Let's Take A Vote...

Ya... I spotted my foul the second time I glanced at the tail of the thread. I was making a joke about the little lightning bolts that go between the air and ground elements. :-)

Ya... I spotted my foul the second time I glanced at the tail of the thread. I was making a joke about the little lightning bolts that go between the air and ground elements. :-)

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No, the logarithm is real physics. The E field between concentric cylinders goes as 1/r. Integrating that gives a log of the ratio of radii. (with a minus sign in the exponent.)

If I cut the width in half I only get some 30% improvement. Keeping the traces as short as possible is much more important. (I think)

George H.

Really? I'm only 51 or 3? But whatever, I still figure I'm an old fart too.

Old fart was mostly meant as a term of endearment.

I don't know Terman at all. (should I take the book home for a night or two?) I remembered that JR (my boss) had pulled it off the shelf when I=92d asked a similar question about the inductance of traces.

George H.

Who knows??? I know. You are deluded or just a liar. I would never say anything so silly.

John

It's not silly, it's the height of mixing ignorance, bloviation and manic depression. ...Jim Thompson

You can't find the post because there isn't one. You and JT are so determined to oppose anything I say that I can, usually without actually trying, make you look like fools.

For Pete's sake, I actually own an electrostatic voltmeter. I bet you don't.

Here's the cover of the catalog, which I also have:

ftp://jjlarkin.lmi.net/Sensitive.JPG

These meters are cool. Accurate, infinite impedance, true RMS.

John

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Concentric infinitely-long cylinders is a case that has a closed-form solution. Finite parallel plates, wire over ground plane, microstrip, twisted pair, things like that probably don't. The equations you see are usually approximations with restrictions on geometry.

Maybe fringing limits the improvement as you go skinnier. ATLC or Sonnet Lite would let you sim cases. I'd try it but I don't think I could accurately x-acto traces much skinnier than 15 mils maybe.

John

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Geometries where the Laplacian separates, or 2-D geometries which can be conformal-mapped into something nice, are about the only times you'll get a closed-form solution. You need the conductor surfaces to be curves of constant coordinate (e.g. the plane X=0 in Cartesian coordinates or r=1 cm in cylindrical coordinates. I recall reading in Morse and Feshbach that there are (iirc) only seven coordinate systems in which the Laplacian separates, so the list of nice geometries is fairly short.

(The two wire problem can be conformal mapped to a parallel planes problem, iirc, and you can use that to solve the wire-over-ground problem by the method of images.)

Cheers

Phil Hobbs

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For what it's worth, for wire-over-ground-plane, Appcad complains if the separation is less than about 4 wire diameters, so if there is a closed-form solution, Agilent doesn't use it. I could see the small-separation case getting very messy. Wadell does some horrible cases, like Multiwire (enameled wire partially squished into dielectric) and wire above insulator with ground plane opposite, but they are ugly approximations.

I just c-meter or TDR stuff like this, maybe do a few cases and graph it.

John

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Hi John, I don't know any of those names, but don't waste any time doing this. The input circuit, I'm thinking about has all sorts of other stuff.. (switches and terminal blocks) hanging on the input and I 'think' the trace capacitance is minimal.... Ahh, the major contribution may be in the terminal block.?? Thanks?

George H.

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Ahh, thanks Phil, you awaken memories from grad school. In any problem you can replace an equi-potential surface with a conductor. (The equi-potential surface at the mid-point between two wires is a plane.)

George H.

(this is either an example in Jackson or a problem.)

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Thanks John, I didn't mean to get you all worked up. My input has ~7pF of capacitance. most of it in swithes and terminal blocks. (Hmm, that's good, our noise apparatus is shipping and I've been wondering what I'm going to be measuring to test them...)

George H.

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If you ever find time on your hands, play with this:

It's actually very clever. The core algorithms are impressively simple, and it makes neat color displays. I've used it for messy cases like calculating the impedances of buried (inner layer) microstrips and such.

John

There speaks someone who by his own admission relies on futzing with the numbers instead of algebra or understanding the physics.

I always loved the analytical symmetry tricks and conformal transformations. But in my era computers were the method of choice.

How come you have read Morse&Fishback Methods of Theoretical Physics in two massive volumes and never found the time to flick through Feynman? (the latter is a lightweight by comparison - you could flash read it)

The nasty bit is allowing for frequency dependent surface current skin effects in real conductors and computing accurately the fringe fields on awkwardly shaped solenoids. A trick managed in practice by deviously shaped pole pieces on the top flight mass spectrometers. There is a strong patent by one maker that still prevents other manufacturers from having a perpendicular focal plane for their collectors.

I worked on porting ion optics programs from mainframes very early on.

Regards, Martin Brown

I think i "made a case" that the "gain" was not too hot, using rough numbers for input power to switch states, and power handling capability. For an infinite "gain", either the power to switch states must be zero, and/or the power handling capability must be infinite. Clearly, NEITHER exists.

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Makes sense that trimming trace width gives less and less an improvement as the (untrimmed) width decreases - reason? as you said, (capacitive) fringing.

Power gain is Pload/(Pcoil*DutyCycle), where Dutycycle is the fraction of time that the coil is energized. In plain English, power gain is averaged load power divided by averaged coil power. That has no upper bound as duty cycle approaches zero. In, say, a home thermostat that uses one AA battery, Dutycycle might be a few tens of PPM, which is why the battery will last a year or two. Probably the clock/LCD run the battery down more than the relay does.

So the argument devolves to whether a number that is unboundedly large can be referred to as "infinite." Go for it.

John