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-txline
• 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

1. Before: matlab-manage-pcb-material — set up substrate and conductor
2. This skill: Design the passive component (inductor, capacitor, balun, resonator)
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-integrate-pcb-circuit — cascade into circuit

Quick Reference

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

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

1. 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.

1. 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.

1. No `design()` for inductors/capacitors. spiralInductor and interdigitalCapacitor have no design() method. Set dimensions manually or use optimize().

1. Inductance/capacitance are frequency-dependent. Both require a frequency argument — no DC extraction. Parasitic effects shift the value at high frequencies.

1. DeEmbed matters for capacitance. Without DeEmbed=true, extracted capacitance includes feed line contributions.

1. SpiralShape is case-sensitive. Use 'Square', 'Circle', 'Hexagon', 'Octagon'.

1. Behavioral vs full-wave accuracy. Behavioral S-parameters diverge near SRF (inductors) or finger resonances (capacitors).

1. Height must be a cumulative substrate boundary. For Thickness=[t1, t2], valid Heights are t1, t1+t2. Applies to all objects in this skill.

1. spiralInductor requires multi-layer substrate. The underpass feed routing needs ≥ 2 dielectric layers. A single layer errors with "More than one substrate is required."

1. GroundPlane dimensions. Keep ground plane ≥ 2× the component footprint to avoid truncating fringing fields.

1. No `design()` for baluns. balunCoupledLine and balunMarchand have no design() method. Use section-design functions or optimize().

1. No `design()` for split-ring resonators. Only resonatorRing supports design().

1. `splitRing` is a shape, not a component. Cannot be analyzed directly — attach to resonatorSplitRingCustom or embed in a pcbComponent.

1. PhaseShift units are degrees. The PhaseShift parameter in design(phaseShifter, ...) is degrees, not radians.

1. `stubRadialShunt` has no `design()` method. Set dimensions manually or use optimize().

1. 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 setup
• matlab-analyze-em — S-parameters, fields, mesh control
• matlab-optimize-pcb-design — optimize() syntax, objectives, solvers
• matlab-integrate-pcb-circuit — pcbElement circuit integration
• matlab-design-pcb-filter — SIW filters can embed split-ring resonators
• matlab-assemble-pcb-layout — Custom CSRR structures via pcbComponent + Boolean ops
• matlab-design-pcb-coupler — Related coupled-line structures

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