This is a follow-up to How to make a phase shifter?, it seems one answer is to simply have different lengths of coax going to each antenna. However, how do I calculate the difference in length given the desired phase and frequency? My first assumption was that the signal should move at the speed of light, and so the calculation would be:
wavelength * (phase shift in degrees/360)
But then I remembered reading somewhere that a signal does not move at the speed of light through regular cable, but rather a fraction slower (2/3? 3/4?). Do I need to take the material the cable is made with into account?
Edit: To be clear, I'm hoping for a direct equation I can use to determine how to cut the length of cable in front of me.
Best Answer
Velocity factor is the proportion of c (speed of light) that a signal travels at in a cable: -
VF = \$\dfrac{1}{c\sqrt{LC}}\$
Where L and C are the distributed inductance and capacitance per metre length of the cable. Little "c" is the speed of light.
You can use \$\epsilon_R\$ as well because \$\mu_R\$ can be assumed to be unity: -
VF = \$\dfrac{1}{\sqrt{\epsilon_R}}\$
So (with the assumption that VF = 1) if you have a piece of coax that is 7.5m long and you feed it with a 10 MHz sinewave, the delay (phase shift) will be 90 degrees. If it's 15m long then the delay will be 180 degrees. A 30m length will look like the same phase as the original sinewave expect it will be lagging by one full wavelength.
If VF = 0.6667 (for example) the signal takes longer to travel a fixed distance than the speed of light hence, to obtain a 90 degree phase shift at 10MHz requires a length of cable that is 0.667 x 7.5m = 5m.
If all you can find is the characteristic impedance and capacitance per unit length you can also calculate VF like this: -
VF = \$\dfrac{1}{C\cdot Z_0}\$ because \$Z_0 = \sqrt{\dfrac{L}{C}}\$