--- name: matlab/matlab-design-pcb-txline source: https://app.decimal.ai/s/matlab-matlab-design-pcb-txline@1/SKILL.md source_sha256: 20bb7f03bb89 --- # 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 ```matlab ms = microstripLine; show(ms); % Design for target impedance at frequency ms = design(microstripLine, 3e9); Z0 = getZ0(ms); ``` ### Properties ```matlab 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 ```matlab 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): ```matlab % 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 ```matlab 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): ```matlab 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 ```matlab 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 ```matlab 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 ```matlab cpw = design(coplanarWaveguide, 5e9); Z0 = getZ0(cpw); sp = sparameters(cpw, linspace(1e9, 10e9, 51), 'SweepOption', 'interp'); rfplot(sp); ``` ## Coupled Transmission Lines ### Edge-Coupled Microstrip ```matlab 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 ```matlab freq = 3e9; Zeven = getZEven(cms, freq); % Even-mode impedance Zodd = getZOdd(cms, freq); % Odd-mode impedance Zdiff = 2 * Zodd; % Differential impedance ``` ### Edge-Coupled Stripline ```matlab 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 ```matlab 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 ```matlab ms_diff = microstripLineCustom(TraceType='Differential', ... TraceWidth=0.002, TraceSpacing=0.0005); show(ms_diff); ``` ### Differential with Aggressor Traces ```matlab 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) | ```matlab 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): ```matlab 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](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. ```matlab 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. ```matlab 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. ```matlab 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 ```matlab 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: ```matlab 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): ```matlab 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): ```matlab 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`: ```matlab Z0 = getZ0(ms); % Should be ~50 ohm ``` ## transmissionLineDesigner App Interactive app for designing and analyzing transmission lines: ```matlab 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). 12. **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. 13. **pcb2D rlgc takes scalar frequency**: `rlgc(p, freq)` requires a scalar, not a vector. Loop or call once at the frequency of interest. 14. **pcb2D trace2D Center is x-position only**: `trace2D.Shape.Center` controls horizontal position. Vertical is from layer stacking order. Set `Center = [x_offset 0]`. 15. **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." 16. **Crosstalk port count depends on aggressor configuration**: Both aggressors → 6-port; one → 4-port; none → 2-port. `RightCoupledTraceGap=Inf` removes that aggressor. 17. **TraceGap is edge-to-edge, not center-to-center**: Measures gap between nearest edges, not trace centers. 18. **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 ---- Copyright 2026 The MathWorks, Inc.