Capacitance of a thin line conductor inside a grounded square shield
Keywords:
capacitance, grounded square shield, thin line conductorAbstract
In this paper, by using separation of variables in Laplace’s equation, we derive a formula for the capacitance of a thin line conductor positioned inside a grounded square shield at one of its cross-section symmetry axes. The formula, which is in the form of a slow convergent series, is transformed into the sum of two series, one of which can be summed in a closed form, and the other one is a very rapidly convergent series and may be replaced accurately enough by its first term. As a result a very simple formula for the capacitance is obtained. Based on this formula, we give some numerical results for the capacitance versus the conductor position inside the shield. In particular, when the conductor is at the center of the shield our results are compared with the results obtained from an aviabile empirical formula for different values of the shield size.
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