A fast analytical model for TSV-based toroidal inductors

Passive inductors are essential in many functional components and are used in applications such as low noise amplifiers, power amplifiers, filters, and LC voltage-controlled oscillators and mixed-signal applications. Based on TSV technology, compact three-dimensional inductors can be processed, with a smaller area and a larger design space for inductance values and quality factors. This paper uses simulation and actual machining tests to obtain an accurate design method for three-dimensional inductors. Using empirical formulas and fitting methods, fast calculations and quick design optimization can be realized. We first propose a calculation model for the inductance value of a TSV-based toroidal inductor based on the problem that the inductance value of the toroidal inductor needs to be repeatedly adjusted with the help of electromagnetic simulation tools when designing the inductance value of the toroidal inductor. The inductance calculation model is in good agreement with the electromagnetic simulation and the measured values, and the deviation is less than 10%. The model can be used as an aid to TSV-based toroidal inductor design, avoiding the tedious steps of trial and commissioning at design time.