/2.
Yes, I know. Did I give some indication I was confused somewhere?
@@jamesnagel2872 No you were not confused - you were good. I was not trying to lecture you, but to point out that you incorrectly mentioned that the beta is the Propagation Constant instead of Phase Constant. And also gave a simpler way to derive your final formula on the first line.
@@tze-venAh, I think I see what you’re saying.
You are correct that the terms “propagation constant” and “phase constant” are not the same thing. However, the distinction is subtle. The main difference is when the transmission line has attenuation. In that case, the propagation constant also accounts for attenuation. For lossless lines, however, they simplify into the same thing and are thus interchangeable.
@@tze-vengreat work 👌👏👍
Should you be doing this with your coax coiled in a tight loop?
Awesome! Just had a chance watching this 3 year old video. Could someone explain why Vp=0.67c?
Thank you and will look into your other videos!
73… 😊
Dear James. I have tried to measure 50 Ohm cable with l=10.07m, 382pF total capacitance and 5,405MHz frequency where on Smith chart is short point. Regarding your calculations I am getting around 121 Ohm. Where I am wrong?
Thank god for technology!Now we can consider a VNA a household item!
😁
Half way along a Smith chart is 90 degrees isn't it?
In other words going from open (right side) to short (left side) takes half a circle or 90 degrees. so the cable's length is half of that or 45 electrical degrees because the signal travels forward & back.
Nice demonstration, seems like nanovna is good as capacitance meter at low frequencies.
Thanks for the great explanation, quick but clear! One question though, you mention you're not measuring the inductance at low frequency as it varies too much. Does that make the value you now got specific to the 33MHz frequency at which you found the 1/4 wavelength propagation?
There is a "transition" bandwidth where the characteristic inductance varies, but it eventually stabilizes as the frequency gets very large. It happens because the skin depth is decreasing with frequency. Eventually, the skin depth gets so small that the current can be approximated as a thin sheet along the conductor edges, and this is where the inductance stabilizes.
You would be a talented teacher. Interesstig video.
Great video. Thank you!
Thanks for the video. Why beta*l=pi/2? Could you explain this passage better? Why pi/2?
Because when he dialed the marker on the smith chart to the short (closed) position, the first passage over the horizontal line, this is the frequency where the specific piece of cable that is hoked to the NanoVNA acts as a quarter line "stub" for the given frequency, so effectively you used the NanoVNA to find out the what is the frequency where that happens for this cable, where.
So now that he knows that at this electrical length, beta*l, the cable is exactly pi/2, a quarter wave.
The nanoVNA can be set up to read out the impedance directly without going through a bunch of calculations.
Hi John, the nanoVNA can't directly measure the characteristic impedance of a feedline. There are numerous ways to determine (or approximate) the characteristic impedance of a feedline using the nanoVNA. There are easier methods using the nanoVNA but James looked at it from a classical transmission line theory approach which was indeed interesting (brought back memories from my college days studying transmission lines and propagation of energy).
Thank you
THANKS !!!!!!!!!
Huh?
I have no idea what your talking about? Been a ham for 45 years
han is ok, at least you weren't a hun.