Loop and Partial Inductance

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Basis of Inductance

Eric Bogatin. What Really Is Inductance? [https://speedingedge.com/wp-content/uploads/BTS006_What_Is_Inductance-2.pdf]

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Self-Inductance & Mutual Inductance

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image-20260124210821758\[\begin{align} N_a &= L_a I_a + \color{red}M_{ab}I_b \\ N_b &= L_b I_b + \color{red}M_{ab}I_a \end{align}\]

Induced voltage

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Partial Inductance

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Loop Self & Mutual Inductance

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Loop Mutual Inductance

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Equivalent Inductance of Multiple Inductors

image-20260125212328197 \[ L_\text{series} = L_1 + L_{12} + L_2 +L_{12} = L_1 + L_2 + 2L_{12} \]

\[ L_\text{parallel} = (L_1 + L_{12})\parallel (L_2 + L_{12}) = \frac{L_1L_2 +L_{12}(L_1+L_2)+L_{12}^2}{L_1+L_2+2L_{12}} \]

Partial Inductance

Loop Inductance is the sum of partial self-inductance and partial-mutual inductance

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Magnetic Vector Potential (磁矢势)

Youjin Deng. 5-3 静磁场的基本规律 [http://staff.ustc.edu.cn/~yjdeng/EM2022/pdf/5-2(2022).pdf]

磁场不能用标量势描述

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self partial inductance

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mutual partial inductance

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Ex. two-wire

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[https://www.oldfriend.url.tw/Q3D/ansys_ch_Partial_Loop_Inductance.html]

reference

Bogatin, E. (2018). Signal and power integrity, simplified. Prentice Hall. [pdf]

Paul, Clayton R. Inductance: Loop and Partial. Hoboken, N.J. : [Piscataway, N.J.]: Wiley ; IEEE, 2010. [pdf]

Spartaco Caniggia. Signal Integrity and Radiated Emission of High‐Speed Digital Systems. Wiley 2008

ISSCC2002. Special Topic Evening Discussion Sessions SE1: Inductance: Implications and Solutions for High-Speed Digital Circuits [vSE1_Blaauw], [vSE1_Gauthier], [vSE1_Morton, [vSE1_Restle]]

Y. Massoud and Y. Ismail, "Gasping the impact of on-chip inductance," in IEEE Circuits and Devices Magazine, vol. 17, no. 4, pp. 14-21, July 2001 [https://sci-hub.se/10.1109/101.950046]

Clayton R. Paul, Partial Inductance [https://ewh.ieee.org/soc/emcs/acstrial/newsletters/summer10/PP_PartialInductance.pdf]

Cheung-Wei Lam. Common Misconceptions about Inductance & Current Return Path [https://ewh.ieee.org/r6/scv/emc/archive/022010Lam.pdf]

Randy Wolff. Signal Loop Inductance in [Pin] and [Package Model] [https://ibis.org/summits/feb10/wolff.pdf]

ANSYS Q3D Getting Started LE05. Module 5: Q3D Inductance Matrix Reduction [https://innovationspace.ansys.com/courses/wp-content/uploads/sites/5/2021/07/Q3D_GS_2020R1_EN_LE05_Ind_Matrix.pdf]