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name: matlab-design-pcb-filter description: "Bandpass, lowpass, bandstop filter design — hairpin, coupled-line, combline, stub, SIW for frequency selection and harmonic rejection. TRIGGER: user asks to design, create, or analyze any RF filter (bandpass, lowpass, highpass, bandstop, hairpin, coupled-line, combline, stub, SIW). Invoke BEFORE writing code — filter class names differ from what you would guess. SKIP: EM simulation/S-parameter extraction of an existing filter (use matlab-analyze-em), general PCB layout assembly (use matlab-assemble-pcb-layout), material/stackup setup only (use matlab-manage-pcb-material), optimization sweeps (use matlab-optimize-pcb-design)." license: https://www.mathworks.com/content/dam/mathworks/license/pmrl/license.md metadata: author: MathWorks version: "1.0"

Designing RF Filters

When to Use

• Designing bandpass filters (coupled-line, hairpin, open-loop, combline, interdigital, SIW)
• Designing lowpass filters (stepped-impedance)
• Designing bandstop or notch filters (spurline, stub-based)
• Extracting coupling matrices from measured S-parameter data (measuredFilter)
• Selecting a filter topology for a given bandwidth, selectivity, or size requirement

When NOT to Use

• Designing transmission lines for impedance control — use matlab-design-pcb-transmission-line
• Designing couplers or splitters — use matlab-design-pcb-coupler
• Designing passive components (inductors, capacitors, baluns) — use matlab-design-pcb-passive
• Setting up substrate or conductor materials — use matlab-manage-pcb-material
• Optimizing filter dimensions after design — use matlab-optimize-pcb-design

Typical Workflow

1. Before: matlab-manage-pcb-material — set up substrate and conductor
2. This skill: Design the filter (catalog object or custom geometry)
3. Check mesh/memory: memoryEstimate(obj, fc, 'RetainMesh', true) — inspect auto-mesh density before committing to a full solve
4. After: matlab-analyze-em — validate S-parameters → matlab-optimize-pcb-design — tune dimensions → matlab-write-pcb-layout — export Gerber

Quick Reference — Filter Selection

| Filter Object | Type | Poles | Best For | |---------------|------|-------|----------| | filterCoupledLine | Bandpass | 2–8 | General microstrip BPF | | filterHairpin | Bandpass | 2–8 | Compact BPF, folded resonators | | filterOpenLoop | Bandpass | 4/6/8 | Compact quasi-elliptic | | filterCombline | Bandpass | 2–6 | Narrow-band, high-Q | | filterInterdigital | Bandpass | 2–8 | Wideband, good stopband | | filterStepImpedanceLowPass | Lowpass | 3–9 | Distributed LPF | | filterStub | LP/HP/BS | N stubs | Flexible stub topology | | filterSpurline | Bandstop | 1–2 | Compact notch filter | | SIWFilter | Bandpass | 2–6 | High-Q waveguide-in-PCB | | measuredFilter | Bandpass | N | Model extraction from measurements |

Bandpass Filters

Coupled-Line Filter

f = filterCoupledLine;
f = design(filterCoupledLine, 3e9);    % Design at 3 GHz
show(f);
sp = sparameters(f, linspace(1e9, 5e9, 101), 'SweepOption', 'interp');
rfplot(sp);

Key properties: FilterOrder, CoupledLineLength, CoupledLineWidth, CoupledLineSpacing, PortLineLength, PortLineWidth.

Hairpin Filter

Folded coupled-line resonators for compact size:

f = design(filterHairpin, 3e9);
show(f);
memoryEstimate(f, 3e9, 'RetainMesh', true);  % Check mesh density before solving
sp = sparameters(f, linspace(1e9, 5e9, 101), 'SweepOption', 'interp');
rfplot(sp);

Key properties: FilterOrder, CoupledLineLength, CoupledLineWidth, CoupledLineSpacing, PortLineLength, PortLineWidth, Spacing, ResonatorOffset, FeedOffset.

Chebyshev Response

Pass FilterType and RippleFactor to design() for equiripple passband response:

f = design(filterHairpin, 1.8e9, FBW=10, FilterType='Chebyshev', RippleFactor=0.5);

FilterType options: 'Butterworth' (default), 'Chebyshev'. FBW sets fractional bandwidth (%). RippleFactor sets passband ripple in dB (default 0.5) — only applies to Chebyshev.

