Capacitance of coplaner (adjacent) plates

[tommyers]

Hi,

Does anyone know an equation/approximation/model or other to estimate the capacitance between two coplanar (adjacent) plates?

I know that for parallel plates: C = E0*Er*(A/d). I also know that the capacitance decrease as the plates move from a parallel to a coplanar geometry as the electric field becomes non-uniform.

I have been modelling parallel plates using a Boundary Element Method - I was wondering whether such a method would hold for a coplaner geometry?

Any help or thoughts would be much appreciated!

Regards

Tom

 

[marcusl]

There is a closed-form solution for the two-dimensional stripline problem, that is, for infinitely long coplanar strips. It is solved by conformal mapping to a parallel plate (well, parallel strip) geometry where the answer is known and simple. Collin works it out in Field Theory of Guided Waves (2nd ed), and I think Smythe may as well (Static and Dynamic Electricity).

I don't know of any analytic solution for finite coplanar plates, and I'll let more knowledgeable folks comment on numerical modeling.

 

[ATGM]

Looking around on <http://www.phenix.bnl.gov/phenix/WWW/muon/phnotes/PN125/node1.html> I came across the following:
"For the CSRC chambers the dominant contribution to the capacitance seen by the preamplifiers is the strip-to-strip capacitance. The capacitance between adjacent strips having a thickness, t, width, w, and separation, s, laying on a dielectric with constant, k, is approximately given by,

C(pf/cm) = 0.12t/w + O.O9(1+k)1og_10(l + 2w/s + w^2/s^2).

The second term dominates. Using k=3.5 (kapton), w=10 mm, s = 0.5 mm, t = 2 microns, the capacitance is 1.1 pf/cm. For the prototype test chamber the capacitance was measured to be 1.33 pf/cm in close agreement to the calculated value. We expect the maximum capacitance will be less than 500 pf for all stations so a basic requirement of the front-end electronics is that it must perform to specifications with an input capacitance of 500 pf or less."

I have not tried it out yet or done more than a few minutes search for a more solid reference.

 

[ATGM]

Please note, in the last post there is a "1" at the start of "log" and an "l" instead of a "1" after the log. The perils of cut and paste.

 

[tommyers]

Hi ATGM,

Thank you for this useful link. I am submitting my thesis on Thursday, but I am continuing to work in this area.

I found that Maxwell 2D software provided a very good approximation for coplanar geometries, plus it also produced electric field intensity plots; which helped in the design of my application.

Are coplanar electrodes a passing interest to you or have you an area of research or application in mind?

Regards,
Tom

 

[ATGM]

Hi Tom,

I am interested in it from the perspective of adjacent PCB pads or traces, specifically in debugging a breadboarded filter that keeps almost working without quite doing it. With time and dedication I might have re-installed the free version of Sonnet to see if the simple equation in the link is useable. Playing for a few minutes in a borrowed field simulator it looks as if the equation is in the ball park for a configuration with no ground plane. For finite pads, at least, it seems as if the real world is not as constant in equivalent capacitance over frequency as the equation states.

Hope the thesis is well accepted.

Andrew

 

[reovalis]

There is a closed-form solution for the two-dimensional stripline problem, that is, for infinitely long coplanar strips. It is solved by conformal mapping to a parallel plate (well, parallel strip) geometry where the answer is known and simple. Collin works it out in Field Theory of Guided Waves (2nd ed), and I think Smythe may as well (Static and Dynamic Electricity).

I don't know of any analytic solution for finite coplanar plates, and I'll let more knowledgeable folks comment on numerical modeling.

Hey Marcus,

Regarding a coplanar, parallel strip capacitor and referenced Field Theory of Guided Waves by Collin. Could you point me to the page where he derives this? I can't seem to find it. THANKS!

 

[marcusl]

He doesn't solve a coplanar capacitor, he solves for the capacitance (and characteristic impedance) of an infinitely long parallel strip transmission line, also known as coplanar waveguide. See Collin ch. 4.