Practical inductance calculation for planar magnetics with track-width-ratio

This paper presents a method of calculating the inductance of a generalized racetrack planar spiral winding when the track widths for each turn are varied with a constant Track-Width-Ratio (TWR). TWR is an effective method to control parasitics in planar windings, minimizing resistance and controlling leakage inductance. It simply defines how the trace width of each turn should change as we approach the center of the core. After an octagonal simplification is performed to simplify the geometry, the self and mutual inductances are calculated using equations derived from Greenhouse and Grover. The calculation is compared to experimental winding measurements with high accuracy.