Crosstalk in Transmission Lines

Posted on Edited on In

image-20260419092048803

Electric field coupling (also called capacitive coupling) occurs when energy is coupled from one circuit to another through an electric field

Two circuits above a signal return plane.

Magnetic field coupling (also called inductive coupling) occurs when energy is coupled from one circuit to another through a magnetic field

Two circuits above a signal return plane

For instance

  • magnetic coupling between multiple inductors
  • capacitive coupling between multiple transmission lines

image-20260808160818333

Transmission Line

image-20260530103816500

param. extraction from ABCD matrix

Chapter 4.5. High Frequency Passive Devices [https://www.cambridge.org/il/files/7713/6698/2369/HFIC_chapter_4_passives.pdf]

image-20260416212059482

for lossless T-line, \(\gamma = j\beta\)

image-20260418110304117

Capacitive Coupling

Faraday cage

image-20260808160638564

Magnetic Coupling

Darabi H. Radio Frequency Integrated Circuits and Systems. 2nd ed. Cambridge University Press; 2020.

image-20260711102418048

shield_ground_loop_faraday_induction

NEXT & FEXT

Backward (near-end) crosstalk & Forward (far-end) crosstalk

Mohammad Abu Khater, ISCAS2019 tutorial: High-Performance Printed Circuit Boards (PCBs)

image-20260923232807253

Consider a small section at distance (x) from the input:

  1. The aggressor’s edge reaches it at time \(x/v\), generating a small noise pulse.
  2. That pulse travels forward on the victim through the remaining distance \(\ell-x\)

Its arrival time at the far end is therefore

\[ t_{\text{arrival}} =\underbrace{\frac{x}{v}}_{\text{aggressor reaches section}} +\underbrace{\frac{\ell-x}{v}}_{\text{noise reaches far end}} =\frac{\ell}{v} \]

Noise generated earlier travels farther; noise generated later travels less. The pulses overlap, so adding more coupled sections increases their summed amplitude

Each short section contributes in proportion to its length and the edge slope: \[ dV_F\propto dx\,\frac{\Delta V}{t_r} \quad\Longrightarrow\quad \boxed{V_{F,\text{peak}}\propto \ell\,\frac{\Delta V}{t_r}} \]

Here, \(\ell\) means the length over which the traces run alongside each other.

For comparison, backward noise arrives at \(x/v+x/v=2x/v\), so contributions from different locations spread out in time. That explains why extending a sufficiently long coupled line mainly increases the backward pulse’s duration

relative dielectric constant vs permittivity

img

The relative dielectric constant characterizes some of the electrical properties of an insulator

Return Path

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

image-20250705171613361

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)

image-20250705170949035

skin effect & Dielectric loss

image-20250705170028485

EMX simulation

setup:

image-20250706004037966

frequency sweep:

image-20250706010943996

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

image-20250706010216105

Tline Approximation

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

image-20250817105056325

N-section LC Model

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]

image-20250817105203031image-20250817105308602

image-20260115210350617

RLGC by Open/Short Circuit

RLGC can be extracted from measurements of a transmission line's input impedance under open-circuit and short-circuit terminations at a specific frequency

image-20260412110152719

Dr. Muehlhaus Consulting & Software GmbH, lumpedmodel [https://github.com/VolkerMuehlhaus/lumpedmodel]

Transmission line from S2P data into RLGC lumped model

plot \[ \boxed{R= \text{Re}(\gamma Z_c)} \qquad \boxed{L= \frac{\text{Im}(\gamma Z_c)}{\omega}} \qquad \boxed{G= \text{Re}\left(\frac{\gamma}{Z_c}\right)} \qquad \boxed{C= \frac{\text{Im}\left(\frac{\gamma}{Z_c}\right)}{\omega}} \]

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
37
38
39
# https://github.com/VolkerMuehlhaus/lumpedmodel/blob/main/rlgc_from_s2p/rlgc_from_s2p.py


# input data, must be 2-port S2P data
sub = rf.Network(args.s2p, z0=args.z0_ohm)

# physical length must be supplied by user
length = args.l_um*1e-6

# target frequency for pi model extraction
f_target = args.f_ghz*1e9

assert f_target < freq.stop

# get index for exctraction
f = freq.f
ftarget_index = rf.find_nearest_index(freq.f, f_target)
omega = 2*np.pi*f[ftarget_index]

z11=sub.z[0::,0,0]          # z11, the open impedance
y11=sub.y[0::,0,0]          # 1/y11, the short impedance
Zline = np.sqrt(z11/y11)    # characteristic impedance of the line

gamma0 = 1/length * np.arctanh(1/(Zline*y11))   # propagation constant

# electrical phase  = β · length        = gamma0.imag * length   ✓
# attenuation       = α                 = gamma0.real            (no wrap)
# period=np.pi/2 instead of the default 2π reflects the branch period of arctanh
gamma_wideband =  gamma0.real + 1j*np.unwrap(gamma0.imag*length, period=np.pi/2)/length


gamma_ftarget = gamma_wideband[ftarget_index]
Zline_ftarget = Zline[ftarget_index]


R = (gamma_ftarget*Zline_ftarget).real
L = (gamma_ftarget*Zline_ftarget).imag / omega
G = (gamma_ftarget/Zline_ftarget).real
C = (gamma_ftarget/Zline_ftarget).imag / omega

Transmission Line [pdf]

image-20260412110316910

Decoupling Capacitor

image-20250705175343498

image-20260125205518872

image-20260125205941736

image-20260125211108504

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

90o Turns

Mohammad Abu Khater, ISCAS2019 tutorial: High-Performance Printed Circuit Boards (PCBs)

image-20260923225838811

Hyperbolic Functions

image-20260418105248415

reference

信号完整性揭秘:于博士SI设计手记

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

High-speed Serial Interface Lect. 9 – Noise [http://tera.yonsei.ac.kr/class/2017_2_2/lecture/Lect%209%20Noise.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]

Sam Palermo, ECEN720: High-Speed Links Circuits and Systems Spring 2025 Lecture 9: Noise Sources [https://people.engr.tamu.edu/spalermo/ecen689/lecture9_ee720_noise_sources.pdf]