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Equations for cables

Here's a discussion of the analysis of transmission lines..it was removed from cables for obvious reasons, and sent to whiners woad...go figure..the precursor is available over at cables..

An ideal transmission line comes in only three forms..coaxial, waveguide, and free space (barely, as all em waves will diverge). This construct defines absolutely, the location of the electric field (only within the dielectric), and, the location of the magnetic field..(again, only within the dielectric).

By running through the equations for a coaxial geometry, you will find that the relation between L and C is such that (L * C)/1034 = DC. I can provide web links for the base equations of this derivation if you wish.

This is inviolate..it is a consequence of sheer physics..nothing more..nothing less...plus, I've tested quite a few cables to verify the accuracy, as well as applied the test results from various vendors as well as Gene's test data. Dead nuts for all coaxes, parallel runs, and absolutely everything to date..

Now, If you plot L vs C on a graph, with DC = 1, you get a curve of the form 1/x. Any coax made with either air or vacuum will fall onto that line. In addition, the prop speed of any coax on that line WILL have a propagation speed of C...that being the speed of light.

Next...plot a family of curves on that graph, representing DC=2, 3, 4, 5..etc..each of those curves has a constant propagation speed.

Now, you have a useful graph...

If you measure any coax for L and C, and put that point on the graph, you will find you can by inspection, you can see the prop speed and the effective dielectric constant of the system..for coaxes, of course, the effective dielectric coeff is exactly the DC of the insulation material.

Now....here's the really interesting stuff..and obviously, the stuff you do not understand..not your fault actually, it is a bit obscure. I'm surprised with you, as I've explained it many times, on multiple forums..

All transmission lines will be above that DC=1 line..all. Again, that is inviolate, it is a consequence of the equations, and any data point below that line represents faster than light propagation. I haven't seen that since the Radio-electronics article in the 80's..

But, parallel pairs, and also your CC construct, have issues...None of them absolutely contain either the electric or the magnetic field. As a consequence of that, the inductance and the capacitance will both be a bit more. Capacitance because the field lines outside the dielectric are stored energy within a dielectric of value 1 (air), and the mag field lines outside the wires also is stored energy.

Those stored energies are higher inductance and higher capacitance. As you may recall, I have been saying effective dielectric coefficient.. In other words, this is what the transmission line "sees" as a result of it's geometry. And since that is what the t line "sees", it will act as if the dielectric is actually that number..it will have that prop speed, and it will have that impedance.

Go ahead, test this yourself..make the graph, and take any cable made and apply the L and C to the graph. Then, measure it's prop speed and characteristic impedance..you will also find that it is inviolate..


The graph I detail is extremely useful, provides all the tools to create any transmission line at all, and to understand the tradeoffs in that design. It works for coax, it works for parallel wires, and it works for any hybrid..Prove it to yourself.....measure some CC for prop and impedance..

BTW, I already did this for 33 Belden coaxes from their web data..here's the results from another spreadsheet.(sorry the table doesn't line up properly.

belden dielectric cap induct product DC
82240 fep 26.4 70 1848 1.79243453
88241 fep 19.5 126 2457 2.383123181
735A1P ffep 17.5 0.97 16.975 0.016464597
6539Y8 ffep 13.5 107 1444.5 1.401066925
1153A ffep 16.2 93 1506.6 1.461299709
1151A ffep 16.5 93 1534.5 1.488360815
1506A ffep 16.1 97 1561.7 1.514742968
1695A ffep 16.1 103 1658.3 1.608438409
1426A fhdp 16.3 97 1581.1 1.533559651
1505F fhdp 17 94 1598 1.549951503
735A1 fhdp 17.7 190 3363 3.261881668
1694A fhdpe 16.2 106 1717.2 1.66556741
7808A fpe 23 60 1380 1.338506305
1858A fpe 17.3 97 1678.1 1.627643065
8214 fpe 26 65 1690 1.639185257
8221 fpe 16.3 104 1695.2 1.644228904
513945 fpe 16.1 106 1706.6 1.65528613
8219 fpe 26.5 65 1722.5 1.67070805
573945 fpe 16.9 109 1842.1 1.78671193
8238 frsfpe 20.5 115 2357.5 2.286614937
1186A gifpe 16.2 97 1571.4 1.524151309
8237 pe 28.5 79 2251.5 2.183802134
8218 pe 20.5 115 2357.5 2.286614937
8263 pe 20.5 115 2357.5 2.286614937
8216 pe 30.8 77 2371.6 2.30029098
8262 pe 30.8 77 2371.6 2.30029098
8259 pe 30.8 92 2833.6 2.748399612
8700 pp 55.2 49 2704.8 2.623472357
83242 tfe 29 67 1943 1.88457808
83284 tfe 29 67 1943 1.88457808
83264 tfe 19.5 100 1950 1.891367604
1671B tfe 29.5 70 2065 2.002909796
1672J tfe 19.5 109 2125.5 2.061590689

As you can see by inspection, the 735A1P DC is off, they state .97 nH, a typo..and the 735A1 is also an outlier, I suspect the 190 nH number is also incorrect..

I've run this for all the zips I tested, from all Gene's data, and they all conform to the analysis as well..So far, all data, from every source, without exception, is in conformance to this analysis, your CC included..

BTW, you are paralleling the capacitances, but geometrically, the transmission line does not understand the added volume taken up by the geometry..so in effect, the T-line coefficients are presenting to the world as a different dielectric coefficient..parallel higher density...you are approaching this problem as if it were a volume efficiency one..that is a correct one for all other cases, but for transmission lines, it is incorrect..

I located the prop post which had the graph, unfortunately the link was to a diy location.."http://www.diyaudio.com/forums/attachment.php?s=&postid=338750"..apparently, after a while, the links become no good..I think I'm gonna hafta have a sticky setup at AH, or a wiki or permanent set up at diy, to give a solid link for discussion.

As for your attitude?...please, stick with a technical discussion, and leave the attitude where it belongs...there is no reason for it here..especially from a moderator who is supposed to maintain civility here.

Obviously, rather than say "sorry, I misunderstood", it was necessary to remove the record of poor behaviour. Hopefully, here it won't be moved just because someone posted his way into a corner.

Cheers, John



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Topic - Equations for cables - jneutron 10:59:46 12/01/04 (3)


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