Author Topic: Coplanar Waveguide with Ground  (Read 12224 times)

0 Members and 1 Guest are viewing this topic.

Offline Randall W. LottTopic starter

  • Regular Contributor
  • *
  • Posts: 180
  • Country: us
Coplanar Waveguide with Ground
« on: August 29, 2012, 02:25:40 pm »
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.
- Randy
 

Offline Short Circuit

  • Frequent Contributor
  • **
  • Posts: 439
  • Country: nl
    • White Bream electronics R&D
Re: Coplanar Waveguide with Ground
« Reply #1 on: August 29, 2012, 03:09:59 pm »
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)
 

Offline robrenz

  • Super Contributor
  • ***
  • Posts: 3035
  • Country: us
  • Real Machinist, Wannabe EE
Re: Coplanar Waveguide with Ground
« Reply #2 on: August 29, 2012, 03:15:09 pm »
(not sure why the copper thickness cannot be entered in this calculation)

Isn't it under options base copper weight and plating thickness?  Then it shows the  total at the bottom.

Offline Short Circuit

  • Frequent Contributor
  • **
  • Posts: 439
  • Country: nl
    • White Bream electronics R&D
Re: Coplanar Waveguide with Ground
« Reply #3 on: August 29, 2012, 04:14:25 pm »
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 Maybe in a newer version of the tool.
 

Offline Randall W. LottTopic starter

  • Regular Contributor
  • *
  • Posts: 180
  • Country: us
Re: Coplanar Waveguide with Ground
« Reply #4 on: August 29, 2012, 05:50:53 pm »
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.
- Randy
 

Offline robrenz

  • Super Contributor
  • ***
  • Posts: 3035
  • Country: us
  • Real Machinist, Wannabe EE

Offline Randall W. LottTopic starter

  • Regular Contributor
  • *
  • Posts: 180
  • Country: us
Re: Coplanar Waveguide with Ground
« Reply #6 on: August 30, 2012, 03:57:15 am »
The formulas to calculate this mention Elliptic Integrals K(k), which I don't understand.
Does anyone know how to use the "K" function?
what is K function?

It's an elliptic integral.  I don't know how to use it in this case.
- Randy
 

Online IanB

  • Super Contributor
  • ***
  • Posts: 12570
  • Country: us
Re: Coplanar Waveguide with Ground
« Reply #7 on: August 30, 2012, 04:06:19 am »
The formulas to calculate this mention Elliptic Integrals K(k), which I don't understand.

Here is the information you are looking for:

http://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_first_kind

Note 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.htm

The iterative procedure is explained on this page:

http://en.wikipedia.org/wiki/Arithmetic-geometric_mean

When understanding the chemandy calculator, it helps to remember that:

(1 - k)(1 + k) = (1 - k2)

Using that substitution confirms that the K(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).
« Last Edit: August 30, 2012, 04:09:10 am by IanB »
 

Offline robrenz

  • Super Contributor
  • ***
  • Posts: 3035
  • Country: us
  • Real Machinist, Wannabe EE
Re: Coplanar Waveguide with Ground
« Reply #8 on: August 30, 2012, 11:21:20 am »
Using that substitution confirms that the K(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).

A 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.
« Last Edit: August 30, 2012, 02:04:44 pm by robrenz »
 

Online IanB

  • Super Contributor
  • ***
  • Posts: 12570
  • Country: us
Re: Coplanar Waveguide with Ground
« Reply #9 on: August 30, 2012, 02:19:08 pm »
The Beauty of Maple compared to most other mathematical programs is that it can work and solve symbolically only, if desired.

It'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.
 

Offline robrenz

  • Super Contributor
  • ***
  • Posts: 3035
  • Country: us
  • Real Machinist, Wannabe EE
Re: Coplanar Waveguide with Ground
« Reply #10 on: August 30, 2012, 02:43:56 pm »

Offline Randall W. LottTopic starter

  • Regular Contributor
  • *
  • Posts: 180
  • Country: us
Re: Coplanar Waveguide with Ground
« Reply #11 on: August 30, 2012, 08:33:49 pm »
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.
- Randy
 

Offline MDG

  • Newbie
  • !
  • Posts: 5
  • Country: us
Re: Coplanar Waveguide with Ground
« Reply #12 on: August 30, 2012, 10:36:56 pm »
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.html

You 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.html  and the cited references.
(Note that K'(k) in the above link is the same as K(k').)
 


Share me

Digg  Facebook  SlashDot  Delicious  Technorati  Twitter  Google  Yahoo
Smf