A simple analytical model to accurately predict self-resonance frequencies of on-silicon-chip inductors in TEM mode and eddy current mode

For the first time, a simple analytical model in the form of explicit formulas was derived for on-silicon-chip inductors. This analytical model can accurately calculate self-resonance frequencies (f_SR) in TEM mode and eddy current mode corresponding to very high and very low substrate resistivities (ρ_Si). Furthermore, this derived model can predict and explain the interesting result that f_SR keeps nearly a constant independent of ρ_Si in TEM and eddy current modes but is critically determined by the inductance and parasitic capacitances. The simple model is useful in on-silicon-chip inductor design for increasing f_SR under specified inductance target for broadband RF circuit design and applications.