Speed of waves through coaxial cable experiment

[martinv]

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:

The speed at which energy or signals travel down a cable is actually the speed of the electromagnetic wave, not the movement of electrons. Electromagnetic wave propagation is fast and depends on the dielectric constant of the material. In a vacuum the wave travels at the speed of light and almost that fast in air. Propagation speed is affected by insulation, so that in an unshielded copper conductor ranges 95 to 97% that of the speed of light, while in a typical coaxial cable it is about 66% of the speed of light

Experiment 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+

Inner Conductor -  Solid Silver Plated Copper Clad Steel
Dielectric Solid PTFE
Shield: Silver-Plated Copper Flat Ribbon Braid
Aluminum-Polymide Tape Interlayer 36 GA
Silver-Plated Copper Braid (90%k)
Jacket Blue FEP

What is around the conductor affects speed, not the conductor itself.  See last 2 paragrahps in this article:
http://www.ultracad.com/articles/propagationtime.pdf

So 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 = 2.07
Velocity Factor = 0.695

The '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.
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How long does it take the wave to travel from one end of each cable to the other?

We have: 208,355,758 m/S
1/208,355,758  = 
4.8nS/m = 4.8nS/3.28ft = 1.5nS/ft

10ft cable *1.5nS =  15nS delay
20ft cable *1.5nS = 30nS delay

At what frequency will the signals be 180º out of phase
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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 = 33.3MHz
10ft cable = 1/15nS = 66.7MHz

So 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.
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Measurements confirm the theory:

Calculated pattern is
33.3 MHz - 180 deg Out of phase
66.7MHz  - In phase
100MHz  - 180 deg Out of phase
133.3MHz- In phase
166.7MHz - 180 deg Out of phase
200MHz - In phase

Measured results pictured below:
Channel 1 = Yellow Trace = 20 ft cable
Channel 2 = Blue Trace = 10 ft cable
Math 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.
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[robrenz]

Nice job.