matlab-design-pcb-transmission-line

name	matlab-design-pcb-transmission-line
description	Microstrip, stripline, CPW, differential pairs, and crosstalk analysis for impedance-controlled PCB interconnects. TRIGGER: user asks to design or analyze a transmission line (microstrip, stripline, CPW, coplanar, differential pair), extract RLGC or per-unit-length parameters, compute trace impedance, analyze a PCB trace cross-section, or perform crosstalk/coupling analysis. Invoke BEFORE writing code — preferred over RF Toolbox analytical functions (txlineMicrostrip, txlineStripline, txlineCPW). SKIP: EM simulation/S-parameter extraction of an existing component (use matlab-analyze-em), material/stackup definition only (use matlab-manage-pcb-material), building custom non-catalog geometry (use matlab-assemble-pcb-layout), optimization sweeps (use matlab-optimize-pcb-design).
license	https://www.mathworks.com/content/dam/mathworks/license/pmrl/license.md
metadata	{"author":"MathWorks","version":"2.0"}

Designing Transmission Lines

When to Use

• Designing microstrip, stripline, or CPW transmission lines for impedance control
• Modeling differential pairs with or without aggressor traces for NEXT/FEXT crosstalk
• Analyzing 2D cross-sections for fast per-unit-length RLGC extraction
• Creating SIW (substrate integrated waveguide) lines
• Using design() to auto-size lines for target impedance at a given frequency

When NOT to Use

• Building custom PCB structures from shapes — use matlab-assemble-pcb-layout
• Setting up substrate or conductor materials — use matlab-manage-pcb-material
• Running S-parameter or field analysis after design — use matlab-analyze-em
• Cascading transmission lines with other components — use matlab-integrate-pcb-circuit

Tool Selection Priority

1. RF PCB Toolbox (default): microstripLine, pcb2D, stripLine, coplanarWaveguide, etc.

   • 2D field solver — accurate for loss, coupling, and arbitrary stackups
   • Use for any RLGC, impedance, cross-section, or transmission line design task

2. RF Toolbox (fallback only): txlineMicrostrip, txlineStripline, txlineCPW

   • Analytical closed-form approximations, less accurate
   • Use ONLY when: the user explicitly names these functions, or states RF PCB Toolbox is unavailable

Typical Workflow

1. Before: matlab-manage-pcb-material — set up substrate and conductor
2. This skill: Design and analyze the transmission line
3. Check mesh/memory: memoryEstimate(obj, fc, 'RetainMesh', true) — inspect auto-mesh before solving
4. After: matlab-analyze-em — validate S-parameters → matlab-optimize-pcb-design — tune → matlab-integrate-pcb-circuit — cascade

Quick Reference

Object	Topology	Key Properties
microstripLine	Single microstrip on ground	Length, Width, Height, GroundPlaneWidth
stripLine	Signal embedded in dielectric	Length, Width, Height, GroundPlaneWidth
coplanarWaveguide	CPW on substrate	Length, Width, Height, SlotWidth, GroundPlaneWidth
coupledMicrostripLine	Edge-coupled microstrip pair	Length, Width, Spacing, Height
coupledStripLine	Edge-coupled stripline pair	Length, Width, Spacing, Height
microstripLineCustom	Custom coupled/differential microstrip	TraceType, TraceWidth, TraceSpacing, aggressor traces
stripLineCustom	Custom coupled/differential stripline	TraceType, TraceWidth, TraceSpacing
pcbBendCustom	Custom bend discontinuity (R2025a)	BendShape, Height, GroundPlaneWidth
pcb2D	2D cross-section analysis	BoardWidth, BoardCenter, Layers
SIWLine	Substrate integrated waveguide	Length, Width, ViaSpacing, ViaDiameter

Microstrip Line

Basic Creation and Design

ms = microstripLine;
show(ms);

% Design for target impedance at frequency
ms = design(microstripLine, 3e9);
Z0 = getZ0(ms);

Properties

ms = microstripLine;
ms.Length = 20e-3;
ms.Width = 5e-3;
ms.Height = 1.6e-3;            % Substrate height
ms.GroundPlaneWidth = 30e-3;
ms.Substrate = dielectric("FR4");
ms.Conductor = metal("Copper");

Analysis

ms.Conductor = metal("Copper");       % Required for rlgc (finite conductivity)
Z0 = getZ0(ms);                       % Characteristic impedance (no frequency argument)
td = propagationDelay(ms, 3e9);       % Propagation delay (scalar frequency)
params = rlgc(ms, 3e9);              % RLGC per unit length (scalar frequency)

freq = linspace(1e9, 6e9, 51);
sp = sparameters(ms, freq, 'SweepOption', 'interp');  % S-parameters (frequency vector OK)
rfplot(sp);

