By Minglin Ma, Yuan Chen, Zhijun Li, Xue Zhang and Xiangliang Jin, Xiangtan University, China

The demand for low-power, low-cost and high-integration wireless communication systems is driving the development of on-chip passive devices for radio frequency integrated circuits (RFICs).

Among the passive circuit designs, on-chip spiral transformers are particularly important and widely used in RFICs, including mixers, low-noise amplifiers, power amplifiers and oscillators. There’s an increasing demand for on-chip transformers that require accurate lumped-element models, suitable for circuit simulation and design optimisation. Modelling the transformer and obtaining its model parameters are always of great concern for engineers and circuit designers.

Several compact transformer models and circuit parameter-determining approaches have been proposed over the years, including a double π model with 42 components and expressions for spiral transformers, an automatic parameter determination and scaleable modelling method for transformers, and a generalised four-port transformer model with an ideal transformer in its core.

Commonly-used transformer models don’t include high-order effects with increasing frequency, which can result in underestimated power consumption of the circuit model when compared to the actual transformer performance.

Certain physics-based modelling methods for calculating the transformer model parameters from geometry and the necessary semiconductor process have also been developed. However, these process parameters are not always well defined for modelling purposes. In addition, some expressions are merely empirical formulas that depend on a specific fabrication process. Thus, some of the models’ parameters are totally or partially determined by fitting and optimisation procedures.

We propose a new T-lumped-element circuit model for circle-shaped planar transformers. This model accurately captures conductor losses in the transformer windings as well as the substrate parasitic losses over a broad frequency range. The values of the T-lumped elements of the circuit model are determined from two-port S-parameter data obtained from measurements…