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

1. 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

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)

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:

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

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

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.

1. 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.

1. 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."

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

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

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

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

1. trace2D uses Shape, not Width/Thickness: Set t.Shape = shape.Rectangle(Length=traceWidth, Width=metalThickness). Note: shape.Rectangle.Length = trace width, .Width = metal thickness. A pcb2D requires at least one 'Ground' type trace.

1. pcb2D rlgc takes scalar frequency: rlgc(p, freq) requires a scalar, not a vector. Loop or call once at the frequency of interest.

1. pcb2D trace2D Center is x-position only: trace2D.Shape.Center controls horizontal position. Vertical is from layer stacking order. Set Center = [x_offset 0].

1. Same-layer traces need array, not separate cells: For coupled/differential traces on the same metal layer, use Layers={[sig1, sig2], sub, gnd}. Separate cells {sig1, sig2, sub, gnd} treats them as different metal layers and errors: "dielectric layer must be between metal layers."

1. Crosstalk port count depends on aggressor configuration: Both aggressors → 6-port; one → 4-port; none → 2-port. RightCoupledTraceGap=Inf removes that aggressor.

1. TraceGap is edge-to-edge, not center-to-center: Measures gap between nearest edges, not trace centers.

1. Use `TraceWidth`, not `Width`: microstripLineCustom and stripLineCustom use TraceWidth. Setting Width silently has no effect.

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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