Network Analysis and Scattering parameters

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Mixed-Mode S-parameter

12 May 2021 Introduction to Mixed-Mode S-parameters [https://blog.teledynelecroy.com/2021/05/introduction-to-mixed-mode-s-parameters.html]

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Troy Beukema (IBM Research, Yorktown Heights, NY). 03-Sep-2009. Topics in Design and Analysis of High Data Rate SERDES Systems [https://ewh.ieee.org/r5/denver/sscs/Presentations/2009_09_Beukema.pdf]

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Bert Simonovich. A Guide for Single-Ended to Mixed-Mode S-parameter Conversions [https://www.signalintegrityjournal.com/articles/1832-a-guide-for-singleended-to-mixedmode-s-parameter-conversions]

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single-ended S-parameters

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Mixed-mode S-parameters

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Missing Term in KVL

Prof. Kolb/Whites. EE 382 Applied Electromagnetics Lecture 8: Maxwell's Equations and Electrical CIrcuits [http://montoya.sdsmt.edu/ee382/lectures/382Lecture8.pdf]

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Transmission-line

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Telegrapher’s equations

EECS 723- Microwave Engineering Spring 2.1 -The Lumped Element Circuit Model for Transmission Lines

1/20/2005 [https://www.ittc.ku.edu/~jstiles/723/handouts/2_1_Lumped_Element_Circuit_Model_package.pdf]

note [https://www.ittc.ku.edu/~jstiles/723/handouts/section_2_1_The_Lumped_Element_Circuit_Model_package.pdf]

present [https://www.ittc.ku.edu/~jstiles/723/handouts/section_2_1_The_Lumped_Element_Circuit_Model_present.pdf]

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Transmission Line Wave Equation

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Characteristic Impedance (\(Z_0\))

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Remember, S-parameters don't mean much unless you know the value of the reference impedance (it's frequently called Z0).

simulator will read sp file's Z0 parameter

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The default Z0 exported by EMX is 50

Complex Propagation Constant \(\gamma\)

TODO 📅

Input impedance (Line Impedance)

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Reflection Coefficient

TODO 📅

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Steady-State Solution (DC voltage division)

Sam Palermo. [https://people.engr.tamu.edu/spalermo/ecen689/lecture3_ee689_tlines.pdf]

Kyoung-Jae Chung. Special Topics in Radiation Engineering (High-voltage pulsed power engineering) [https://ocw.snu.ac.kr/sites/default/files/NOTE/Lecture_03_Transmission%20line%20theory.pdf]

David R. Jackson. [https://courses.egr.uh.edu/ECE/ECE3317/SectionJackson/Class%20Notes/Notes%208%203317%20Transmission%20Lines%20(Bounce%20Diagram).pdf]

Shouri Chatterjee [https://web.iitd.ac.in/~shouri/ell112/material/txline.pdf]

How can I go from transmission line model to lumped elements model? [https://physics.stackexchange.com/a/386603]

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E157 Introduction to Radio Frequency Circuit Design [https://pages.hmc.edu/mspencer/e157/fa24/]

Shen Lin. On-Chip Inductance and Coupling Effects [http://eda.ee.ucla.edu/pub/asic.pdf]

A. Deutsch et al., "When are transmission-line effects important for on-chip interconnections?," in IEEE Transactions on Microwave Theory and Techniques, vol. 45, no. 10, pp. 1836-1846, Oct. 1997

Ho, Ron. “Chip Wires: Scaling and Efficiency.” (2003). [https://www-vlsi.stanford.edu/people/alum/pdf/0303_Ho_Wires.pdf]

—. ISSCC 2007 T3: Dealing with Issues in VLSI Interconnect Scaling, by Ron Ho

Tony Chan Carusone. ISSCC 2017 T6: Signal Integrity Analysis for Gb/s Links

Byungsub Kim ISSCC 2022 T11: "Basics of Equalization Techniques: Channels, Equalization, and Circuits"

Voltage scattering

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transmitted voltage \[ V= \frac{2Z_l}{Z_l+R_0}\frac{V_s}{2}= \frac{Z_l}{Z_l+R_0}\cdot V_s \]

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CHAPTER 6 Transmission-Line Essentials for Digital Electronics [https://ws.engr.illinois.edu/sitemanager/getfile.asp?id=178]

CHAPTER 7 Transmission-Line Analysis [https://ws.engr.illinois.edu/sitemanager/getfile.asp?id=199]

Voltage Transfer Function

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Troy Beukema (IBM Research, Yorktown Heights, NY). 03-Sep-2009. Topics in Design and Analysis of High Data Rate SERDES Systems [https://ewh.ieee.org/r5/denver/sscs/Presentations/2009_09_Beukema.pdf]

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Impulse Response from S-Parameters (channel)

David Banas. A comparison of different techniques (i.e. - windowing, vector fitting, etc.) for extracting the impulse response from S-parameters. [https://github.com/capn-freako/ImpulseResponseFromSparameters/tree/main]

Sam Palermo. ECEN720: High-Speed Links Circuits and Systems Spring 2025 - Lecture 3: Time-Domain Reflectometry & S-Parameter Channel Models [https://people.engr.tamu.edu/spalermo/ecen689/lecture3_ee720_tdr_spar.pdf]

Troy Beukema (IBM Research, Yorktown Heights, NY). 03-Sep-2009. Topics in Design and Analysis of High Data Rate SERDES Systems [https://ewh.ieee.org/r5/denver/sscs/Presentations/2009_09_Beukema.pdf]

