A Physics-Based Equivalent-Circuit Model for On-Chip Symmetric Transformers With Accurate Substrate Modeling

A physics-based equivalent-circuit model for on-chip symmetric transformers is presented with all the model elements driven from fabrication specifications. Two extra coupled transformer loops are used for each coil to model the parameters of skin effect, proximity effect, and reflective effect of the substrate eddy current, respectively. Model accuracy under free space is first demonstrated using an electromagnetic field solver without considering substrate loss. Several sets of transformers were fabricated on a standard 0.18- mum 1P8M RF CMOS technology to further verify the accuracy and scalability of the proposed model. By careful comparison of S -parameters, coil inductance, quality factor,coupling coefficient, and maximum available gain between measured data and simulated data, model accuracy, and scalability are verified over a wide range of geometry configurations.