Coplanar Waveguide with Ground - Page 1
Forum section: electronics / projects

author: Randall W. Lott
author_rank: Regular Contributor
timestamp: August 29, 2012, 02:25:40 pm
content: Hi, I'm working on developing a MATLAB script that will calculate the gap between a trace and the surrounding planes in a CPWG.I want to calculate "W" given all other variables.The formulas to calculate this mention Elliptic Integrals K(k), which I don't understand.Here's the formula I'm trying to follow:Does anyone know how to use the "K" function?Thank you.

author: Short Circuit
author_rank: Frequent Contributor
timestamp: August 29, 2012, 03:09:59 pm
content: Sorry, I've no idea on the math stuff,but why not use an existing calculator?A little bit of fiddling with the dimensions to get the desired impedance;(not sure why the copper thickness cannot be entered in this calculation)

author: robrenz
author_rank: Super Contributor
timestamp: August 29, 2012, 03:15:09 pm
content: Quote from: Short Circuit on August 29, 2012, 03:09:59 pmIsn't it under options base copper weight and plating thickness? Then it shows the total at the bottom.

author: Short Circuit
author_rank: Frequent Contributor
timestamp: August 29, 2012, 04:14:25 pm
content: Yes, but the program does not allow to select another value when CW is selected,works with the other trace models, just not with CW. Maybe in a newer version of the tool.

author: Randall W. Lott
author_rank: Regular Contributor
timestamp: August 29, 2012, 05:50:53 pm
content: I know I'm just being a picky nerd, but I wanted to solve the problem. I just hate leaving things unresolved, even if they don't have much reason.I was aware of calculators and RF design software, but thank you for that anyway!There's a special feeling that you get when you finally solve a problem that's been ongoing. I hope to reach that point.

author: robrenz
author_rank: Super Contributor
timestamp: August 30, 2012, 01:23:45 am
content: Try this,http://chemandy.com/calculators/coplanar-waveguide-with-ground-calculator.htm

author: Randall W. Lott
author_rank: Regular Contributor
timestamp: August 30, 2012, 03:57:15 am
content: Quote from: Mechatrommer on August 30, 2012, 12:54:20 amIt's an elliptic integral. I don't know how to use it in this case.

author: IanB
author_rank: Super Contributor
timestamp: August 30, 2012, 04:06:19 am
content: Quote from: Randall W. Lott on August 29, 2012, 02:25:40 pmHere is the information you are looking for:http://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_first_kindNote especially the last line that gives this formula:This computational method using the arithmetic-geometric mean is used in the calculator referenced by robrenz here:http://chemandy.com/calculators/elliptical-integrals-of-the-first-kind-calculator.htmThe iterative procedure is explained on this page:http://en.wikipedia.org/wiki/Arithmetic-geometric_meanWhen understanding the chemandy calculator, it helps to remember that:(1 -k)(1 +k) = (1 -k2)Using that substitution confirms that theK(k)function used by chemandy corresponds to this definition:You could use the above definition directly if you had a convenient way of doing a numerical integration (e.g. a scientific calculator or an on-line calculation tool).

author: robrenz
author_rank: Super Contributor
timestamp: August 30, 2012, 11:21:20 am
content: Quote from: IanB on August 30, 2012, 04:06:19 amA student license of Maple would be great here. The Beauty of Maple compared to most other mathematical programs is that it can work and solve symbolically only, if desired. I am a mathematical nitwit and I have solved and understood many a problem that is way over my head by slogging thru first symbolically then numerically on my sons student licence of maple. I have found that I can learn a lot more when a program can do and show the mechanics of the heavy lifting. I can't do integrals or derivatives by hand but I understand how to use them to solve a problem and maple allows me to do that.

author: IanB
author_rank: Super Contributor
timestamp: August 30, 2012, 02:19:08 pm
content: Quote from: robrenz on August 30, 2012, 11:21:20 amIt's nice when programs like Maple can do symbolic integration, but unfortunately not all integrals can be solved analytically. The elliptic integral above is one of those as it happens. There is no analytic solution to the problem and one way or another it must be solved numerically.

author: robrenz
author_rank: Super Contributor
timestamp: August 30, 2012, 02:43:56 pm
content: Agreed, Maple help page on eliptic integralshttp://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/elliptic2

author: Randall W. Lott
author_rank: Regular Contributor
timestamp: August 30, 2012, 08:33:49 pm
content: Thank you very much. I should be able to write a script in MATLAB that will loop until CN=0. I appreciate it. I was unaware that it had to be done numerically.

author: MDG
author_rank: Newbie
timestamp: August 30, 2012, 10:36:56 pm
content: If you have a recent release of Matlab then you can use the built-in function for "complete elliptic integral of the first kind" (which is K(k) )http://www.mathworks.com/help/techdoc/ref/ellipke.htmlYou can also avoid elliptic integrals entirely by using an approximation for the ratio K(k)/K(k'). See equations 12.4 and 12.5 here:http://qucs.sourceforge.net/tech/node86.htmland the cited references.(Note that K'(k) in the above link is the same as K(k').)