Scaling of parasitic capacitance with magnetic component physical size

Larger magnetic components offer higher efficiency and higher power capability. However, increased component size can exacerbate switching loss and EMI through increased parasitic winding capacitance. In this paper, we use a first-order model to explore the impact of varying component size on winding capacitance of single-layer and multi-layer windings. Different constraints are considered, such as a fixed number of turns and a fixed inductance. This analysis shows that the capacitance increases between linearly and cubically with component size, which highlights the challenge of creating large components with a small winding capacitance. Next, we consider the effect of winding capacitance on the $Q$ and temperature rise of an air-core solenoid inductor, and show that increased component size only improves magnetic performance to a point. The theory was validated by measuring the resistance, capacitance and inductance of two different size inductors. The scaling model predicted the winding capacitance with an error of 1.9% and quality factor with an error of 2.9%.