Multi-conductor transmission line impedance

"Cage dipole"

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Paul Hovnanian     mailto:Paul@Hovnanian.com
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oh, cage dipole NOT gage dipole!

The TV antennas I've measured were made from about 1/32" aluminum sheet that was rolled into 3/8" tubing, with the ends flatened. I think I have a couple pieces of scrap, if you need more accurate dimensions.

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ess

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a 32 inch long member would then have around

32/(0.0005*pi()*3/8)/(0.0254*27e6)=3D0.08 at 350MHz that's only 0.2 ohms considering these antennas are resonating elements the R needs to be small

Joerg schrieb:

Hello,

I calculated some theoretical coaxial cables with even less impedance than 10 ohms. For this example, I used Teflon as insulator with a dielectric constant of 2.

outer diameter inner diameter impedance 5 mm 1 mm 68 ohm 5 mm 4 mm 9.46 ohm 5 mm 4.5 mm 4.47 ohm 5 mm 4.7 mm 2.62 ohm 5 mm 4.8 mm 1.73 ohm 5 mm 4.9 mm 0.86 ohm 5 mm 4.95 mm 0.43 ohm

But for 500 A, an outer diameter of 50 mm and inner diameter of 49 mm would be better and the impedance is the same 0.86 ohm. You might even use 200 mm and 196 mm. I did not found formulas for rectax or squareax cables, if both conductors cross section are rectangles ore squares instead of circles.

Bye

Joerg schrieb:

Hello,

but this kind of copper tape might be impure copper with much higher specific resistance and not pure copper used for electric conductors.

Bye

Interesting, 5 mm diameter is the same width as two 10 Awg wires.

Will come back later with the DC, 100kHz, 1MHz, and 10MHz characteristics of a 16 inch 'coax' made using your 4.9mm/5mm structure.

50mm conductor is a bit large. about like having the fat end of a baseball bat as the conductor. Although at these currents, probably a good idea.

That may be ok. Tim said he isn't too worried about losses because it's a very short pulse, so not much heat. Usually the mismatch between load and cable impedances is what gets you for short pulses, it messes up the pulse shape. Right now I have just such a design pickle where I'd need a balun with a couple of ohms max impedance. But you can't buy that off the shelf so either my client will have to wind their own or I have to find another solution. The latter would, of course, be much better.

And electricity is cheaper over here :-)

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Regards, Joerg

http://www.analogconsultants.com/

Hi, Joerg,

What's your signal like? Sounds like something that would be interesting to do with copper tape or some such. Or maybe a multilayer PC board, in production.

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John Larkin                  Highland Technology Inc
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Robert Macy schrieb:

Hello,

this calculator here

delivers some interesting numbers for the capacity and inductance per length: C/length I/length outer diameter inner diameter impedance pF/ft nH/ft 5 mm 4 mm 9.46 ohm 151 13.6 5 mm 4.5 mm 4.47 ohm 321 6.42 5 mm 4.7 mm 2.62 ohm 547 3.77 5 mm 4.8 mm 1.73 ohm 829 2.49 5 mm 4.9 mm 0.86 ohm 1,676 1.23 5 mm 4.95 mm 0.43 ohm 3,370 0.61 5o mm 49.5 mm 0.43 ohm 3,370 0.61

50 mm is really a bit large, but what about 10 or 20 mm? A thin insulation lowers the inductance, but the capacity goes up. Driving 3.37 nF/ft with 500 ns edges might be a problem, but with currents of several 100 amps it should be no problem.

Bye

I have to "whoop" a load that has a slightly varying voltage (moves 2-3V but fast) with a current of an amp or so for 1-2nsec. IOW sink a current in there for this short time. The current amplitude does not have to be precise, just fast and literally CM-free.

Datasheets of baluns are the pits these days, there is literally no info in there anymore. No inductance, no leakage inductance, no saturation data, nothing. Calling mfgs about it has also become quite useless. Also, I'd rather do this one with catalog parts because I don't get to guide the layout.

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Regards, Joerg

http://www.analogconsultants.com/

=A0 =A0 =A0 =A0 =A0 =A0 C/length I/length

=A0 =A0151 =A0 =A0 13.6

=A0 =A0321 =A0 =A0 6.42

=A0 =A0547 =A0 =A0 3.77

=A0 =A0829 =A0 =A0 2.49

=A0 =A01,676 =A0 1.23

=A03,370 =A0 0.61

=A03,370 =A0 0.61

what frequency is that calculated?

COAX Single [trying to approx inner cond. 4.9mm OD and outer cond.

5.0mm ID use 10mil shim tube, OD radius=3D0.096 ID radius=3D0.098 16 inches long

FREE SPACE L(in nH) R(in milliohms) DC 8.55 1.90

100kHz 8.15 2.79 320kHz 6.16 7.32 1MHz 3.81 14.2 10MHz 2.32 45.2

*IF* the capacitance stays constant, then Zo is dropping as frequency increases, almost in half!

Pretty lousy coax. but great for getting that 700 A to where you wanted.

CONCLUSION Side by side conductors NEVER as good as coax style conductor to get the impedance down.

What if two plates were used? The carriers would bunch at the edges raising resistance. But what if the plates were convex facing each other? Then there would be a tendency for the carriers to 'bunch' at the closest location. Perhaps, with a proper shape, like a hyperbolic shape, the distribution can be forced to become uniform.

Well, I might just dump the energy out of an inductor into it. I guess that would be called a sledgehammer method.

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Regards, Joerg

http://www.analogconsultants.com/

Funny you should mention that...

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John Larkin         Highland Technology, Inc

jlarkin at highlandtechnology dot com
http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro   acquisition and simulation

We're talking about relatively high frequencies and huge currents. Does skin depth have any bearing on the choice of cable geometry?

Why, does this constitute a sin that has to be confessed some day? :-)

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Regards, Joerg

http://www.analogconsultants.com/

No, but we just tested a prototype laser driver that can put up to an amp into a beast of a laser diode (like, 700 pF!) and get a 200 ps optical pulse out. It *does* store energy in an inductor and dump it into the load.

The optical pulse is gorgeous. Electrically, probing around, the board is a horror. But it's hard to probe something that's switching half an amp in 100 ps or so... what the hell does "ground" mean any more?

--

John Larkin         Highland Technology, Inc

jlarkin at highlandtechnology dot com
http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro   acquisition and simulation

That's sometimes the best "gooser" method, essentially a glorified step-up converter but it does only one cycle per shot.

Nice. That sure is RF-transistor or SRD turf, I have never had to do pulses this short.

But it's not 7.52V across the laser diode, right? That would really be redlining it unless it is a very short wavelength version.

It means whatever Sutro Tower says it is :-)

--
Regards, Joerg

http://www.analogconsultants.com/

:

cfm

=A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0C/length I/length

/ft

=A0 =A0 =A0 =A0151 =A0 =A0 13.6

=A0 =A0 =A0321 =A0 =A0 6.42

=A0 =A0 =A0547 =A0 =A0 3.77

=A0 =A0 =A0829 =A0 =A0 2.49

=A0 =A0 =A01,676 =A0 1.23

=A0 =A0 =A03,370 =A0 0.61

=A0 =A03,370 =A0 0.61

ong

=A0 =A0 =A0 =A01.90

=A0 =A0 =A02.79

=A0 =A0 =A07.32

=A0 =A0 =A0 14.2

=A0 =A0 45.2

yes