Part 1 – Checking the Velocity Factor of the Coax Cable
I have a homebuilt Collinear Antenna on one of my two ADS-B receivers. It’s a 8 element antenna, built without any real effort of making sure that all the elements where the right length. So it’s about time to try to do it properly.
To build a good antenna, you would preferably use a Vector Network Analyzer so you can do proper measurements of your antenna design. With it you can easily check stuff like SWR and optimize the impedance of the antenna at the frequency it’s intended to be used at. In my case 1090MHz for ADS-B. But if you don’t have the money to spend, you have to improvise. I’m going to build a 12 element Collinear Antenna out of cheap RG-58 coax cable. But to calculate the right length of each element, we need to know the Velocity Factor, or the signal speed through the cable compared to light traveling in vacuum. So let’s do the measurements.
I got a long stretch of some old RG-58 coax cable that was used for connecting a cash register to a server a long time ago. You could just go by the velocity factor values you find on the internet for RG-58, which the almighty Google says is 0.66. But using this value in my case would be wrong, and the calculations would end up with an antenna way out of the optimal performance, as we shall see.
The Measurement Setup
Here’s what we are going to do. Send a pulse with fast rise time (in my case a pulse with 9.5 ns rise time) from a signal generator at relatively long pulses, in my case with a Siglent SDG2122X 120MHz Waveform generator (Actually a hacked SDG2042X.) The pulse goes into an oscilloscope, with a T-BNC connection. Connect the coax cable to the other BNC connector on the T-connector. When the pulse is sent, it first shows up as a quick rise on the oscilloscope, but the signal will travel down the unterminated coax cable and reflect back. This will double the signal when it reaches back to the oscilloscope. So using cursors, we can measure the travel time of the signal and divide it by two to get the propagation time.
Ok, and let’s connect the unterminated cable. Now we see the adding of the returning signal from the coax cable.
The pulse width should be long enough, because we want to be able to measure short cables. If you don’t have a signal generator with a fast rise time (the faster the better), you can actually build a pulse generator with extremely fast raise and fall edges of about 1.2 ns for about a dollar. Here’s a video on how to build it.
Here’s the settings on my signal generator with 8.4ns rise time. I’ve set the output to 50 Ω impedance to match the connections at the oscilloscope.
Calculating the Velocity Factor of the Coax Cable
So now it’s time to use the cursors on the scope for measuring the time for the signal to go to the end of the unterminated cable and echo back.
So the Δ between the start of the pulses are 91ns. The propagation time is half of that, 91÷2=45.5ns for the signal to go one way through the coax cable. The cable is 950 cm long and the distance light travels in vacuum in 1 ns is 29.99709 cm.
950cm ÷ 45.5ns ÷ 29.99709ns = 0.696038 Velocity Factor. The factor is 0.696 times the speed of light.
Will the specified value of 0.66 and 0.696 VF make a difference when doing the calculations for the lengths of the sections of the antenna? Lets check.
The formula for calculating the length of each element is:
c = speed of light in vacuum 299 792 458 meters per second.
f = Frequency, 1090MHz for ADS-B
Length of element = (half wave length in meter) 0.2750389523 ÷ 2 = 137.5194761468 * (VF)0.696 * (convert to cm) 100 = 9.4888438541 cm
So the length of each of the elements should be 9.49 cm with this cable. But how much would it have differed if I used the official velocity factor from the manufacturer? Then the result would have been 9,08 which is almost 5 % off target. Will this make a difference? We’ll see when I build an antenna. You can find a handy calculator for calculating both ½ and ¼ wave length for collinear antennas with build instructions here.
In the next installment, I’ll do the assembly of the antenna and do some comparisons against my Flightaware Antenna and my old bodged together collinear antenna.