Network Analysis and Scattering parameters

Posted on Edited on In

image-20241124184248887

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]

image-20250713101205684

Transmission-line

image-20250718223340699

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]

image-20250713102519144

image-20250713102641016

Transmission Line Wave Equation

image-20250718220504696

image-20250713104729920

image-20250718224751665

Characteristic Impedance (\(Z_0\))

image-20250713112912199

image-20250713113651799

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

image-20220430214052538

image-20220430214136970

image-20220430214419283

The default Z0 exported by EMX is 50

Complex Propagation Constant \(\gamma\)

TODO 📅

Input impedance (Line Impedance)

image-20250718231905402

Reflection Coefficient

TODO 📅

image-20250719081121034

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]

image-20250713090925198

image-20250713084136902

image-20250713091613844

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

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]

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

image-20250719072111526

image-20241112201300108

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

image-20250719010415229

image-20250719081657119

image-20250719081836680

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

image-20241030220203806

image-20241030220131714

image-20241030222403947

Reflection Coefficients

image-20241030222906229

image-20241030222923491

Rational Fit

Matlab/rationalfit

To resolve the convergence problem of s-parameter in Spectre simulator - rationalfit and write Verilog-A

image-20220630224525565

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
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-]

Simulating S-parameters in a time domain

image-20250705210519145

Spar in AC simulation

image-20250816221249094

image-20250816221939979

image-20250816222126241

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). doi:10.1109/dac.1999.781313

Cadence IEEE IMS 2023, Introducing the Spectre S-Parameter Quality Checker and Rational Fit Model Generator [https://support.cadence.com/apex/ArticleAttachmentPortal?id=a1O3w000009lplhEAA]

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]