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#1
Mar812, 11:11 AM

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?



#2
Mar812, 12:15 PM

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" 


#3
Mar812, 02:31 PM

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!



#4
Mar812, 04:27 PM

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 justbeforebedtime calculation, so I might have made a misstake somewhere....) 


#5
Mar812, 07:59 PM

P: 3,883

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 [tex]U=\frac 1 {\sqrt{\mu_0 \epsilon_0 \epsilon_r}}[/tex] Where U is the velocity of propagation. 


#6
Mar812, 09:47 PM

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. 


#7
Mar912, 08:54 AM

P: 66

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!! 


#8
Mar912, 09:17 AM

P: 66

F95toil, What is the formula to calculate the resonant length using the velocity factor? Thanks.



#9
Mar912, 12:18 PM

P: 3,883

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


#10
Mar912, 01:43 PM

Sci Advisor
PF Gold
P: 2,241

Then calculate the wavelength using the usual lambda=cp/f relation 


#11
Mar912, 06:26 PM

Sci Advisor
P: 4,016

Wavelength in air = speed of light / frequency
= 300 000 000 meters/second / frequency in Hz = 300 / frequency in MHz..... usually more convenient. example: the wavelength of a signal of frequency 50 MHz in air is (300 / 50) or 6 meters. A quarter wave length is 0.25 times the above value or you could modify the formula to 75 / frequency in MHz example a quarter wave at 39 MHz is 75 / 39 or 1.92 meters. In a transmission line (eg coax) the formula becomes (velocity factor * 75 / frequency in MHz) example a quarter wave at 39 MHz in coax with a velocity factor of 0.72 is (0.72 * 75 / 39) or 1.38 meters. Velocity factor is a number between 0 and 1 which is the ratio of the speed of radio waves in the transmission line divided by the speed of radio waves in air. 


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