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This is Jack's
occasional outlet for thoughts about designing and programming embedded systems. It's a complement to my bi-weekly newsletter The Embedded Muse. Contact me at jack@ganssle.com. I'm an old-timer engineer who still finds the field endlessly fascinating (bio).
    

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Fun With Transmission Lines

August 16, 2018

In the digital world we thrive in a pristine world of zeros and ones. Logic elements cleanly switch. Analog messiness doesn't exist.

Except that's not entirely true. Digital is merely an idealized version of the real analog universe.

And then there's transmission lines and RF issues. Drive a clean digital signal down a track on a PCB and all sorts of weirdness can happen.

One of the best books on electronics, The Art of Electronics, by Horowitz and Hill, has a cool example of this. Want to generate a pulse from a step waveform? Well, we'd normally design a bit of logic to do so, but their thought experiment is pretty eye-opening.

Suppose you've got a bit of coax. If it's terminated by a short circuit, a step fed into it will generate a reflection that is the inverse of the applied step. That reflection is delayed by a length of time equal to the round-trip length of the coax. It will null out all but an initial pulse of the step.

RG-58U has a characteristic impedance (Z0) of 50 ohms, so we configure the circuit thusly:

Schematic of a grounded transmission line

I configured my arbitrary waveform generator to create a pulse with a reasonable sharp leading edge (8 ns - the best it can do) and monitored both the AWG's output (on channel 1) and the input to the coax (the right side of the resistor). The result:

Scope of a grounded transmission line

You can see the reflected signal turns the step waveform from the AWG to a pulse.

At first I was wondering why the voltage goes to, and stays at, zero volts after the pulse. D'oh - the far side of the coax is grounded.

Horowitz and Hill claim the ratio of the two signals is (R-Z0)/(R+Z0), where R is the terminating resistor at the coax's far end - 0 ohms in this example. The experimental results are reasonably close to this. I suspect the non-perfect rise time affects the result.

RF electronics is quite interesting and a lot of fun. One of the best references on the subject, if you don't want to go into the dreaded details of Maxwell's Laws, is The ARRL Handbook for Radio Communications. The ARRL is the advocacy group for radio hams. I've had a license since 1969 (callsign N3ALO), but have always enjoyed building and understanding radios more than using them.

Feel free to email me with comments.

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