Fifth-Order Hairpin

f = filterHairpin;
f.FilterOrder = 5;
f = design(f, 2.4e9);
show(f);

Open-Loop Filter

Quasi-elliptic response with cross-coupling:

f = filterOpenLoop;
f.NumPoles = 6;
f.FeedOffset = 0.5e-3;
show(f);
sp = sparameters(f, linspace(1e9, 5e9, 101), 'SweepOption', 'interp');
rfplot(sp);

Key Properties: NumPoles (4/6/8), ResonatorLength, ResonatorWidth, SplitGap, GapHorizontal, GapVertical, FeedOffset, CoupledResonatorGap, QuadrupletGap, QuadrupletOffset.

Combline Filter

Short-circuited resonators, excellent for narrow-band. Note: filterCombline does not have a design function — set properties manually:

f = filterCombline;
f.FilterOrder = 3;
f.Height = 1.6e-3;
show(f);

Key Properties: FilterOrder, ResonatorLength (scalar or vector), ResonatorWidth, ResonatorSpacing (scalar or vector), ResonatorOffset, FeedOffset, Capacitor (loading capacitance — distinctive to combline).

Interdigital Filter

Alternating short-circuited resonators, wideband. Note: filterInterdigital does not have a design function — set properties manually:

f = filterInterdigital;
f.FilterOrder = 4;
f.Height = 1.6e-3;
show(f);
sp = sparameters(f, linspace(3e9, 7e9, 101), 'SweepOption', 'interp');
rfplot(sp);

Key Properties: FilterOrder, ResonatorLength (scalar or vector), ResonatorWidth (scalar or vector), ResonatorSpacing (scalar or vector), ResonatorOffset, ViaDiameter (scalar or vector — distinctive to interdigital), FeedOffset, IsShielded, Connector.

Lowpass Filters

Stepped-Impedance Lowpass

f = filterStepImpedanceLowPass;
f = design(filterStepImpedanceLowPass, 2.5e9);
show(f);
sp = sparameters(f, linspace(0.1e9, 5e9, 101), 'SweepOption', 'interp');
rfplot(sp);

Key properties: FilterOrder, HighZLineWidth, LowZLineWidth, HighZLineLength, LowZLineLength.

Bandstop / Notch Filters

Spurline Filter

Compact notch using coupled-line section on one side:

f = filterSpurline;
show(f);
sp = sparameters(f, linspace(1e9, 6e9, 51), 'SweepOption', 'interp');
rfplot(sp);

Double spurline for deeper rejection:

f = filterSpurline;
f.LineType = 'Double';
show(f);

Key Properties: LineType ('Single'/'Double'), CoupledLineLength, CoupledLineWidth, CoupledLineSpacing, LineGap (gap between coupled line and output line — distinctive to spurline), IsShielded, Connector.

Stub Filters (Open/Short)

The filterStub object supports open-circuit stubs (bandstop) and short-circuit stubs (highpass):

f = filterStub;
f.StubLength = [6e-3 6e-3 6e-3];
f.StubWidth = [0.5e-3 0.5e-3 0.5e-3];
f.StubOffsetX = [-6e-3 0 6e-3];
f.StubShort = [0 0 0];         % 0=open (bandstop), 1=short (highpass)
f.StubDirection = [0 0 0];     % 0=below, 1=above trace
f.SeriesLineWidth = 1.8e-3;
f.SeriesLineLength = 12e-3;
show(f);

Key Properties: StubLength (vector), StubWidth (vector), StubFeedOffsetX (vector), StubShort (0=open, 1=short; vector), StubDirection (0=down, 1=up; vector), SeriesLineLength, SeriesLineWidth, IsShielded, Connector.

Radial Stub

rs = stubRadialShunt;
rs = design(stubRadialShunt, 5e9);
show(rs);

SIW Bandpass Filter

SIWFilter uses NumResonators (not FilterOrder), and Substrate is read-only (set via internal resonator objects):

f = SIWFilter;
f.NumResonators = 4;
show(f);
sp = sparameters(f, linspace(8e9, 14e9, 51), 'SweepOption', 'interp');
rfplot(sp);

Measured Filter Extraction

measuredFilter extracts a coupled-resonator circuit model (coupling matrix, external Q, unloaded Q) from measured or simulated 2-port S-parameter data. This enables filter tuning, diagnosis, and comparison against ideal synthesis targets.