Inverted / Suspended Microstrip

Model inverted or suspended configurations with multi-layer substrates (air gaps):

% Inverted: air below trace, substrate above ground
ms = microstripLine;
ms.Substrate = dielectric(Name={"Air","FR4"}, EpsilonR=[1 4.4], ...
    LossTangent=[0 0.02], Thickness=[0.5e-3 1.6e-3]);
ms.Height = 0.5e-3 + 1.6e-3;

% Suspended: air / substrate / air
ms.Substrate = dielectric(Name={"Air","FR4","Air"}, EpsilonR=[1 4.4 1], ...
    LossTangent=[0 0.02 0], Thickness=[0.3e-3 0.8e-3 0.3e-3]);
ms.Height = sum([0.3e-3 0.8e-3 0.3e-3]);

Stripline

Stripline has the signal trace embedded between two ground planes.

Symmetric Stripline

sl = stripLine;
sl.Length = 20e-3;
sl.Width = 3e-3;
sl.Height = 3.2e-3;            % Total dielectric height (top + bottom)
sl.GroundPlaneWidth = 30e-3;
sl.Substrate = dielectric("Teflon");
sl.Conductor = metal("Copper");
show(sl);

Asymmetric Stripline

Use multi-layer dielectric with different thicknesses above and below. Height = cumulative thickness of layers below the signal (a layer boundary, not the total):

sl = stripLine;
sl.Substrate = dielectric(Name={"FR4","FR4"}, EpsilonR=[4.4 4.4], ...
    LossTangent=[0.02 0.02], Thickness=[0.8e-3 1.6e-3]);
sl.Height = 0.8e-3;    % Signal at the boundary between the two layers

Suspended Stripline

sl = stripLine;
sl.Substrate = dielectric(Name={"Air","FR4","Air"}, ...
    EpsilonR=[1 4.4 1], LossTangent=[0 0.02 0], ...
    Thickness=[0.5e-3 0.8e-3 0.5e-3]);
sl.Height = 0.5e-3;    % Signal at Air/FR4 boundary (0.5mm from ground)
sl = design(stripLine, 3e9);  % Or design for 50-ohm at target freq

Coplanar Waveguide

Basic CPW

cpw = coplanarWaveguide;
cpw.Length = 20e-3;
cpw.Width = 2e-3;          % Center conductor width
cpw.SlotWidth = 0.5e-3;    % Gap between center and ground
cpw.Height = 1.6e-3;
cpw.GroundPlaneWidth = 10e-3;
show(cpw);

Design and Analyze

cpw = design(coplanarWaveguide, 5e9);
Z0 = getZ0(cpw);
sp = sparameters(cpw, linspace(1e9, 10e9, 51), 'SweepOption', 'interp');
rfplot(sp);

Coupled Transmission Lines

Edge-Coupled Microstrip

cms = coupledMicrostripLine;
cms.Length = 20e-3;
cms.Width = 2e-3;
cms.Spacing = 0.5e-3;      % Gap between traces
cms.Height = 1.6e-3;
cms.Substrate = dielectric("FR4");
show(cms);

Even/Odd Mode Impedance

freq = 3e9;
Zeven = getZEven(cms, freq);   % Even-mode impedance
Zodd = getZOdd(cms, freq);     % Odd-mode impedance
Zdiff = 2 * Zodd;             % Differential impedance

Edge-Coupled Stripline

csl = coupledStripLine;
csl.Length = 20e-3;
csl.Width = 2e-3;
csl.Spacing = 0.3e-3;
csl.Height = 3.2e-3;
csl.Substrate = dielectric("Teflon");

Multi-Layer Coupled Lines

cms = coupledMicrostripLine;
sub = dielectric("FR4", "Teflon");
sub.Thickness = [1.0e-3 0.5e-3];       % Set Thickness BEFORE assigning to component
cms.Substrate = sub;
cms.Height = 1.5e-3;

Custom Transmission Lines and Crosstalk Analysis

microstripLineCustom and stripLineCustom model differential pairs with optional aggressor traces for NEXT/FEXT crosstalk analysis.

