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However there is a slight complication.
The substrate consists of two media, one consisting of printed circuit board
material, and the other consisting of the resistor’s insulating body. The
height of the top carbon compound layer above the ground plane is **H + h**.
However what is the effective relative permittivity *€ _{T}*
between these two conducting
surfaces?

To answer this question we consider the
two media to represent capacitors in series. Each has a capacitance proportional
to their relative permittivity *€ _{h}*
and

...1

and

...2

for some constant
*k*
depending on physical geometries of
L and W. The total capacitance *C _{T}*
is then given by

. ...3

We will now propose that their exists an
equivalent composite permittivity *€ _{T}* that would predict the
same total capacitance

...4

Substituting

...5

and

...6

we can show that

This total composite permittivity *€ _{T}*
can then be used in standard circuit simulation models for a micro-stripline
approximation displayed above, and could include the resistor conductivity also
as a parameter.

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