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Composite Permittivity Of PCB and Resistor Body

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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 H , and inversely proportional to each substrate’s height h and H. This suggests that 

   ...1

and

   ...2

for some constant k  depending on physical geometries of L and W. The total capacitance CT  is then given by

. ...3

We will now propose that their exists an equivalent composite permittivity T that would predict the same total capacitance CT  given the total separation h + H. This implies,

  ...4

Substituting 

...5

and 

 ...6

we can show that

   ...7

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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