Designing Passive Components
When to Use
- Designing spiral inductors or interdigital capacitors for RF circuits
- Extracting inductance, capacitance, or self-resonant frequency from passive components
- Creating ring or split-ring resonators for filtering or metamaterial applications
- Designing coupled-line or Marchand baluns for balanced-to-unbalanced conversion
- Building Schiffman phase shifters or radial stubs
When NOT to Use
- Designing transmission lines (microstrip, stripline, CPW) — use
matlab-design-pcb-transmission-line
- Designing filters (bandpass, lowpass, bandstop) — use
matlab-design-pcb-filter
- Designing couplers or splitters — use
matlab-design-pcb-coupler
- Setting up substrate materials — use
matlab-manage-pcb-material
- Running EM analysis after design — use
matlab-analyze-em
Typical Workflow
- Before:
matlab-manage-pcb-material — set up substrate and conductor
- This skill: Design the passive component (inductor, capacitor, balun, resonator)
- Check mesh/memory:
memoryEstimate(obj, fc, 'RetainMesh', true) — inspect auto-mesh density before committing to a full solve
- After:
matlab-analyze-em — validate S-parameters → matlab-optimize-pcb-design — tune dimensions → matlab-integrate-pcb-circuit — cascade into circuit
Quick Reference
| Task | Code |
|---|
| Spiral inductor | ind = spiralInductor |
| Interdigital capacitor | cap = interdigitalCapacitor |
| Extract inductance | L = inductance(ind, freq) |
| Extract capacitance | C = capacitance(cap, freq, DeEmbed=true) |
| Behavioral S-params | S = sparameters(obj, freq, Behavioral=true) |
| Ring resonator | r = design(resonatorRing, freq) |
| Split-ring (custom) | r = resonatorSplitRingCustom |
| Split-ring (square) | r = resonatorSplitRingSquare |
| Coupled-line balun | b = balunCoupledLine |
| Marchand balun | b = balunMarchand |
| Phase shifter | ps = design(phaseShifter, freq, PhaseShift=90) |
| Radial stub | stub = stubRadialShunt |
| Optimize | optimize(obj, freq, ...) |
Spiral Inductors
Creating and Configuring
ind = spiralInductor;
ind.SpiralShape = 'Square'; % 'Square' | 'Circle' | 'Hexagon' | 'Octagon'
ind.InnerDiameter = 5e-4;
ind.Width = 2.5e-4;
ind.Spacing = 2.5e-4;
ind.NumTurns = 4;
ind.Height = 1.016e-3; % Must be a cumulative substrate layer boundary
ind.GroundPlaneLength = 5.6e-3;
ind.GroundPlaneWidth = 5.6e-3;
RFIC Substrates (Silicon/SiO2)
ind = spiralInductor;
ind.Substrate = dielectric('Name', {'Silicon','SiO2'}, ...
'EpsilonR', [11.9, 4.1], 'LossTangent', [0.005, 0], ...
'Thickness', [300e-6, 3e-6]);
ind.Height = 303e-6; % Signal trace at top of stack
Spiral Shape and Q-Factor Tradeoffs
| Shape | Q-Factor | Notes |
|---|
'Circle' | Highest | Best electrical performance |
'Octagon' | High | Close to circular; easier to fabricate |
'Hexagon' | Moderate | Compromise |
'Square' | Lowest | Easiest to manufacture; current crowding at corners |
Ground Plane Proximity Effect
Smaller Height increases capacitive coupling to ground, reducing inductance, Q-factor, and self-resonant frequency. Account for this when the PCB stackup constrains Height.
Inductance Extraction
L = inductance(ind, 600e6); % Scalar frequency → scalar (H)
L = inductance(ind, linspace(100e6, 1e9, 30)); % Vector → vector
Self-Resonant Frequency (SRF)
At SRF, parasitic capacitance resonates with inductance — impedance peaks, then the inductor behaves as a capacitor. Design so the operating band stays below SRF/3 to SRF/2.
freq = linspace(100e6, 10e9, 201);
L = inductance(ind, freq);
% Sign change: L > 0 (inductive) → L < 0 (capacitive) at SRF
Visualization
show(ind)
current(ind, 600e6)
charge(ind, 600e6)
[E, H] = EHfields(ind, 4e9, [0; 0; 1]);
Interdigital Capacitors
Creating and Configuring
cap = interdigitalCapacitor;
cap.NumFingers = 4;
cap.FingerLength = 0.0137;
cap.FingerWidth = 3.16e-4;
cap.FingerSpacing = 3e-4;
cap.FingerEdgeGap = 3.41e-4;
cap.TerminalStripWidth = 5e-4;
cap.PortLineWidth = 1.9e-3;
cap.PortLineLength = 3e-3;
cap.Height = 7.87e-4;
Capacitance Extraction
C = capacitance(cap, 5e9); % Raw
C = capacitance(cap, 5e9, DeEmbed=true); % De-embedded
C = capacitance(cap, 5e9, DeEmbed=true, IncludeParasitics=true); % With parasitics
- DeEmbed removes feed line effects to isolate the capacitor.
