Fast and Efficient Analytical Parameters Fitting for On-Chip Inductors

There are numerous papers dealing with modeling of on-chip inductors. This paper presents first closed-form simple analytic expressions for parameters of a single-pi equivalent circuit fitted to measured or simulated S-parameter data in the least-square error sense. The presented method could be useful for quick estimation of the main equivalent parameters of onchip spiral inductors in a required frequency range. This can simplify inductor geometry optimization through iterative EM field solver simulations, by providing an instant insight on nature of the obtained S-parameters. Moreover an equivalent circuit can be extracted for transient SPICE simulations. The proposed formulae have been verified on several measured and simulated S-parameters of spiral on-chip inductors manufactured in various technologies. The results show very good agreement between the fitted data and the equivalent circuit.