Simulating long cable/wire lengths

snipped-for-privacy@yahoo.com wrote in news:e79bbf17-d127-41a5-ad82- snipped-for-privacy@d21g2000prf.googlegroups.com:

Lork Kelvin derived the cable equations for the TransAtlantic Cable. Google up "Cable Equations" and see what happens. You'll likely find many Neuroscience and biophysics links. If you can find a paper by Rall, it will probably cite the engineering papers.

Easiest is to buy 4000ft of cable and hook it up. ed

There are line simulators for just such tests available from test equipment makers. OTOH, 100 m is pretty short. Why simulate at all? Just put up a 100 m spool of cable in some unwanted corner and be done with it.

Indeed. Four of these, for example:

Best regards, Spehro Pefhany

Wasn't that done by Michael Pupin?

Jerry

Jerry Avins wrote in news:b42dnSs1D_va4uPanZ2dnUVZ snipped-for-privacy@rcn.net:

Wikipedia on "Transmission Line"

"Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable. The model correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher's equations."

...

I guess I was thinking of loading coils. They probably were in the first transatlantic telephone cable.

Jerry

Jerry Avins wrote in news:X4WdnWhSoLPbPuPanZ2dnUVZ snipped-for-privacy@rcn.net:

You might get a kick out of the Rall Handbook of Physiology Chapter, if you can find it: Core conductor theory and cable properties of neurons W Rall - Handbook of Physiology, 1977

He used Cable Theory to model just about all of the passive properties of the axon and dendritic tree! This was my first exposure to hyperbolic trig functions. I knew what they were, and I knew there were keys for them on my calculator, but I had no clue what they solved.

I'm curious about how closely the model conforms to reality. Signal speed in real neurons goes up, linearly I think, with diameter. Much of the early work was done at Woods Hole because of the availability there of the large giant sea squid that made experimenting easier. In higher animals, signal speed is increased greatly by the myelin sheathing that surrounds the axon. The sheathing is not continuous, and the nerve impulse jumps from gap to gap without needing to propagate chemically inside. The whole subject is fascinating.

Jerry

Jerry Avins wrote in news:1LOdnTjbYd2HWePanZ2dnUVZ snipped-for-privacy@rcn.net:

I teach a physiology course specifically aimed at engineers who know circuits and diffeqs.

For unmyelinated axons (vel. proportion to sqrt(radius) ) and the dendritic tree, the equations do extremely well (assuming you can measure the parameters accurately). The equations still work well for myelinated axons ( vel proportional to radius, as you've said), but the model gets a little complex, as the membrane resistance can't be considered constant along the length. There are some assumptions made at the endpoints and bifurcations, but they do OK.

The nerve impulse itself isn't entirely regulated by this, but by active pores that open and shut based on membrane voltage. A little current goes in, and if the membrane voltage exceeds a threshold, then a positive feedback process starts on that patch of membrane. The current then propagate passively down the axon, following the cable equations, and if all is working, it brings the adjacent patch above threshold, and the process continues down the axon (in both directions, actually, if you inject current into the middle of the axon!)

The Nobel work by Hodgkin and Huxley was done on squid giant axons (if it were done on giant squid axons, there wouldn't be much to work on, but I'm always making that spoonerism myself). The nifty thing about that prep is you can actually run wires down the axon, or you can roll the goop out with a squeegee and substitute your own goop.

While this groundwork was going on ay Woods Hole, the foundations for continental drift were being assembled at Lamont-Dougherty, and both were frequently written up in _Scientific_American_. Those were interesting years, even for a bystander.

Jerry

I agree, simple is better. For any alternative you have to design, build, and verify; then justify with papers. It might be reasonable if the test fixture was going to be manufactured but not in a one-off. Try ebay, you might make a profit when you sell it back.

Ray

This is going to be ugly because you have to unwind the cable. Otherwise the capacitive coupling would be the predominant effect.

Vladimir Vassilevsky DSP and Mixed Signal Consultant