On the self-capacitance of solenoidal coils

Expressions for the self-capacitance of single-layer solenoidal coils both balanced and with one end grounded are established by considering the electromagnetic field solution along a sheath helix of infinite length. A transmission line equivalent circuit is developed that permits the determination of the driving point admittance of the coil. Adaptation of this expression for the admittance to a coil of finite length leads to a semi-empirical formula for the self-capacitance. Further, it provides a physically illuminating explanation for the experimentally based practice of taking the self-capacitance as a single lumped capacitance connected across the coil terminals and of taking the effective inductance as the direct current inductance of the coil. The results are shown to be in excellent agreement with existing measurements of self-capacitance.