## [SI-LIST] Re: Capacitance calculator

• From: John Barnes <jrbarnes@xxxxxxxxx>
• To: si-list@xxxxxxxxxxxxx
• Date: Fri, 20 Sep 2002 12:42:40 -0400

```Tim,
Were you simulating two wires in a continuous medium, or two insulated
wires in air?

>From Appendix E of my book, Electronic System Design: Interference and
Noise Control Techniques-

Two-wire transmission line in a medium with effective relative
permittivity Er' ( = Er for the medium if essentially all the electric
field lines are contained within the one medium; will be between 1 and
Er if some of the field lines are in the medium and some in air):

!<-D->!     !<-D->!
___         ___
/   \       /   \
!     !     !     !
\___/       \___/

!<--- S ----!

shape_factor = ( 1 / pi ) * ln ( (S/D) + sqrt( ((S*S)/(D*D)) - 1 ) )

Cu = capacitance per unit length = 8.854 * Er' / shape_factor pF/m

If the wires are insulated, with an overall diameter of S, we can model
them as a twisted-pair with hard insulation and a twist angle of 0, so

Er' = 1 + ( (0.25) * ( Er - 1 ) )

The relative permeability of insulators and most metals is about 1.  So
the magnetic field, and therefore the inductance, is not affected by the
insulation around the wires.  The reduction in capacitance over wires
submerged in a medium will also show up as:
*  Higher impedance, proportional to sqrt( L / C ) .
*  Shorter propagation time, proportional to sqrt( L * C ) .

John Barnes KS4GL
dBi Corporation
http://www.dbicorporation.com/
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