- IncludeParasitics adds parasitic inductance/resistance from the finger structure.
Behavioral S-Parameters
Both spiralInductor and interdigitalCapacitor support fast behavioral models:
S = sparameters(ind, freq, Behavioral=true); % ~instant
S = sparameters(cap, freq, Behavioral=true);
Use for initial exploration; switch to full-wave (Behavioral=false, the default) for validation. Before a full-wave solve, always check mesh density:
memoryEstimate(ind, fc, 'RetainMesh', true); % Check auto-mesh before full-wave
sp = sparameters(ind, freq, 'SweepOption', 'interp');
Ring Resonators
resonatorRing is a microstrip ring resonator coupled to two feed lines via a gap.
r = resonatorRing;
r.RingRadiusOuter = 0.01;
r.RingWidth = 4e-3;
r.CouplingGap = 1e-3;
r.PortLineLength = 0.01;
r.PortLineWidth = 5e-3;
r.Height = 1.6e-3;
r.GroundPlaneWidth = 0.04;
Frequency-Based Design
r = design(resonatorRing, 1.8e9); % 50 Ω default
r = design(resonatorRing, 2.5e9, Z0=75); % 75 Ω
Split-Ring Resonators
Two object types: resonatorSplitRingCustom (pluggable shape) and resonatorSplitRingSquare (pre-configured square).
Custom Split-Ring Resonator
r = resonatorSplitRingCustom;
sr = splitRing(Type="Hexagon", NumRings=3);
sr.SplitSide = [2 3 5];
r.Resonator = sr;
r.FeedType = 'Tapped'; % 'Tapped' (default) or 'Coupled'
r.PortLineLength = 0.01;
r.PortLineWidth = 7.5e-4;
r.Height = 8.13e-4;
Square Split-Ring Resonator
r = resonatorSplitRingSquare;
r.RingLengthInner = 3.6e-3;
r.RingWidth = 5e-4;
r.RingSpacing = 3e-4;
r.SplitGap = 5e-4;
r.CouplingGap = 2.5e-4;
r.NumResonator = 5;
r.ResonatorSpacing = 4e-3;
For the full splitRing shape property table, CSRR ground-plane etching, and SIW integration patterns, see references/resonators-detail.md.
Coupled-Line Baluns
balunCoupledLine is a 3-section coupled-line balun (balanced-to-unbalanced converter).
b = balunCoupledLine;
b.NumCoupledLineSection = 3;
b.CoupledLineLength = 0.0153;
b.CoupledLineWidth = 4e-4;
b.CoupledLineSpacing = 1.4e-4;
b.OutputLineLength = 0.0124;
b.OutputLineWidth = 1.53e-4;
b.OutputLineSpacing = 0.011;
b.Height = 1.3e-3;
balunCoupledLine has no design() method. Use designCoupledLine, designOutputLine, designUncoupledLine for section-by-section sizing from impedance targets. See references/resonators-detail.md for the full API.
Marchand Baluns
balunMarchand is a broadband balun using λ/4 coupled-line sections.
bm = balunMarchand;
bm.CoupledLineLength = 0.0178;
bm.CoupledLineWidth = 3e-3;
bm.CoupledLineSpacing = 1.5e-4;
bm.OutputLineLength = 0.016;
bm.OutputLineWidth = 2.9e-4;
bm.Height = 1.6e-3;
No design() method. Set dimensions manually or use optimize().
Phase Shifters
phaseShifter is a Schiffman-type phase shifter using coupled-line sections.
ps = design(phaseShifter, 1.8e9); % Default phase shift
ps = design(phaseShifter, 1.8e9, PhaseShift=90); % 90° phase shift
Properties
ps.NumSections = 1;
ps.PortLineLength = 0.01;
ps.PortLineWidth = 5e-3;
ps.Height = 1.6e-3;
ps.SectionShape = ubendRightAngle; % Default U-bend shape
Radial Stubs
stubRadialShunt creates a single- or double-radial stub shunt. Radial stubs provide wideband short-circuit behavior compared to rectangular stubs.
stub = stubRadialShunt;
stub.StubType = "Single"; % "Single" (default) or "Double"
stub.OuterRadius = 8.5e-3;
stub.InnerRadius = 1.2e-3;
stub.Angle = 90; % Range [5, 175] degrees
stub.PortLineWidth = 2.5e-3;
stub.PortLineLength = 0.0137;
stub.Height = 1.6e-3;
For double-stub vector property configuration, see references/resonators-detail.md.
