Accurate Systematic Model-Parameter Extraction for On-Chip Spiral Inductors

A systematic model-parameter-extraction technique is presented for accurately modeling on-chip spiral inductors in radio frequency integrated circuits (RFICs). The model is a pi-circuit with an additional parallel <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> network connecting both vertical branches to account for substrate coupling. The extraction starts with extracting the series inductance and resistance at low frequencies. Then, the oxide capacitance is evaluated in an intermediate frequency range. Afterward, the substrate effects including the substrate resistance and capacitance, as well as coupling, are extracted at higher frequencies. All the lumped circuit element values are analytically determined by the network analysis from the measured network parameters ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> - or <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -parameters). The proposed approach thus can provide better circuital interpretations of the inductor behaviors for facilitating the design of RFIC inductors. Square and circular CMOS spiral and octagonal BiCMOS7 spiral inductors are investigated to test this technique. Highly accurate frequency responses by the extracted parameters are obtained over a wide frequency band without any optimization. This reveals the validation and capability of the proposed parameter-extraction method.