Signal Integrity Characterization

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TDR Impedance

Amit Bahl, How TDR Impedance Measurements Work [https://www.protoexpress.com/blog/tdr-impedance-measurements/]

Minh Quach. Signal Integrity Consideration and Analysis 4/30/2004 Frequency & Time Domain Measurements/Analysis [https://ewh.ieee.org/r5/denver/sscs/Presentations/2004_04_Quach.pdf]

江上渔樵, 在ADS中查看TDR的3种方法 [https://zhuanlan.zhihu.com/p/420350734]

VtStep vs TDR

Abhargava, TDR Analysis using Agilent ADS [https://abhargava.wordpress.com/wp-content/uploads/2014/01/performing-tdr-analysis-using-agilent-ads.pdf]

Mike Steinberger, TDR: Reading the Tea Leaves [https://siguys.com/wp-content/uploads/2016/01/TDR_TeaLeaves.pdf]

image-20260419164454411

image-20260419165629435

image-20260420215923585 \[ \color{red}Z_T(t) = Z_0\cdot \frac{1+\Gamma}{1-\Gamma} \]

S11 vs TDR

Vladimir Dmitriev-Zdorov, Mentor Graphics, DesignCon 2014, Computation of Time Domain Impedance Profile from S-Parameters: Challenges and Methods [link]

Samtec, High Speed Characterization Report PCIEC-064-1000-EC-EM-P-85 [https://suddendocs.samtec.com/testreports/hsc-report_pciec-85_web.pdf]

image-20260420232932030

image-20260420232956757

w/ IFFT

比尔盖子, Frequency domain S11 conversion to time domain TDR [https://electronics.stackexchange.com/a/626063/233816]

HFSS™ 3D Layout Window Functions and Time Domain Plotting [https://ansyshelp.ansys.com/public/Views/Secured/Electronics/v252/en/Subsystems/HFSS3DLayout/Content/ReportsandPostProc/WindowFunctionsandTimeDomainPlotting.htm]

Time Domain Measurements using Vector Network Analyzer ZVR [https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/dl_application/application_notes/1ez44/1ez44_0e.pdf]

scikit-rf plot_z_time_step

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S₁₁(f)
   │  (extrapolate_to_dc → uniform grid starting at 0 Hz)
   ▼
W(f) · S₁₁(f)                 ← windowed(): half-window, 1 at DC, 0 at f_max,
                                normalize=False (preserves S(0))
   │  (np.fft.irfft + fftshift)
   ▼
h(t)  – impulse response       ← impulse_response()
   │  (cumulative_trapezoid)
   ▼
Γ_step(t)  ∈ [−1, 1]           ← step_response()
   │  Z(t) = z0 · (1+Γ)/(1−Γ)   (clamp Γ=1)
   ▼
Z(t)  – plotted vs t (in ns)   ← plot_attribute() with attribute='z',
                                conversion='time_step'

Graphical illustrations of multiplicy the spectrum of a step function with a rectangular window to produce a finite edge in the time domain

image-20260420230505339

Window function with \(w[0] = 1\) and \(w[f_{max}]\)=0 ensure \(\Gamma(+\infty)\) and \(\Gamma(0)\) are correct

Jim Nadolny, Samtec. Technical Note Transformation of Samtec Connector Test Data For 85 ohm Differential Impedance Applications, [https://suddendocs.samtec.com/notesandwhitepapers/technical-note_85ohm-reference-z-xform_web.pdf]

[ADS: 1-10] TDR Impedance (Part 2) TDRインピーダンス解析 [https://youtu.be/ACINktqpM50]

ADS tdr_sp_imped

image-20260420235747173

Peter Goossens, Transformation of time domain TDR to its frequency domain S11 (Return Loss) using FFT [https://www.gquipment.com/blog/transformation-of-time-domain-tdr-to-its-frequency-domain-s11-return-loss-using-fft]

image-20260420224211467

image-20260420223849838

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# Pseudo code, laying out the essential steps only
# Trace data is in x_values
sampling_interval = np.mean(np.diff(x_values))
#  First derivative
diff_gamma_values = np.gradient(gamma_values)
# FFT
fourier_data = fft(diff_gama_values)
# Get the frequencies corresponding to the FFT result
frequencies = np.fft.fftfreq(len(diff_gama_values), d=sampling_interval)
# Calculate the magnitude of the complex Fourier transform data
magnitude = np.abs(fourier_data)
# Return loss
magnitude = 20 * np.log10(magnitude)
# Plot (frequency, magnitude)

w/ RFE

rational fraction expansion (RFE)

TODO 📅

Time-Domain Transmission (TDT)

TODO 📅

image-20260420220101203

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

image-20260110134112029

image-20260110134010253

Using S Parameters to Estimate Q

Jeff Walling. ECE 5984 Using S Parameters to Estimate Q [https://youtu.be/PXgM6pGIRvk]

TODO 📅

reference

Bogatin, Eric. 2020. Bogatin’s Practical Guide to Transmission Line Design and Characterization for Signal Integrity Applications / .Eric Bogatin. Artech House.

keysight, Signal Integrity Characterization Techniques [pdf]

Tim Wang-Lee, DesignCon 2026 KEF: Mastering TDR and De-embedding Through Simulation and Measurement [link]

Csaba SOOS, Signal and Power Integrity Design Practices [https://indico.cern.ch/event/358837/attachments/714663/1930957/Signal_and_Power_Integrity_Practices.pdf]

Sam Palermo, ECEN689: Special Topics in High-Speed Links Circuits and Systems Spring 2012 Lecture 3: Time-Domain Reflectometry & S-Parameter Channel Models [https://people.engr.tamu.edu/spalermo/ecen689/lecture3_ee689_tdr_spar.pdf]