What is the MTL model?

The Multi-conductor Transmission Line (MTL) model represents a cable as a series of distributed per-unit-length parameters: R (resistance), L (inductance), C (capacitance), and G (conductance) matrices. For an N-conductor cable: each matrix is N×N. The diagonal elements represent self-parameters (self-inductance, capacitance to ground). The off-diagonal elements represent mutual parameters (mutual inductance, mutual capacitance between conductors). The MTL telegrapher's equations: dV/dz = -(R+jωL)I and dI/dz = -(G+jωC)V. Solution gives voltage and current at every point along the cable for any excitation. Valid when cable cross-section is small compared to wavelength (typically up to 10-100 MHz). Above this range, higher-order modes and radiation effects require full-wave modeling.

How is shield transfer impedance modeled?

The shield's transfer impedance Zt connects the external cable model to the internal conductor model: V_internal = Zt × I_external × length. For braided shields: Zt has two components. (1) Diffusion term: Zt_d = Rs/(2πa) where Rs = 1/(σδ) is the surface resistance. This term decreases with frequency as skin depth decreases. (2) Porosity term: Zt_p models leakage through the braid apertures. This term increases with frequency. The combination creates a Zt minimum (typically 1-10 MHz for braided shields). Below the minimum: diffusion dominates. Above: porosity dominates. Solid shields (semi-rigid, corrugated): porosity term is zero. Zt decreases monotonically with frequency (pure diffusion). CAD implementation: Zt is entered as a frequency-dependent impedance per meter. CST Cable Studio and FEKO both accept measured or analytical Zt data.

What simulation tools model cable EMC?

(1) CST Cable Studio (Dassault Systèmes): purpose-built for cable EMC modeling. Imports 3D cable routes from CAD, applies MTL and Zt models, predicts crosstalk and radiated emissions. Hybrid solver combines MTL (efficient for long cables) with full-wave (accurate for radiation). (2) FEKO (Altair): method of moments (MoM) solver handles cable radiation and coupling in complex environments. Cable models integrated with vehicle or aircraft structures. Used extensively in automotive and aerospace EMC. (3) ANSYS HFSS: finite element full-wave solver. Best for cable/connector transitions and detailed connector models. Computationally expensive for long cables. (4) SACAMOS (open-source): specialized MTL solver for cable bundles. Developed by Nottingham University. Handles complex cross-sections. (5) SPICE: lumped-element cable models for circuit-level simulation. Adequate for low frequencies but does not capture radiation or distributed effects above ~1 MHz.

EMC Simulation

Cable EMC Model

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MTL: N×N RLCG matrices, telegrapher's equations dV/dz = -(R+jωL)I. Shield: Zt (diffusion + porosity). Full-wave: radiation prediction. Hybrid: MTL (long cables) + MoM (radiation). Tools: CST Cable Studio, FEKO, ANSYS HFSS, SACAMOS. Valid below λ/10 cross-section. Predicts conducted/radiated emissions, susceptibility, crosstalk.

Method: MTL + full-wave

Shield: Zt model

Tool: CST Cable Studio

Understanding Cable EMC Models

Predicting cable EMC behavior through simulation is increasingly essential as systems become more complex and EMC testing more expensive. A cable EMC model captures the cable's distributed parameters (RLCG), shielding performance (Zt), and radiation characteristics so that engineers can predict emissions, crosstalk, and susceptibility before building hardware. The challenge is balancing model accuracy (full-wave) with computational efficiency (MTL) for cables that may be meters long with dozens of conductors.

MTL Equations

Transfer impedance:
V_induced = Z_T×I_shield×L
Z_T = R_DC+jωM₁₂ Ω/m

Shielding effectiveness:
SE = 20log(Z_T,unshielded/Z_T,shielded)

Surface transfer admittance:
Y_T = jωC₁₂/L (for aperture coupling)

Cable Modeling Tool Comparison

Tool	Method	Cable Focus	Frequency	Strength
CST Cable Studio	MTL + hybrid	Purpose-built	DC-GHz	Long cable bundles
FEKO	MoM	Integrated	DC-GHz	Vehicle/aircraft
ANSYS HFSS	FEM	Connectors	MHz-GHz	Connector detail
SACAMOS	MTL	Open-source	DC-100 MHz	Complex bundles
SPICE	Lumped	Circuit-level	DC-1 MHz	System co-sim

Key Equations

Maxwell’s equations (time-harmonic):
∇×E = −jωμH
∇×H = jωεE + J

Wave equation:
∇²E + k²E = 0, k = ω√(με)

Skin depth:
δ = 1/√(πfμσ)

Comparison

Shield type	Z_T @1MHz	Z_T @100MHz	SE @100MHz	Application
Single braid	1–10 mΩ/m	10–100 mΩ/m	40–60 dB	Standard
Double braid	0.1–1 mΩ/m	1–10 mΩ/m	60–80 dB	High perf
Semi-rigid	0.01–0.1 mΩ/m	0.1–1 mΩ/m	80–100 dB	Test/cal
Foil + braid	0.5–5 mΩ/m	5–50 mΩ/m	50–70 dB	Instrument
Corrugated	0.01–0.05 mΩ/m	0.05–0.5 mΩ/m	80–100 dB	Telecom

Common Questions

Frequently Asked Questions

MTL?

N×N RLCG matrices per unit length. Telegrapher's equations: dV/dz, dI/dz. Self and mutual parameters. Valid when cross-section ≪ λ (to ~100 MHz). Efficient for long cables with many conductors. SACAMOS, CST Cable Studio.

Zt modeling?

Transfer impedance = diffusion (skin effect, decreases w/ freq) + porosity (braid leakage, increases w/ freq). Minimum at 1-10 MHz. Solid shields: pure diffusion. Entered as freq-dependent Ω/m. Critical for shielded cable modeling.

Tools?

CST Cable Studio (hybrid MTL+full-wave), FEKO MoM (vehicle/aircraft), HFSS FEM (connector transitions), SACAMOS (open-source MTL), SPICE (lumped, low freq). CST Cable Studio is purpose-built for cable EMC.

Related Terms

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