Hopefully, the Element14 team will consider fast edges to be an RF topic.
I have really enjoyed participating in Project14 events, as its allowed me to explore topics that I don't have any direct experience in with the support and advise of the Element14 community.
For this month's project, I will attempt to try and perform fluid level sensing with Time Domain Reflectometry (TDR).
I post this project as a basic outline presently for feedback or suggestions.
Some of the project graphics put together thus far, that I will cleanup in the coming days:
Measurement Coaxial Line
Technically all that is needed is a waveguide, but this would require trying to design, fabricate and match a launcher to a waveguide.
So, to keep things "simple" (the fast edges are making this project complex enough) I will construct porous air-core coaxial line out of a piece of copper plumbing pipe with a wire pulled taught down the center.
The length of the measurement coax is completely arbitrary, I just used what I had lying around. Though if you are intending to scope the TDR waveforms with an entry-level DSO like me, I would suggest the longer the better.
In hindsight taking a trip to the hardware store to source some copper pipe caps would be far easier as you could solder them on with a blow torch. Hand soldering FR4 coupons into the pipe ends was quite tedious and slow. I had to let my soldering iron preheat the pipe for at least a minute before I could get the smallest amount of solder to flow near the iron tip (the copper pipe is one big heatsink).
The 24AWG wire is soldered to the BNC connector then the wire is feedthrough the copper tube. The BNC connector is held in place with tension from the center conductor. I'm certain those more mechanically competent than I could find a better mounting solution, perhaps taping a mounting hole or soldering a brass jam nut. The 24 AWG wire is pulled taught and then soldered at the end. The oversized hole was the result of trying to drill press machine the mounting plugs, which did not work as well as I had hoped. However, it is also large enough to allow water to ingress into the coax line.
Now that I have the actual dimensions, I can calculate the characteristic impedance and the velocity factor along the coaxial line.
I calculated the reflection coefficient on each impedance boundary transitioning from Za to Zb shown in the table below.
When you look at the TDR response on an oscilloscope there is a lot going on and I was having a hard time keeping track of everything off the top of my head. So I constructed a TDR lattice diagram for the first 4 significant reflections.
For measurement purposes we really only care about timing V2 and V6. However, V12 is the pulse I eagerly wish to see on my oscilloscope, as not only is it a TDR pulse through water, it should propagate at almost 1/9 the speed of light.
I calculated each reflection with first incident TDR pulse normalized to an amplitude of 1, the results are shown in the table below:
Replotting all the Spice parameter step results as a gif:
I was able to dig up a TDR pulser I constructed a few years ago on copper clad:
I connected the TDR pulser up to my oscilloscope as shown in the Ascii diagram:
TDR Pulser - RG58 -> _|_ -> RG58 -> (Open/Short/Load)
The roundtrip TOF on 3 ft (6 ft effective) of RG58 was approximately 9.5 ns. This results in a measured propagation velocity of 1.58 ns/ft which is only 2 percent off the quoted specification of 1.54 ns/ft. Equivalently, this discrepancy is equivalent to an extra 1.5 in of line length which is comparable to the length added by the BNC-T and BNC-FF coupler. All in all, I think that is pretty awesome, to see signals propagate at 2/3 the speed of light on my oscilloscope. With a small pulse duration it is easier to discern on a scope plot that the second pulse waveform is the actual reflected TEM wave (so awesome!). For the digital readout phase of the project I will launch much longer duration pulse from a GPIO pin and study the reflections from the rising edge.
Now its time to make some measurements on the copper pipe measurement coax.
After many days of great suspense wondering if this is even going to work at all, we have first launch! I connected the tdr pulser to the measurement coax and launched the first TDR pulse into the DUT.
Playing at the speed of light, this is too much fun! We expect the roundtrip TOF along a 1.15 m distance (2.3 m roundtrip) travelling at the speed of light (velocity factor of 100%) to 7.7 ns.
The size of this fluid level measurement coax is in scale with something the size of rain barrel, which I don't keep in close proximity to my oscilloscope. So, this first water launch test was conducted by placing the end of the copper pipe into a 2 L water pitcher and recording the ensuing TDR waveform. The water level on the copper pipe was approximately 22 cm. With water now present in the measurement coax we have reduced the roundtrip air distance from 2.3 m to 1.86 m. Ideally, we should see the water reflection advance 1.4 ns ahead of the shorted end reflection.
Considering this is a time difference of 1 ADC sample period on my oscilloscope, I am beyond thrilled with how well I was able to observe a TDR pulse reflection off of water .
The roundtrip TOF through 22 cm of water is 13.1 ns. This would be the second pulse after the water reflection which happens to coincide with 2 roundtrips in the air portion of the coax. We are likely seeing a small amount of a TDR pulse transmit through water, though nothing conclusive just yet. I need to place this in a much larger water column to clearly discern between the 2 reflections. Chasing this reflection is purely for science, the digital readout will only need to time the difference between first and second reflection.
I recently splurged, and redeemed past Project14 shopping carts on some cables, fast comparators, and a time to digital converter IC.
I have high hopes these components are up to to the challenge of making TDR measurements with picosecond resolution:
- TI TDC7200
- MAX999 Comparator
More to come...