TDR of a neutron detector tube

This area is for discussions involving any fusion related radiation metrology issues. Neutrons are the key signature of fusion, but other radiations are of interest to the amateur fusioneer as well.
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Rich Feldman
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TDR of a neutron detector tube

Post by Rich Feldman » Thu Aug 09, 2018 2:57 am

Did anyone else ever wonder how a thin-wire detector tube would behave as a coaxial transmission line? I found out in the lab the other day. The subject was my BF3 tube that we talked about here 19 months ago. viewtopic.php?f=46&t=11254&p=74207

At very high frequencies, it looked like an unterminated transmission line with a prop delay of 0.75 ns and a characteristic impedance of about 320 ohms. That's remarkably high for a coaxial geometry. It's consistent with a conductor diameter ratio of about 200. For example, 0.8 inches and 0.004 inches.

It was easy to measure by Time Domain Reflectometry, using an instrument that's ubiquitous in my line of work. The voltages are 10000 times smaller, and timescales 1000 times faster, than those of interest for neutron detection. TDR detects spatial variations in the impedance of an electrical transmission line. Here's one comprehensive tutorial:
Instrument in picture above is connected to a coaxial cable, SMA-to-BNC adapter, BNC-to-HN adapter (or so I was told here), and the gas-filled tube under test.

Last night's observations are adequately matched by a simple electrical model:
* Coax cable impedance of 50 ohms.
* The connector adapter stack amounts to about 0.2 ns of 50 Ω line.
* The tube is another 0.25 ns of 50 Ω line, then 0.75 ns at impedance of about 320 Ω, then open circuit.

I'd never even heard of impedance that high in a coaxial geometry. The vast majority of cables are designed for 50 Ω or 75 Ω. Value depends on the insulator's dielectric constant, and on logarithm of the conductor diameter ratio. It's the same as sqrt(L/C) per unit length of the cable medium. Here are some formulas and an online calculator: ... utoff.aspx

Guess there's time for a closer look at the display and its interpretation.
The screen shows two saved traces and one live trace. Horizontal scale is 2 ns/div. Vertical scale is 200 milli "rho" per division, referring to the ratio of reflected voltage to incident voltage.

Green trace is TDR waveform with nothing (open circuit) at the end of the probe cable. The instrumented end of the cable is connected to an oscilloscope channel and a voltage step generator. (A few hundred mV, with combined risetime < 50 ps, just like similar level instruments in the 1970's.) At the exposed end of the cable, the step reflects back with +100% amplitude and is sampled by the 'scope.

The red trace is waveform with both connector adapters in place, but no BF3 tube. Red step is later than green step by the amount of connector delay, round-trip. Red trace has some minor wiggles from impedance imperfections at the connections.

White trace shows what happens when the tube is connected. The 50 ohm enviroment, with no major reflections, continues for a while past the HN connector. At the beginning of the 320 ohm section, the voltage step is mostly reflected but partly transmitted, according to the rules for such things. The transmitted step is 100% reflected at the far end of 320 Ω section. At the 50 Ω junction on the return trip, it's partly transmitted to where we can see it, but mostly re-reflected with reversed voltage polarity. It rings back and forth in the 320 Ω section, which is very poorly matched on both ends.

For extra fun, here's a simulation produced with a freshly downloaded copy of LTSpice.
bf3_sim.PNG (10.13 KiB) Viewed 4471 times
bf3_cir.PNG (8.67 KiB) Viewed 4471 times
All models are wrong; some models are useful. -- George Box

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Rich Feldman
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Re: TDR of a neutron detector tube

Post by Rich Feldman » Wed Jan 30, 2019 8:16 pm

With HV bias supply in hand now, I'm preparing and modeling circuits to view normal signals from the tube.

The BF3 tube's own capacitance is accurately known from the TDR experiment.
I figure it's 5.0 pF before the fine wire section, plus 2.3 pF for the fine wire section.
SMA-BNC-HN connector adapters add 4.0 pF.

Are those values consistent with other readers' experiences with datasheets or circuit measurements?

Here's the derivation:

Transmission line references present formulas for characteristic impedance
coax1.JPG (22.27 KiB) Viewed 3218 times
as well as the electrical circuit model: uniformly distributed capacitance and inductance.
coax2.JPG (20.92 KiB) Viewed 3218 times
images from ... impedance/

Let's take an arbitrary length of transmission line, with total capacitance C and total inductance L.
Characteristic impedance Z0 is sqrt(L/C), in ohms, and is independent of the line length. You could measure the value using an ordinary ohmeter, at the end of a semi-infinite transmission line. :-) Total propagation delay Td is sqrt(LC), in seconds, and is directly proportional to line length.

We can work it backwards, if impedance and delay are known (e.g. by direct measurement with TDR instrument).
C = Td/Z0. L = Td*Z0.
For example, any 50 ohm line long enough for 1000 ps of delay has 20 pF of capacitance. The physical length would be in the range of about 150 mm to 300 mm, depending on dielectric material.
So I just applied the C = Td/Z0 formula to values from the TDR experiment in OP.


p.s. Got a minor gripe about the line-charging illustration above. It shows a positive (in upper conductor) voltage step propagating from left to right. So the direction of charging current is from positive (upper) battery terminal into the line. Red arrows point the other way, because the writer wants to show which way the electrons are drifting. IMHO the "negative electrons moving counter to the direction of electric current" should be taught and then put on a back shelf, to avoid confusion with conventional current.

Electrical sign conventions were established more than 200 years ago. Telegraphs, telephones, DC and AC electric lighting, and three-phase power grids were designed accordingly. Then electrons were discovered, and happened to be negative. That does not mean the convention was ever wrong. It just became confusing to the simple-minded when electron theory entered the curriculum.

Current is transfer of electric charge. Often, but not exclusively, by motion of electrons. A detail that generally doesn't matter in circuit analysis -- the arrows in a diode or transistor symbol show the conventional current direction. When we look at currents inside semiconductor devices, gas-filled tubes, electrolytes, and fusors, charge carriers include holes and ions of many kinds.
All models are wrong; some models are useful. -- George Box

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