Direct extraction of equivalent circuit parameters for on-chip spiral transformers

This paper compares model differences of transformers measured in 4-port and 2-port configurations. Although 2-port configuration is more appropriate for measurement and application, it brings tremendous difficulties to the model's parameter extraction. In this paper, a physics-based equivalent circuit model and its corresponding direct extraction procedure are proposed for on-chip transformers. The extraction is based on the measurement of 2-port configuration instead of the 4-port type, and it can capture the model parameters without any optimization. In this procedure, a new method has been developed for the parameter extraction of the ladder circuit, which is commonly used to represent the skin effect. Thus, this method can be transferred to the modeling of other passive devices, such as on-chip transmission lines, inductors, baluns, etc. In order to verify the procedure's efficiency and accuracy, an on-chip interleaved transformer in a 90 nm 1P9M CMOS process has been fabricated. We compare the modeled and measured self-inductance, the quality factor, mutual reactive and resistive coupling coefficients. Excellent agreement has been found over a broad frequency range. (semiconductor integrated circuits)