The RF studies use passive, positive-permittivity, nonmagnetic materials. Their first purpose is to compare ideal planar laminates. They do not infer electrical properties from elastic modulus, carbon content or the T700 name. Enter measured dielectric data at the relevant frequency; the supplied values are teaching examples.
RF theory companion ↓ PDF · Word with editable equations ↓
From simple to advanced
Standard includes series/parallel mixing, the Looyenga law, Maxwell–Garnett and normal-incidence laminate transmission. Advanced models use the existing Pro tier; Commercial includes them. Advanced also includes lossless 1D TLM and periodic-layer Floquet–Bloch studies; these are not arbitrary 3D full-wave solvers.
Wiener series and parallel
Standard · RF study
Positive lossless dielectric bounds; complex directional estimates.
Looyenga / Landau–Lifshitz–Looyenga
Standard · RF study
One cube-root mixing law, not two independent models.
Maxwell–Garnett
Standard · RF study
Dilute subwavelength spherical inclusions in a host.
Normal-incidence laminate TMM
Standard · RF study
Coherent isotropic nonmagnetic layers between air half-spaces.
Bruggeman symmetric EMT
Advanced / Pro · RF study
Two positive-permittivity phases; no explicit contact network.
EM Mori–Tanaka
Advanced / Pro · RF study
Scalar principal-axis ellipsoidal field approximation.
EM self-consistent
Advanced / Pro · RF study
Scalar principal-axis self-consistency; spherical case equals Bruggeman.
Differential effective medium
Advanced / Pro · RF study
Incremental mixing with time-step refinement check.
Coated sphere and interphase
Advanced / Pro · RF study
Concentric subwavelength coated spheres; no dynamic Mie scattering.
Generalized multiphase EMT
Advanced / Pro · RF study
Spherical multiphase Bruggeman with convergence checks.
Oblique polarized laminate TMM
Advanced / Pro · RF study
TE or TM waves; scalar isotropic layers, no polarization conversion.
1D transmission line matrix
Advanced / Pro · RF study
Normal-incidence lossless delay-line mesh with pulse decay, energy and mesh-refinement safeguards. Explicit Run required; not a 3D solver.
1D Floquet–Bloch periodic layers
Advanced / Pro · RF study
Lossless isotropic A/B unit-cell eigenvalues, folded Bloch phase and stop-band attenuation at normal incidence. Not arbitrary-cell homogenization.
Method references: Clemson transmission-line matrix overview and periodic bilayer characteristic matrices and Bloch dispersion. CDS implements the bounded one-dimensional cases described above.
Equations and interpretation
Passive complex permittivity
Relative permittivity is dimensionless. Conductivity σ is in S/m, ω = 2πf is in rad/s and ε₀ is vacuum permittivity. The exp(−iωt) convention makes positive imaginary permittivity passive. Enter dielectric loss separately from conductivity so the same loss is not counted twice.
Maxwell Garnett mixing
Here v is inclusion volume fraction, h denotes host and i denotes inclusion. The scalar spherical approximation is appropriate for dilute, subwavelength inclusions. A numerical solution at a large fraction does not establish physical validity or account for a touching conductive network.
Power balance and shielding
R, T and A are reflected, transmitted and absorbed power fractions. Shielding effectiveness SE is in dB. This definition includes both reflection and absorption. It is not an absorption-only measure and does not predict the performance of a finite enclosure with seams.
Material models are not interchangeable
Looyenga and Landau–Lifshitz–Looyenga name the same cube-root mixing law here. Spherical self-consistency reduces to the Bruggeman result; the Advanced principal-axis option exposes a depolarization factor. Neither method reconstructs an actual contact network. Series and parallel values are ordered Wiener bounds only for real, positive, lossless phases; lossy complex values are directional estimates.
The coated-sphere model first homogenizes the core and shell, then mixes coated particles into the host. Core fraction refers to core volume divided by coated-particle volume. The outer inclusion fraction is a separate number. Generalized multiphase EMT uses a bounded Bruggeman iteration and refuses to return an unconverged result.
Run an RF laminate study
- Start the matching EM exercise or create an EM case from Models. Run it separately from structural, thermal and moisture load cases.
- For a mixing study, enter host and inclusion dielectric properties and volume fractions. Advanced geometry factors describe a scalar principal-axis approximation, not a full anisotropic tensor.
- For transmission, enter explicit A and B layer properties, thicknesses, AB repeat count and frequency interval. Advanced TMM adds incidence angle and TE/TM polarization.
- Inspect reflection, transmission, absorption and shielding curves together. Confirm energy balance and repeat the study with a narrower frequency interval to resolve resonances.
Effective properties can currently be transferred manually into a TMM layer: enter the effective real permittivity and loss tangent, with conductivity set to zero when the effective loss already includes it. Mechanical laminate thicknesses and EM properties are not automatically coupled. Do not substitute a single directional effective property into an isotropic stack without justifying that approximation.
A result you can check
At 10 GHz, use a lossless dielectric with relative permittivity 4 and thickness 3.747405725 mm between air regions. Its refractive index is 2 and its thickness is one quarter of the wavelength inside the material. The analytic slab result is R = 0.36, T = 0.64 and A = 0. The calculated shielding is approximately 1.9382 dB. This is reflection from an ideal dielectric slab, not absorption.
Resolution and limits
The sweep samples 101 frequencies. Highly resonant stacks may require a narrower interval; a smooth curve is not proof that every resonance was resolved. The stack recursion avoids exponential growth for opaque layers. Transmission below the display floor is shown as 300 dB shielding, not as a precise experimentally measurable value. DEM compares two integration refinements, and multiphase EMT checks its residual.
All studies exclude finite edges, antennas, magnetic media, negative permittivity and thermal feedback. The 1D TLM study uses lossless delay cells, interface scattering, matched air ports and a unit impulse at normal incidence. Two resolutions must agree within two percentage points; unresolved late echoes are rejected. Inspect the reported thickness rounding error. The 1D Floquet–Bloch study solves λ² − tr(M)λ + 1 = 0 for a lossless periodic A/B cell and plots folded Re(Kd)/π and stop-band Im(K). Evanescent decay is not absorption. These methods do not provide arbitrary-cell homogenization or 2D/3D geometry.
References
- Byrnes, Multilayer optical calculations — coherent planar layers and polarization conventions.
- COMSOL, Effective relative permittivity in effective media and mixtures — mixing-law context.
- Electromagnetic effective-medium modelling with core–shell inclusions — scope of coated-particle approximations.
Workbench availability: released models, inputs and compatible study paths. The wider theory library includes reference formulations not available in every Workbench solve.