Properties (microstripLineCustom; stripLineCustom has same interface, Teflon default, embedded between ground planes)

Property	Default	Description
TraceType	'Single'	'Single' or 'Differential' (NOT 'Single-ended')
TraceLength	0.05	Trace length (m)
TraceWidth	0.002	Signal trace width (m)
TraceSpacing	0.002	Spacing between differential pair traces (m)
Height	0.0016	Substrate height (m)
GroundPlaneWidth	(read-only)	Ground plane width — auto-computed, cannot be set
LeftCoupledTraceGap	0	Gap to left aggressor trace (m); 0 = no left aggressor
RightCoupledTraceGap	0	Gap to right aggressor trace (m); 0 = no right aggressor
Substrate	FR4	Dielectric object
Conductor	PEC	Metal object

Differential Microstrip

ms_diff = microstripLineCustom(TraceType='Differential', ...
    TraceWidth=0.002, TraceSpacing=0.0005);
show(ms_diff);

Differential with Aggressor Traces

ms_diff = microstripLineCustom(TraceType='Differential', ...
    TraceWidth=0.002, TraceSpacing=0.0005, ...
    RightCoupledTraceGap=[0.003, 0.003], ...
    LeftCoupledTraceGap=0);
show(ms_diff);

NEXT/FEXT Extraction

With aggressor traces, the S-parameter matrix is 6-port. Port mapping:

Port	Trace
1, 2	Differential pair (near end, far end)
3, 4	Left aggressor (near end = NEXT, far end = FEXT)
5, 6	Right aggressor (near end = NEXT, far end = FEXT)

ms = microstripLineCustom(TraceType='Differential', ...
    TraceWidth=0.002, TraceSpacing=0.0005, ...
    LeftCoupledTraceGap=0.003, RightCoupledTraceGap=0.003);
ms.Conductor = metal("Copper");

freq = linspace(0.1e9, 10e9, 101);
sp = sparameters(ms, freq, 'SweepOption', 'interp');

% Extract crosstalk from S-parameters
S31_dB = 20*log10(abs(squeeze(sp.Parameters(3,1,:))));  % Left NEXT
S41_dB = 20*log10(abs(squeeze(sp.Parameters(4,1,:))));  % Left FEXT
S51_dB = 20*log10(abs(squeeze(sp.Parameters(5,1,:))));  % Right NEXT
S61_dB = 20*log10(abs(squeeze(sp.Parameters(6,1,:))));  % Right FEXT

RLGC Coupling Matrices

For coupled/differential lines, rlgc returns N×N matrices (off-diagonal = mutual L/C):

ms = microstripLineCustom(TraceType='Differential', ...
    TraceWidth=0.002, TraceSpacing=0.0005, RightCoupledTraceGap=0.003);
ms.Conductor = metal("Copper");
params = rlgc(ms, 5e9);

Custom Bends and Traces (R2025a)

pcbBendCustom and pcbTraceCustom model bend discontinuities and step-impedance transitions. See references/custom-bends-and-traces.md for properties and examples.

SIW Transmission Line

Substrate Integrated Waveguide uses via fences to create a waveguide in PCB.

siw = SIWLine;
siw.Length = 15.3e-3;
siw.Width = 7.4e-3;
siw.ViaSpacing = [1.2e-3 5e-3];   % [along-length, across-width]
siw.ViaDiameter = 0.51e-3;
siw.Height = 0.254e-3;
siw.Substrate = dielectric(Name="RO4003C", EpsilonR=3.38, LossTangent=0.0027, Thickness=0.254e-3);
siw.Conductor = metal("Copper");
show(siw);

sp = sparameters(siw, linspace(20e9, 40e9, 51), 'SweepOption', 'interp');
rfplot(sp);

The SIW has a FeedLine property (a traceTapered object) for the microstrip-to-SIW transition.

2D Cross-Section Analysis

pcb2D

Creates a 2D cross-section model for fast per-unit-length analysis. Much faster than full 3D sparameters for uniform transmission line characterization.

p = pcb2D;
p = pcb2D(Name=Value);

Key Properties:

• Name — Descriptive name for the cross-section
• BoardWidth — Total board width (m)
• BoardCenter — Center position of the board cross-section
• Layers — Cell array of trace2D and dielectric objects defining the stackup

Methods: show(p), sparameters(p, freq), rlgc(p, scalarFreq), propagationDelay(p, scalarFreq)

trace2D

Represents a trace cross-section for use inside a pcb2D object's Layers cell array.

t = trace2D;
t.Type = 'Signal';                                  % 'Signal' (default) or 'Ground'
t.Shape = shape.Rectangle(Length=0.3e-3, Width=35e-6);  % Length=trace width, Width=trace thickness
t.Conductor = metal("Copper");

Key Properties: Type ('Signal'/'Ground'), Shape (shape.Rectangle — Length = trace width, Width = metal thickness), Conductor, TrapezoidalEtchAngle

Building a 2D Model — Single Trace

sub = dielectric("FR4");
sub.Thickness = 0.2e-3;

sig = trace2D;
sig.Type = 'Signal';
sig.Shape = shape.Rectangle(Length=0.3e-3, Width=35e-6);
sig.Conductor = metal("Copper");

gnd = trace2D;
gnd.Type = 'Ground';
gnd.Shape = shape.Rectangle(Length=5e-3, Width=35e-6);

p = pcb2D(BoardWidth=5e-3, Layers={sig, sub, gnd});
show(p);
params = rlgc(p, 10e9);
fprintf('L = %.2f nH/m, C = %.2f pF/m\n', params.L*1e9, params.C*1e12);

