Inductance & Transmission Line

Posted on Edited on In

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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img

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

Current Return Path

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Current return paths are frequency dependent \(Z = R +j\omega L\)

  • Low frequency
    • \(R\) dominates - current use as many returns as possible to have parallel resistances
  • High frequency
    • \(j\omega L\)​ dominates - current use the closest possible return path to form the smallest possible loop inductance
  • Very high frequency
    • The current would be confined to the nearest possible return only at ultra-high frequencies (skin effect)

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skin effect & Dielectric loss

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EMX simulation

setup:

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frequency sweep:

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Cadence October 2020, Analysis of a Figure-Eight Inductor with EMX RAK

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RLC network

[https://web.stanford.edu/class/archive/ee/ee371/ee371.1066/handouts/markChapt.pdf]

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Decoupling Capacitor

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Grounding

Chapter 11 Layout and grounding [http://ieb-srv1.upc.es/gieb/tecniques/doc/EMC/pdfs/ScienceDirect_articles_27Jul2018_12-16-10.699/Chapter-11---Layout-and-grounding_2007_EMC-for-Product-Designers.pdf]

TODO 📅

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]

Yuriy Shlepnev. How Interconnects Work: Characteristic Impedance and Reflections [https://www.linkedin.com/pulse/how-interconnects-work-characteristic-impedance-yuriy-shlepnev/]

—. How Interconnects Work: Bandwidth for Modeling and Measurements [https://www.linkedin.com/pulse/how-interconnects-work-bandwidth-modeling-yuriy-shlepnev/?trackingId=874kpm3XuNyV9D0eP6IioA%3D%3D]

Eric Bogatin. Pop Quiz: When is an Interconnect Not a Transmission Line? [https://www.signalintegrityjournal.com/blogs/4-eric-bogatin-signal-integrity-journal-technical-editor/post/265-pop-quiz-when-is-an-interconnect-not-a-transmission-line]

TeledyneLeCroy/SignalIntegrity Python tools for signal integrity applications [SignalIntegrityApp]

A Look at Transmission-Line Losses [http://blog.teledynelecroy.com/2018/06/a-look-at-transmission-line-losses.html]

How Much Transmission-Line Loss is Too Much? [http://blog.teledynelecroy.com/2018/06/how-much-transmission-line-loss-is-too.html]

Raymond Y. Chen, Raymond Y. Chen. Fundamentals of S Fundamentals of S-Parameter Parameter Modeling for Power Distribution Modeling for Power Distribution System (PDS) and SSO Analysis System (PDS) and SSO Analysis [https://ibis.org/summits/jun05/chen.pdf]