Scalable Equivalent Circuit Model Of Planar Spiral Differential Transformers For CMOS RFICs

Transformers are an important kind of on-chip passive components in CMOS RFICs. They have two kinds of structures: planar spiral transformers and stacked spiral transformers. They can be used in low noise amplifiers (LNAs), voltage control oscillators (VCOs), double balanced mixers (DBMs) and power amplifiers (PAs) to realize the functions of impedance matching, convertion between single-ended signal and differential signal, AC coupling and bandwidth increasement etc., which can enhance the integrity and cut down the cost. Due to the conductive substrate, transformers suffer from serious parasitic couplings at high frequencies. The couplings not only degrade the quality factor (Q) of the components, but also make the modeling work quite difficult. Transformers are affected by four kinds of high frequency effects: skin and proximity effects of metal microstrips, parasitic capacitances between metal microstrips, capacitive coupling loss of substrate, and inductive coupling loss of substrate. Despite of the intensive endeavors in modeling and design communities for the past years, there still lacks a physically-based scalable equivalent circuit model, in which all the above effects are taken into consideration, and all the values of circuit elements can be calculated analytically according to the IC technology parameters and the device's geometric dimensions. Such a problem has been bothering the circuit designers in CMOS RFICs for years.In this thesis, we developed a scalable equivalent circuit model for planar spiral differential transformers based on the physical insights of the above four high frequency effects. Firstly, a 45-element 2-Ï€circuit topology is proposed which can provide correct port behaviors vs. frequencies. And we developed a set of analytical formulas to establish a scalable model, which correlates the values of circuit elements with the technology parameters and device's geometric dimensions. Some model parameters need to be calibrated based on the fitting to the measurement data of several testing devices. Then the schematic simulation results and the device ones using ADS Momentum are compared which demonstrate that they are well-fitted in the frequency range DC~20 GHz before self-resonant frequency. Modeling and simulation of baluns with the same configurations are also taken on the basis of the model presented before, and the frequency range which meets the practical application specifications can be extracted respectively. Additionally, Particle Swarm Optimization (PSO) is an excellent global optimization algorithm, which can be used on curves fitting and parameters extraction in the modeling process. The thesis affords some fundamental introductions. Finally, the measurement methodologies of transformers are described.