Speed of waves through coaxial cable experiment - Page 1
Forum section: electronics / projects

author: martinv
author_rank: Contributor
timestamp: January 12, 2013, 05:52:52 am
content: Just for fun and to play with my new oscilloscope, I wanted to see if I could measure the effects of delay time through a coaxial cable and see the effects vs frequecy.Basically I took 2 equal cables except 1 was twice as long and ran the same rf signal through both using a T splitter, then fed the other ends into 2 channels of my oscilloscope.Not sure if my theory is correct, but it seemed to work out. Here it is:From Wiki:QuoteExperiment 1:2 equivalent coaxial cables, except one is twice as long as the other.An RF signal generator (HP8660D) feeding both using a Y adaptor. The end of each cable is fed into a 2 channel oscilloscope.At any instant in time the signal level is exactly the same at the side of the cables connected to the signal generator. At the other end of the cables the signal will take twice as long to reach the longer cable.How long should depend on the cable properties (type of insulation, conductor, etc).Cable used:Mini-Circuits CBL-10FT-SMSM+QuoteWhat is around the conductor affects speed, not the conductor itself. See last 2 paragrahps in this article:http://www.ultracad.com/articles/propagationtime.pdfSo in my case the Dielectric, which is Solid PTFE between the center conductor and the shield is what matters. The jacket does not matter because the field is on the inside of the shield, not outside. (although I think i've seen cases where a small fraction of the field gets on the outside, and seemed to be most noticable in low quality cables).Solid PTFE:Dielectric Constant = 2.07Velocity Factor = 0.695The 'Velocity Factor' formula:Vp = 1 / SQRT (dielectric constant)The Velocity Factor is the fraction of speed vs the speed of light. So a velocity factor of 1 is the speed of light.So the speed of the signal through my cable should be .695 * the the speed of light. Speed of light is 299,792,458 meters/second.Velocity in my cable is 208,355,758 m/S.--------------------------------------------------How long does it take the wave to travel from one end of each cable to the other?We have: 208,355,758 m/S1/208,355,758 =4.8nS/m = 4.8nS/3.28ft = 1.5nS/ft10ft cable *1.5nS = 15nS delay20ft cable *1.5nS = 30nS delayAt what frequency will the signals be 180º out of phase------------------------------------------------------------------At what frequency will the signals be 180º out of phase and what frequency will they be at 0º?Assume the wave is a 2V P-P sine and is starting at its + peak of 1 Volt.At 15nS the far end of the 10ft cable will have 1V and the half way point of the 20ft cable will have 1V.At some frequency, the begnning and end of the 20ft cable should have 1V at the same time -1V will be at the 10ft center point. The 10ft cable will have 1V at the source and -1V at the end during this same point in time.Since f=1/t,20ft cable = 1/30nS = 33.3MHz10ft cable = 1/15nS = 66.7MHzSo when injecting a +/-1 V, 33.3Mhz sine wave, the far end and source end of the 20ft cable should be at 1 V.(in the format source end, far end)20ft Cable = 1V, 1V (one full cycle)10ft Cable = 1V, -1V (0.5 cycle)At 66MHz,20ft Cable = 1V, 1V (this is 2 full cycles)10ft Cable = 1V, 1V (one full cycle)At 99MHz,20ft Cable = 1V, 1V (3 full cycles)10ft Cable = 1V, -1V (1.5 cycles)This will repeat at 33.3MHz intervals.-------------------------------------------------Measurements confirm the theory:Calculated pattern is33.3 MHz - 180 deg Out of phase66.7MHz - In phase100MHz - 180 deg Out of phase133.3MHz- In phase166.7MHz - 180 deg Out of phase200MHz - In phaseMeasured results pictured below:Channel 1 = Yellow Trace = 20 ft cableChannel 2 = Blue Trace = 10 ft cableMath Channel = Purple Trace = CH1 + CH2. This channel only reached ~0V at the specific out of phase frequencies.NOTE: The RIGOL DS2072 oscilloscope used is only rated for 70MHz. This caused the overall amplitudes to reduce as frequency increased, but the relationships between the channels still makes the results valid for the intended purpose.------------------------------------------------------------------------------------------------

author: robrenz
author_rank: Super Contributor
timestamp: January 12, 2013, 03:55:46 pm
content: Nice job.