Building a 2D Model — Differential Pair (Coupled Traces)

Multiple traces on the same metal layer must be passed as a trace2D array [sig1, sig2], not separate cells:

sub = dielectric("FR4");
sub.Thickness = 0.2e-3;

sig1 = trace2D;
sig1.Type = 'Signal';
sig1.Shape = shape.Rectangle(Length=0.15e-3, Width=35e-6);
sig1.Shape.Center = [-0.2e-3 0];
sig1.Conductor = metal("Copper");

sig2 = trace2D;
sig2.Type = 'Signal';
sig2.Shape = shape.Rectangle(Length=0.15e-3, Width=35e-6);
sig2.Shape.Center = [0.2e-3 0];
sig2.Conductor = metal("Copper");

gnd = trace2D;
gnd.Type = 'Ground';
gnd.Shape = shape.Rectangle(Length=5e-3, Width=35e-6);

p = pcb2D(BoardWidth=5e-3, Layers={[sig1, sig2], sub, gnd});
show(p);
params = rlgc(p, 10e9);  % Returns 2x2 L and C matrices for coupled pair

When to Use pcb2D vs 3D

Scenario	Approach
Impedance/RLGC of uniform cross-section	pcb2D — milliseconds
Discontinuities (bends, steps, stubs)	3D sparameters — minutes
Differential pair coupling	pcb2D with [sig1, sig2] array

Slicing a 3-D Component to 2-D

slice extracts a 2-D cross section from a pcbComponent (convert catalog objects first):

cms = design(coupledMicrostripLine, 3e9);
cms.Conductor = metal("Copper");
pcb2d = slice(pcbComponent(cms));
params = rlgc(pcb2d, 3e9);

design() for Impedance Targeting

The design function sizes a transmission line for a target frequency (and optionally impedance):

ms = design(microstripLine, 3e9);           % Default 50-ohm at 3 GHz
sl = design(stripLine, 5e9);                % Default 50-ohm at 5 GHz
cpw = design(coplanarWaveguide, 10e9);      % Default 50-ohm at 10 GHz

After design, verify with getZ0:

Z0 = getZ0(ms);   % Should be ~50 ohm

transmissionLineDesigner App

Interactive app for designing and analyzing transmission lines:

transmissionLineDesigner

Select line type, set dimensions/materials interactively, analyze impedance/S-parameters/RLGC, and export designs to workspace.

Design Adjustments

Problem	Adjust	Direction
Z0 too high	Width	Increase
Z0 too low	Width	Decrease
Too lossy	Conductor thickness	Increase
Wrong electrical length	Length	Adjust

Pitfalls

1. Use interpolating sweep for S-parameters: Always use sparameters(obj, freq, 'SweepOption', 'interp') — direct sweeps are significantly slower.

2. Check mesh density before solving: Run memoryEstimate(obj, fc, 'RetainMesh', true) before sparameters(). If too dense, coarsen: mesh(obj, 'MaxEdgeLength', lambda/6). See matlab-analyze-em.

3. Height meaning differs by topology: For microstrip, Height = dielectric thickness. For stripline with multi-layer substrate, Height must equal a cumulative layer boundary — it defines where the signal sits in the stack.

4. Width controls impedance: Wider trace → lower impedance. Use design() to auto-size, then adjust manually if needed.

5. Conductor defaults to PEC: Without assigning metal("Copper"), loss will be zero. Always set Conductor for realistic insertion loss.

6. Inverted/suspended microstrip Height rule: For inverted microstrip, create multi-layer dielectric with Name={"Substrate","Air"} and set Height to air layer thickness. For suspended microstrip, Height = sum of air + substrate thickness.

7. Multi-layer stripline Height is a layer boundary, not total: Height must equal a cumulative layer boundary from Thickness vector. Setting Height to total causes "Expected Height must be among the substrate layers."

8. SIW cutoff: SIW has a cutoff frequency below which signals do not propagate. Size the width for operation well above cutoff.

9. getZ0 takes no frequency: getZ0(obj) returns characteristic impedance directly. Do not pass a frequency argument.

10. rlgc requires finite conductivity: Assign metal("Copper") before calling rlgc. Default PEC causes "Conductivity value must be finite with 2D field solver."

11. Multi-layer Name must use cell array: Use Name={"Air","FR4"} (cell array), not Name=["Air","FR4"] (string array).

Related Skills

• matlab-manage-pcb-material — Substrate and conductor setup
• matlab-analyze-em — S-parameter extraction and field analysis
• matlab-integrate-pcb-circuit — Touchstone export, circuit cascading
• matlab-assemble-pcb-layout — Custom trace geometries

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