Highly Efficient Automatic Synthesis of a Millimeter-Wave On-Chip Deformable Spiral Inductor Using a Hybrid Knowledge-Guided and Data-Driven Technique

An inductor is one of the basic passive circuit elements that make up integrated circuits. A hybrid knowledge-guided and data-driven technique (HKDT) that combines prior knowledge of on-chip inductors with a machine learning approach is proposed for designing a millimeter-wave on-chip deformable spiral inductor (DSI). First, a DSI, whose shape is no longer limited to a regular polygon and can be adapted to any rectangular region, is presented. Next, an expanded Wheeler formula is proposed to estimate the inductance of the DSI. Then, two approximate expressions with fitting parameters are deduced for the frequency responses of the inductance and quality factor. After that, two prior knowledge-guided Gaussian process regression (GPR) surrogate models are presented for the inductance and quality factor, with which the feature dimensions of the training data can be significantly reduced. Both models can achieve higher prediction accuracies in the frequency range of interest with lower computational complexity than the traditional GPR model with frequency-domain features when they are used for machine learning-assisted optimization (MLAO). Finally, an automatic inductor synthesis method is implemented by using a multibranch MLAO algorithm, and two examples are presented to validate the proposed synthesis method and illustrate its great capabilities. Ultimately, the HKDT can be extended to and applied for the efficient synthesis of other circuit elements with high accuracy.