Key Properties:

• Sparameters — 2-port S-parameters data (sparameters object)
• FilterOrder — Number of resonators in the model
• CenterFrequency — Passband center frequency (Hz)
• BandWidth — 3-dB bandwidth (Hz)
• CouplingMatrix — Extracted N+2 coupling matrix (populated after extraction)
• QualityFactor — Unloaded quality factor (populated after qualityfactor())

Key Methods:

• residue(mf) — Extract lowpass admittance residues and poles from S-parameter data
• transversalMat(mf) — Calculate transversal coupling matrix from residues
• canonicalCouplingMat(mf) — Rotate transversal matrix to canonical (folded) form
• optimize(mf) — Isospectral optimization of the coupling matrix
• sparameters(mf, freq) — Synthesize S-parameters from the extracted circuit model
• qualityfactor(mf) — Calculate unloaded quality factor

Complete Workflow

% Step 1: Load measured S-parameters and inspect visually
S_meas = sparameters('measured_filter.s2p');
rfplot(S_meas);
% Identify center frequency and bandwidth from the plot

% Step 2: Create measuredFilter with matching initial guess
mf = measuredFilter(Sparameters=S_meas, ...
    FilterOrder=8, ...
    CenterFrequency=2114.6e6, ...
    BandWidth=9.6e6);

% Step 3: Extract residues and poles
residue(mf);

% Step 4: Build transversal matrix, then rotate to canonical form
transversalMat(mf);
M = canonicalCouplingMat(mf);
disp(mf.CouplingMatrix);

% Step 5: Optimize coupling matrix (isospectral flow)
mf = optimize(mf);

% Step 6: Compare extracted model vs measured data
freq = linspace(2.08e9, 2.15e9, 501);
S_model = sparameters(mf, freq);
rfplot(S_meas); hold on;
rfplot(S_model, '--');
legend('Measured', 'Extracted Model');

% Step 7: Quality factor
Q = qualityfactor(mf);
disp(mf.QualityFactor);

Custom Filter Assembly

For topologies not in the catalog, build with pcbComponent:

% Example: custom 2-pole open-loop filter from shape primitives
sub = dielectric("FR4");
sub.Thickness = 1.6e-3;
cond = metal("Copper");

% Build resonator shapes using traceLine, traceRectangular, Boolean ops
% (see matlab-assemble-pcb-layout skill)

pcb = pcbComponent;
pcb.Layers = {filterShape, sub, groundPlane};
pcb.BoardShape = groundPlane;
pcb.BoardThickness = sub.Thickness;
pcb.Conductor = cond;
pcb.FeedDiameter = feedWidth/2;
pcb.FeedLocations = [x1 y1 1 3; x2 y2 1 3];

Multi-Layer Filters

All filter catalog objects support multi-layer dielectrics:

f = design(filterCoupledLine, 3e9);
sub = dielectric("FR4", "Teflon");
sub.Thickness = [0.8e-3 0.4e-3];   % Set Thickness BEFORE assigning to filter
f.Substrate = sub;
f.Height = 1.2e-3;
show(f);

Filter Selection Guide

| Need | Recommended Filter | Notes | |---|---|---| | Bandpass, compact | filterHairpin | Folded resonators save board area | | Bandpass, standard | filterCoupledLine | Supports design(), easiest starting point | | Bandpass, high selectivity | filterInterdigital | Good stopband rejection, wideband | | Bandpass, capacitively loaded | filterCombline | Narrow-band, high-Q, short resonators | | Bandpass, cross-coupling / TZs | filterOpenLoop | Quasi-elliptic, transmission zeros; supports design() | | Bandpass, SIW technology | SIWFilter | High-Q waveguide-in-PCB | | Lowpass, stepped impedance | filterStepImpedanceLowPass | Supports design() | | Bandstop, notch | filterSpurline | Very compact, single or double | | Bandpass/Bandstop, stub-based | filterStub | Flexible open/short stub topology; no design() | | Model extraction from data | measuredFilter | Coupling matrix from measurements |

Design Adjustments

| Problem | Adjust | Direction | |---|---|---| | Passband too wide | FilterOrder, Spacing | Increase order, decrease spacing | | Insertion loss too high | Conductor thickness | Use real metal, increase thickness | | Rejection too shallow | FilterOrder | Increase | | Center freq shifted | Re-run `design(fi