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<p>With the development of high-frequency on-chip power converters toward higher power density and higher integration, rapid and accurate prediction of on-chip coupled inductor parameters has become a key issue in magnetic component design. This paper develops an analytical model for on-chip integrated coupled solenoid inductors in the 10–120&#xa0;MHz range, taking into account the thin-film magnetic core and its demagnetization effect. Based on three-dimensional electromagnetic simulations, this paper investigates the coupling coefficients between coils on the same core and between coils on different cores, and their variation laws over relative permeability values of 100–2000 and soft magnetic thin-film thicknesses of 0.5–2.5&#xa0;μm are obtained. After the demagnetization effect and first-order skin-depth correction are included in the baseline analytical model, a dimensionless residual correction factor <InlineEquation ID="IEq1"><EquationSource Format="TEX">\({\varvec{K}}\)</EquationSource></InlineEquation>, related to relative permeability, soft magnetic film thickness, line spacing, number of turns, and frequency, is introduced to correct the remaining relative deviation of the magnetic-core-induced inductance term and its parameters are identified from simulation data using the equal-weighted least squares method. The corrected model is validated using de-embedded measurement results, and prediction accuracy and error statistics are further analyzed. For the in-sample validation based on 25,612 data points from CSOL6 and CSOL6B, the median absolute percentage error is 11.15%, and the 90th-percentile error is 32.49%. For the out-of-sample CSOL6A validation with 12,806 data points, the mean, median, and 90th-percentile errors are 37.61%, 42.32%, and 51.97%, respectively. These results indicate that the proposed method can capture the main self-inductance variation trends of on-chip coupled solenoid inductors.</p>

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Mathematical inductance modeling and verification for on-silicon integrated solenoid coupled inductors

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Feiyang Feng,
  • Mengyu Liu,
  • Chengle Xue,
  • Tingcong Ye,
  • Sato Takahide,
  • Lei Liu,
  • Ningning Wang

摘要

With the development of high-frequency on-chip power converters toward higher power density and higher integration, rapid and accurate prediction of on-chip coupled inductor parameters has become a key issue in magnetic component design. This paper develops an analytical model for on-chip integrated coupled solenoid inductors in the 10–120 MHz range, taking into account the thin-film magnetic core and its demagnetization effect. Based on three-dimensional electromagnetic simulations, this paper investigates the coupling coefficients between coils on the same core and between coils on different cores, and their variation laws over relative permeability values of 100–2000 and soft magnetic thin-film thicknesses of 0.5–2.5 μm are obtained. After the demagnetization effect and first-order skin-depth correction are included in the baseline analytical model, a dimensionless residual correction factor \({\varvec{K}}\), related to relative permeability, soft magnetic film thickness, line spacing, number of turns, and frequency, is introduced to correct the remaining relative deviation of the magnetic-core-induced inductance term and its parameters are identified from simulation data using the equal-weighted least squares method. The corrected model is validated using de-embedded measurement results, and prediction accuracy and error statistics are further analyzed. For the in-sample validation based on 25,612 data points from CSOL6 and CSOL6B, the median absolute percentage error is 11.15%, and the 90th-percentile error is 32.49%. For the out-of-sample CSOL6A validation with 12,806 data points, the mean, median, and 90th-percentile errors are 37.61%, 42.32%, and 51.97%, respectively. These results indicate that the proposed method can capture the main self-inductance variation trends of on-chip coupled solenoid inductors.