Matlab Design Pcb PassiveSAFE

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---
name: matlab-design-pcb-passive
description: "Spiral inductors, interdigital capacitors, baluns, resonators, phase shifters for impedance matching, DC blocking, and bias tees. TRIGGER: user asks to design or create a spiral inductor, interdigital capacitor, balun, resonator, phase shifter, or other passive RF component. Invoke BEFORE writing code — class names and property patterns are non-obvious. SKIP: filter design (use matlab-design-pcb-filter), coupler/splitter design (use matlab-design-pcb-coupler), transmission line design (use matlab-design-pcb-transmission-line), EM analysis (use matlab-analyze-em), material setup only (use matlab-manage-pcb-material)."
license: https://www.mathworks.com/content/dam/mathworks/license/pmrl/license.md
metadata:
  author: MathWorks
  version: "1.0"
---

# 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

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

| 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

```matlab
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)

```matlab
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

```matlab
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.

```matlab
freq = linspace(100e6, 10e9, 201);
L = inductance(ind, freq);
% Sign change: L > 0 (inductive) → L < 0 (capacitive) at SRF
```

### Visualization

```matlab
show(ind)
current(ind, 600e6)
charge(ind, 600e6)
[E, H] = EHfields(ind, 4e9, [0; 0; 1]);
```

## Interdigital Capacitors

### Creating and Configuring

```matlab
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

```matlab
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:

```matlab
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 s

SAFEgrade B · trust 89/100 Nothing in the source contradicts what it says it does. Grade A is reserved for packages that have also passed the behavioural sandbox.

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No findings outside the package's declared scope.

Gates applied: no_behavioural_pass.