RE: Picofarad Capacitor Standard

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "John H. Couture" <couturejh-at-mgte-dot-com> 


Antonio -

Thank you for your reply to my post. My test capacitor consisted of two
rectangular plates separated by 0.25"
6"x7.42" = 44.5 sq inches. C=40 pf
This compares with your two disks separated by 0.25"
R = 9.56 cm = 44.5 sq inches. C=40pf

You mentioned that the capacitance (test caps) will always be greater than
the ideal value. Note that the tests I made indicated that the test cap
capacitance became less not greater when the plates were closer than 0.25".
This is the intersection point of the test curves. I wonder if this has any
significance because it occurs after the intersection of the curves. It
might relate to edge effects?

Your Inca program is very good. I use the program often to check the outputs
from my own program.

John Couture

---------------------------------------


-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Wednesday, December 10, 2003 8:31 PM
To: tesla-at-pupman-dot-com
Subject: Re: Picofarad Capacitor Standard


Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
  >
  > Original poster: "John H. Couture" <couturejh-at-mgte-dot-com>
  >
  > Paul N, Antonio, All -
  >
  > I have attempted to make a homemade capacitor with a reasonably exact
  > capacitance value at the low picofarad level for toroid research. This
  > capacitor consists of two flat metal plates at a certain distance from
one
  > another. The main problem of this type of capacitor at low pf capacities
  > would be the edge effects. I have tested the capacitor and developed
three
  > curves as shown below to find where they intersect when varying the
distance
  > between the plates. I believe the point of intersection of the curves is
  > where the edge effects are eliminated?

It's not clear that there is really a distance where the capacitor has
the "ideal" capacitance. When the distance is small, the edge obviously
adds capacitance, but when the distance is large, essentially you have
only the capacitances to ground of the plates, and these do not decrease
below a certain value.

  > In other words the plates at .25
  > inches giving 40 pf would be the real world capacitance of the two plates
  > with the elimination of edge effects.

What is the shape and size of the plates?

You say that the capacitor has 40 pF with 0.25" of separation.
My program Inca can simulate plate capacitors with circular plates
with good precision. A circular capacitor with 40 pF and the
plates separated by 0.25" (0.635 cm) would have a radius of
9.56 cm.
The actual capacitance measured depends on how it is measured.
The system has a capacitance matrix:
q1=c11 v1 + c12 v2
q2=c21 v1 + c22 v2
In this case, c11=c22 and c12=c21 (always).
If the bottom plate is grounded, the measured capacitance is
c11. If opposite voltages are applied to both plates, the
capacitance is (c11-c12)/2 (c12 is negative).
If the plates are at small distance, c11~=-c12.

What the simulation shows for this capacitor is:
Separation   ideal   c11  c12
0.00635        40     47  -43
0.01270        20     26  -23
0.02450        10     16  -12
0.05080         5     11   -7
0.10169        2.5    8.3  -3.6
0.20320        1.25   7.3  -1.9
It's evident that the capacitance will always be greater than
the ideal value. The limit value for c11 in this case is the
free-space capacitance of one of the plates, 6.77 pF.

Antonio Carlos M. de Queiroz