Circuit Integration
Wrap passive components in pcbElement for RF Toolbox circuit assembly:
ckt = circuit;
c1 = interdigitalCapacitor;
c2 = interdigitalCapacitor(NumFingers=3);
p = pcbElement(c2, 'Behavioral', false);
add(ckt, [1 2 0 0], c1);
add(ckt, [2 3 0 0], p);
setports(ckt, [1 0], [3 0]);
S = sparameters(ckt, 8e9);
Optimization
All objects in this skill support optimize():
ind = spiralInductor(NumTurns=3);
optimize(ind, linspace(1e9, 3e9, 11), ...
'Properties', {'Width', 'Spacing', 'InnerDiameter'}, ...
'LowerBound', [1e-4, 1e-4, 3e-4], ...
'UpperBound', [5e-4, 5e-4, 1e-3], ...
'Objective', 'maximizeBandwidth');
Multilayer Dielectric Pattern
All objects follow the same pattern — set Thickness before assigning to the component:
sub = dielectric('FR4', 'Teflon');
sub.Thickness = [1.6e-3, 0.8e-3];
obj.Substrate = sub;
obj.Height = 0.8e-3; % Must match a cumulative layer boundary
Pitfalls
-
Use interpolating sweep for S-parameters: Always use sparameters(obj, freq, 'SweepOption', 'interp') for MoM solves. Direct sweeps solve at every frequency point individually and are significantly slower.
-
Check mesh density before solving: Spiral inductors and interdigital capacitors generate dense auto-meshes. Always run memoryEstimate(obj, fc, 'RetainMesh', true) before sparameters(). If memory is excessive, coarsen: mesh(obj, 'MaxEdgeLength', lambda/6). See matlab-analyze-em for full mesh inspection workflow.
-
No design() for inductors/capacitors. spiralInductor and interdigitalCapacitor have no design() method. Set dimensions manually or use optimize().
-
Inductance/capacitance are frequency-dependent. Both require a frequency argument — no DC extraction. Parasitic effects shift the value at high frequencies.
-
DeEmbed matters for capacitance. Without DeEmbed=true, extracted capacitance includes feed line contributions.
-
SpiralShape is case-sensitive. Use 'Square', 'Circle', 'Hexagon', 'Octagon'.
-
Behavioral vs full-wave accuracy. Behavioral S-parameters diverge near SRF (inductors) or finger resonances (capacitors).
-
Height must be a cumulative substrate boundary. For Thickness=[t1, t2], valid Heights are t1, t1+t2. Applies to all objects in this skill.
-
spiralInductor requires multi-layer substrate. The underpass feed routing needs ≥ 2 dielectric layers. A single layer errors with "More than one substrate is required."
-
GroundPlane dimensions. Keep ground plane ≥ 2× the component footprint to avoid truncating fringing fields.
-
No design() for baluns. balunCoupledLine and balunMarchand have no design() method. Use section-design functions or optimize().
-
No design() for split-ring resonators. Only resonatorRing supports design().
-
splitRing is a shape, not a component. Cannot be analyzed directly — attach to resonatorSplitRingCustom or embed in a pcbComponent.
-
PhaseShift units are degrees. The PhaseShift parameter in design(phaseShifter, ...) is degrees, not radians.
-
stubRadialShunt has no design() method. Set dimensions manually or use optimize().
-
Polygonal SplitSide defaults may be invalid. Hexagons require SplitSide from {2, 3, 5, 6}. Always set explicitly for polygonal types with multiple rings.
Related Skills
matlab-manage-pcb-material — Substrate and conductor setupmatlab-analyze-em — S-parameters, fields, mesh controlmatlab-optimize-pcb-design — optimize() syntax, objectives, solversmatlab-integrate-pcb-circuit — pcbElement circuit integrationmatlab-design-pcb-filter — SIW filters can embed split-ring resonatorsmatlab-assemble-pcb-layout — Custom CSRR structures via pcbComponent + Boolean opsmatlab-design-pcb-coupler — Related coupled-line structures
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