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Causality

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causality-passivity correction

P. Triverio, S. Grivet-Talocia, M. S. Nakhla, F. G. Canavero and R. Achar, "Stability, Causality, and Passivity in Electrical Interconnect Models," in IEEE Transactions on Advanced Packaging, vol. 30, no. 4, pp. 795-808, Nov. 2007 [https://sci-hub.ru/10.1109/TADVP.2007.901567]

S. Sercu, C. Kocuba, J. Nadolny, "Causality Demystified", in DesignCon 2015, Jan. 2015 [pdf]

Vinod Arjun Huddar. Causality Problems in Power Delivery Networks [https://www.signalintegrityjournal.com/articles/1217-causality-in-power-delivery-network-in-package-board]

Tyler Huddleston, Signal Edge Solutions. Causality in Practice: How Frequency Sampling and Bandwidth Shape Time-Domain Fidelity [https://www.signalintegrityjournal.com/articles/4061-causality-in-practice-how-frequency-sampling-and-bandwidth-shape-time-domain-fidelity]

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\(H_e(f) = \mathcal{Re}\{H(f)\}\), \(H_o(f) = j\cdot\mathcal{Im}\{H(f)\}\) and \(\enclose{circle}{1}\) , \(\enclose{circle}{2}\)

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Rational Fit

Use the rational function to fit data defined in the frequency domain with an equivalent Laplace transfer function. Using rational function fitting you can create simple models for a required accuracy, model order reduction, zero phase on extrapolation to DC, and causal modeling system among other advantages

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filename  = 'touchstone/ISI.S4P';
s4p = read(rfdata.data, filename);
sdd_params = s2sdd(s2p.S_Parameters, 2);
sdd21 = squeeze(sdd_params(2, 1, :));   % s21
freq = s4p.Freq;

% rational fitting
weight = ones(size(sdd21));
weight(floor(end*3/4):end) = 0.2;
weight(2:10) = 0;

[hfit, errb] = rationalfit(freq, sdd21, 'IterationLimit', [4, 16], 'Delayfactor', 0.98, ...
    'Weight', weight, 'Tolerance', -38, 'NPoles', 32);
[sdd21_fit, ff] = freqresp(hfit, freq);

figure(1)
plot(freq/1e9, db(sdd21), 'b-'); hold on;
plot(ff/1e9, db(sdd21_fit), 'r-'); hold off; grid on;
legend('sdd21', 'sdd21\_fit');
xlabel('Freq (GHz)');
ylabel('magnitude (dB)');


ts = 1e-12;
n = 2^18;
trise = 4e-14;
[yout, tout] = stepresp(hfit, ts, n, trise);
figure(2)
plot(tout*1e12, yout, 'b-'); grid on;
xlabel('Time (ps)');
ylabel('V');
title('Step Response');


% write verilog-A
writeva(hfit, 'channel_32poles.va');

Using S Parameters to Estimate Q

TODO 📅

Jeff Walling. ECE 5984 Using S Parameters to Estimate Q [https://youtu.be/PXgM6pGIRvk?si=YDeh-COQEBXKUiw-]

Reading S-parameters

teledynelecroy. Reading S-parameters [https://blog.teledynelecroy.com/2020/05/]

keysight. How to Interpret Ripple in an S Parameters Measurement [https://docs.keysight.com/kkbopen/how-to-interpret-ripple-in-an-s-parameters-measurement-849642201.html]

You Measured What? Four Must-Know Checks Before Trusting Your Trace S-Parameters [https://www.signalintegrityjournal.com/articles/4083-you-measured-what-four-must-know-checks-before-trusting-your-trace-s-parameters]

TODO 📅

Ripple in an S Parameters

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S11 vs TDR

[https://ewh.ieee.org/r5/denver/sscs/Presentations/2004_04_Quach.pdf]

TODO 📅

Spar in Tran simulation

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Spar in AC simulation

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reference

microwaves101, S-parameters (https://www.microwaves101.com/encyclopedias/s-parameters)

Pupalaikis, P. (2020). S-Parameters for Signal Integrity. Cambridge: Cambridge University Press. doi:10.1017/9781108784863

Coelho, C. P., Phillips, J. R., & Silveira, L. M. (n.d.). Robust rational function approximation algorithm for model generation. Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361). [https://sci-hub.ru/10.1109/dac.1999.781313]

Cadence IEEE IMS 2023, Introducing the Spectre S-Parameter Quality Checker and Rational Fit Model Generator

The Complex Art Of Handling S-Parameters: The importance of extraction and fitting to circuit simulation involving S-parameters [https://semiengineering.com/the-complex-art-of-handling-s-parameters]

Dr. John Choma. EE 541, Fall 2006: Course Notes #2 Scattering Parameters: Concept, Theory, and Applications [https://www.ieee.li/pdf/essay/scattering_parameters_concept_theory_applications.pdf]

Dr. Ray Kwok . Network Techniques: Conversion between Filter Transfer Function and Filter Scattering (SMatrix) Parameters [https://www.sjsu.edu/people/raymond.kwok/docs/project172/FTF%20to%20S-Matrix%20Spring%202011.pdf]

田庆诚教授 台湾中华大学 射频电路基础（公司培训）[https://www.bilibili.com/video/BV1LA41177wr/?p=3&share_source=copy_web&vd_source=5a095c2d604a5d4392ea78fa2bbc7249]

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