Stray Capacitance¶

Comprehensive documentation for parasitic capacitance models

Parasitic (stray) capacitance in magnetic components affects: - High-frequency behavior and resonances - EMI performance (common-mode noise paths) - Switching transients in power converters - Self-resonant frequency of inductors

MKF models several capacitance components: - Turn-to-turn capacitance: Between adjacent turns in a layer - Layer-to-layer capacitance: Between winding layers - Winding-to-core capacitance: Between windings and grounded core - Primary-to-secondary capacitance: Coupling between windings (transformers)

Capacitance Components¶

Turn-to-Turn Capacitance¶

Capacitance between adjacent turns in the same layer:

$$C_{tt} = \varepsilon_0 \varepsilon_r \frac{l_{turn}}{d_{tt}} \cdot k_{fringe}$$

Where: - $l_{turn}$ is the mean turn length - $d_{tt}$ is the turn-to-turn spacing - $k_{fringe}$ accounts for fringing fields

Layer-to-Layer Capacitance¶

For windings with multiple layers:

$$C_{ll} = \varepsilon_0 \varepsilon_r \frac{A_{overlap}}{d_{ll}}$$

Where: - $A_{overlap}$ is the overlapping area between layers - $d_{ll}$ is the layer-to-layer spacing (insulation thickness)

Winding-to-Core Capacitance¶

$$C_{wc} = \varepsilon_0 \varepsilon_r \frac{A_{winding}}{d_{wc}}$$

This capacitance provides a path for common-mode noise in isolated converters.

Available Models¶

Koch¶

Koch's model uses parallel-plate approximation with fringing corrections:

$$C = \varepsilon_0 \varepsilon_r \frac{A}{d} \cdot k_{fringe}$$

Where $k_{fringe}$ accounts for field spreading at conductor edges. Good for turn-to-turn and layer-to-layer capacitance.

Reference: Koch et al. 'Stray Capacitance in Inductors.' IEEE Trans. Power Electronics, 2020

Massarini¶

Massarini's analytical model for winding capacitance includes: - Multi-layer effects - Wire geometry (round, rectangular) - Insulation thickness

Provides separate formulas for different capacitance components.

Reference: Massarini, Kazimierczuk. 'Self-capacitance of inductors.' IEEE Trans. Power Electronics, 1997

Albach¶

Albach's comprehensive capacitance model accounts for: - 2D field distribution - Non-uniform winding spacing - Core proximity effects

Provides good accuracy across various winding configurations.

Reference: Albach et al. 'Calculating stray capacitance.' IEEE Trans. Magnetics, 2011

Duerdoth¶

Duerdoth's coil self-capacitance model uses energy-based approach:

$$C_{self} = \frac{2 W_E}{V^2}$$

Where $W_E$ is the electric field energy stored between turns.

Reference: Duerdoth, W.T. 'Equivalent Capacitance of Transformer Windings.' Wireless Engineer, 1946

Self-Resonant Frequency¶

The self-resonant frequency (SRF) of an inductor is where capacitive and inductive reactances cancel:

$$f_{SRF} = \frac{1}{2\pi\sqrt{L \cdot C_{stray}}}$$

Above the SRF, the inductor behaves as a capacitor. For effective filtering, operate well below the SRF (typically f < SRF/10).

Model Comparison¶

Model	Best For	Complexity
Koch	Turn-to-turn, layer-to-layer	Medium
Massarini	Complete self-capacitance	Medium
Albach	General purpose	High
Duerdoth	Quick estimates	Low

Default Model: Albach provides good balance of accuracy and generality.

Capacitance Minimization Strategies¶

Technique	Effect	Trade-off
Increase turn spacing	Reduces turn-to-turn C	Larger winding window
Section winding	Reduces layer-to-layer C	More complex construction
Shield windings	Controls coupling paths	Additional losses
Bank winding	Reduces distributed C	Higher leakage inductance
Thicker insulation	Reduces all C	Thermal resistance
Progressive winding	Reduces layer-to-layer C	Complex winding pattern

EMI Considerations¶

Common-Mode Capacitance¶

In isolated converters, capacitance between primary and secondary windings ($C_{ps}$) and winding-to-core capacitance ($C_{wc}$) create common-mode noise paths:

$$I_{CM} = C_{ps} \cdot \frac{dV}{dt}$$

To minimize common-mode noise: - Use shield windings (Faraday shields) - Increase primary-secondary spacing - Consider winding orientation

Y-Capacitors¶

External Y-capacitors can shunt common-mode currents but are limited by safety regulations (typically 4.7nF max for Class II equipment).

Usage¶

#include "physical_models/StrayCapacitance.h"

// Configure capacitance model
auto& settings = OpenMagnetics::Settings::GetInstance();
settings.set_stray_capacitance_model(
    OpenMagnetics::StrayCapacitanceModels::ALBACH
);

// Calculate capacitance
auto capacitance = OpenMagnetics::StrayCapacitance();
auto C_stray = capacitance.calculate_stray_capacitance(magnetic, operatingPoint);

// Get individual components
auto C_tt = capacitance.get_turn_to_turn_capacitance();
auto C_ll = capacitance.get_layer_to_layer_capacitance();
auto C_wc = capacitance.get_winding_to_core_capacitance();

Design Guidelines¶

For EMI-Sensitive Applications¶

Minimize primary-secondary capacitance
Consider adding Faraday shields
Place windings symmetrically

For High-Frequency Inductors¶

Keep SRF at least 10x operating frequency
Use single-layer winding if possible
Consider air-core for very high frequencies

For Resonant Converters¶

Capacitance may be a design parameter
Account for capacitance in resonant tank design
Verify with impedance analyzer measurements