# Open Transmission Lines...

by dnyberg2
Tags: lines, transmission
 P: 66 I had an occasion to hook up a piece of open ended coax to a network analyzer. I know the wire has some pF per foot but I expected it to be linear over inches but it wasn't. In other words instead of 5 inches = 5X the pF per foot, the capacitance rises sharply near the end of the coax. Any idea why?
 P: 3,883 You cannot use a network analyzer to measure capacitance like this. I think you miss the concept of transmission line in length approach the wavelength of the frequency. It is not just a capacitor, you have to use solution of wave equation in phasor form to analyze the behavior. For open end tx line, it started out as capacitance. The value increase to infinite ( become short circuit) as length approach λ/4. Then it will flip and become inductive until length approach λ/2, then it will flip back to capacitance.... and on and on for every λ/4 interval. from your example, the wave length of the frequency when you see the jump to very high value is 4X5" which is 20"
 P: 66 This makes sense except, the coax under inspection came at a length of 42". I set the VNA to 49 MHz, Freq of OP, and made measurements as I cut 1" pieces off the end. The coax does indeed flip from capacitance to inductive at ~36" BUT, 36" is NOT a λ/4 of 49 MHz so what else am I missing? Thanks!
 Sci Advisor PF Gold P: 2,241 Open Transmission Lines... The propagation speed in e.g. RG58 coax is about 0.67c (assuming PE dielectric). This means that the wavelength at 49 MHz is roughly 4 meters. And lambda/4 equal to 1m which is approximately 36".... (this is a just-before-bedtime calculation, so I might have made a misstake somewhere....)
P: 3,883
 Quote by dnyberg2 This makes sense except, the coax under inspection came at a length of 42". I set the VNA to 49 MHz, Freq of OP, and made measurements as I cut 1" pieces off the end. The coax does indeed flip from capacitance to inductive at ~36" BUT, 36" is NOT a λ/4 of 49 MHz so what else am I missing? Thanks!
If you have 42", according to f95toli, it is over λ/4, so it should be inductance.

f95toli use RG58 as an example, you have to use your coax to calculate, the dielectric might not be the same and the speed is different.

The equation is $$U=\frac 1 {\sqrt{\mu_0 \epsilon_0 \epsilon_r}}$$

Where U is the velocity of propagation.
 Sci Advisor P: 4,016 The analyser would be an ideal instrument for finding the velocity factor of your coax. Just adjust the frequency until the input impedance drops to a minimum when the opposite end is open circuited. This is usually quite a sharp dip in impedance. You then work out the ratio of this length to a quarter wavelength at the same frequency in air. To find capacitance, you could set the frequency as low as it would go and use a length of line that is a trivial portion of a quarter wave at that frequency. Or, you could use a multimeter that measures capacitance at 1000 Hz. In this case, the length of the coax is not likely to matter.
P: 66
 Quote by vk6kro The analyser would be an ideal instrument for finding the velocity factor of your coax. Just adjust the frequency until the input impedance drops to a minimum when the opposite end is open circuited. This is usually quite a sharp dip in impedance. You then work out the ratio of this length to a quarter wavelength at the same frequency in air. To find capacitance, you could set the frequency as low as it would go and use a length of line that is a trivial portion of a quarter wave at that frequency. Or, you could use a multimeter that measures capacitance at 1000 Hz. In this case, the length of the coax is not likely to matter.

This is great! The coax I am using is a custom made ~50 Ohm invention that is VERY small in DIA. A wire house made it for me, NOT a coax company so, I don't have any idea what the darn dielectric speed is (also known as velocity factor right?) With the post from the one person about how to figure out the velocity factor, I can much better figure out the capacitance. Thanks VERY VERY MUCH!!
 P: 66 F95toil, What is the formula to calculate the resonant length using the velocity factor? Thanks.
P: 3,883
 Quote by dnyberg2 F95toil, What is the formula to calculate the resonant length using the velocity factor? Thanks.
If you want to find the velocity in the coax, get a fix length coax with open end. Run it on a VNA to find the LOWEST frequency that the impedance drop to the lowest. The is the frequency where the λ/4 equal to the length of the coax. Then you times the length by 4 to get the λ. Then times the λ by the frequency to get the velocity.

With this, you can find the $\epsilon_r$ using the formula I gave you using the velocity. $\mu_0$ is the same for non magnetic material which is $4\pi \times 10^{-7}$H/m.