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# Wire over ground transmission line

New for March 2021... under construction. Come back manana!

This page will provide some background on our wire-over-ground calculator, located here. Where did the impedance formula come from?

You can find that equation in the ITT handbook, but it has no attribution. Let's venture a guess as to why: it is solvable with a closed-form equation, just like coax. You don't see any attribution for the coax formula, do you? It turns out that the equation is an approximation of the full equation, which is

There are various web sites that show different geoemetries for the calculation. Don't believe everything you see, the true geometry is that the "height" is measured to the center of the wire (think about how you would use radial coordinates to solve this...) and the dielectric is assumed everywhere, not just under the wire. In this case, the transmission is purely TEM.

The height is to the center of the wire, and the diectric material is everywhere, not just beneath the wire.

This Japanese site has a comprehensive, closed-form solution which is more complicated, and shows that the formula we use is an approximation. So long as H/d is greater than 4, you should not worry about that.

Perhaps the worst case situation you might encounter would be a 1 mil wire, 20 mils above a ground, representing a long wirebond.

http://zakii.la.coocan.jp/tline_e/14_microstripline_z0.htm

Before we get started there are at least four different solutions that are correct. First, you can use the diameter or the radius of the wire. We chose the diameter. And second, you can use natural or base10 logarithms. We kind of like base 10, but if you want to use "ln" all you need to do is change the "138" in the final equation to "60".

https://www.microwaves101.com/calculators/874-wire-over-ground-calculator

Here's a few sites that show the same equation

https://www.eeweb.com/tools/wire-microstrip-impedance/

**Author : **Unknown Editor

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