Electronic Design Automation

CST Studio

Q: When should I use the time-domain solver versus the frequency-domain solver in CST Studio?

The time-domain (transient) solver uses the Finite Integration Technique on a hexahedral mesh and computes broadband S-parameters from a single pulsed excitation, so it is the default choice for wideband structures such as antennas, connectors, and packages where you need many frequency points across a wide span. It scales efficiently to electrically large problems and pairs with PBA (Perfect Boundary Approximation) for accurate curved geometry. The frequency-domain solver uses the finite element method on a tetrahedral mesh and solves one frequency at a time (with adaptive frequency sweep interpolation), which is more efficient for electrically small, high-Q, or strongly resonant structures such as narrowband filters and cavities, and for problems with periodic boundaries like unit-cell metamaterials and phased-array elements. A rule of thumb: wideband and large goes transient, narrowband and resonant goes frequency-domain.

Q: What mesh cell size does CST Studio require for accurate millimeter-wave simulation?

For the time-domain FIT solver, the standard guideline is a minimum of 10 to 20 mesh cells per wavelength at the highest simulated frequency, with finer local refinement where fields vary rapidly. At 60 GHz the free-space wavelength is 5 mm, so 15 cells per wavelength implies a maximum cell edge near 0.33 mm, and in high-permittivity dielectric the wavelength shrinks by the square root of epsilon-r so cells must be proportionally smaller. Thin metal traces, gaps, and dielectric layers should be resolved with at least 1 to 2 cells across their smallest dimension. Mesh quality is verified by running an adaptive mesh refinement pass and confirming the S-parameter change between passes drops below roughly 0.02 in linear magnitude before trusting the result.

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A full-wave 3D electromagnetic simulation package (CST Studio Suite, now part of Dassault Systemes SIMULIA) that solves Maxwell's equations numerically to predict S-parameters, fields, and radiation patterns before hardware is built. Its flagship time-domain solver uses the Finite Integration Technique (FIT) on a structured hexahedral mesh, while a frequency-domain solver applies the finite element method on a tetrahedral mesh for resonant and periodic problems. Engineers use CST Studio to model waveguide components, planar circuits, filters, antennas, and connectors from DC through W-band (110 GHz) and beyond, extracting S-parameters, gain, axial ratio, and EMC coupling that correlate to measured data within a fraction of a dB when the mesh is adequately resolved.

Category: Electronic Design Automation

Primary Solver: FIT time-domain (hexahedral)

Typical Range: DC to > 110 GHz

How the CST Studio Solvers Work

CST Studio Suite originated as the product of Computer Simulation Technology (CST), founded in 1992, and is built around the Finite Integration Technique developed by Thomas Weiland. FIT discretizes the integral form of Maxwell's equations on a pair of staggered grids, producing a set of Maxwell Grid Equations that are mathematically equivalent to the finite-difference time-domain (FDTD) method on Cartesian meshes but generalize cleanly to non-orthogonal and curved geometry. The transient solver excites the structure with a Gaussian pulse and marches the fields forward in time, recovering the full broadband response in a single run via a Fourier transform of the port signals. Because the timestep is bounded by the Courant stability limit, the smallest mesh cell dictates the simulation cost, which is why local mesh control matters so much in practice.

The frequency-domain solver takes a different path. It assembles a large sparse linear system from a tetrahedral FEM formulation, built on vector (edge) basis functions over each tetrahedron, and solves it one frequency at a time, then uses adaptive frequency sweep interpolation to fill in intermediate points. This makes it efficient for high-Q resonators, narrowband filters, and unit-cell models with periodic (Floquet) boundaries where a time-domain pulse would ring for a very long time before settling. CST Studio also bundles an eigenmode solver for cavity and slow-wave structures, an integral-equation solver based on the method of moments for electrically large radiating bodies, and asymptotic ray-based methods for installed-antenna and radar-cross-section problems that are far too large for any volumetric mesh.

Perfect Boundary Approximation and Meshing

A defining feature of the FIT hexahedral solver is Perfect Boundary Approximation (PBA), a sub-cell technique that captures curved metal and dielectric interfaces within a regular grid cell rather than forcing a staircase approximation. PBA lets a relatively coarse hexahedral mesh resolve rounded waveguide irises, bond wires, and chamfered transitions accurately, which keeps cell counts manageable at millimeter-wave frequencies. Convergence is confirmed through adaptive mesh refinement: the solver runs successive passes, doubling local density where the energy error is highest, until the change in the S-parameters between passes falls below a user-set threshold.

Governing Equations

Maxwell Grid Equation (Faraday, integral form):
–∂/∂t ∫∫_A B·dA = ∮_∂A E·ds

Courant stability limit (3D transient timestep):
Δt ≤ 1 / (c × √(1/Δx² + 1/Δy² + 1/Δz²))

Mesh resolution guideline:
Δx ≈ λ_min / N, N ≈ 10 to 20 cells per wavelength, λ = c / (f × √ε_r)

Where B = magnetic flux density, E = electric field, c = speed of light, Δx,Δy,Δz = cell edge lengths, ε_r = relative permittivity. Example: at f = 60 GHz in air, λ = 5 mm, so N = 15 gives Δx ≈ 0.33 mm.

CST Studio Solver Comparison

Solver	Numerical Method	Mesh Type	Best For	Bandwidth per Run
Time Domain (Transient)	FIT	Hexahedral + PBA	Broadband, electrically large structures, antennas, connectors	Full band, single run
Frequency Domain	FEM	Tetrahedral	Resonant filters, high-Q, periodic unit cells	One point, swept
Eigenmode	FEM	Tetrahedral	Cavity modes, slow-wave structures, Q extraction	Modal (no source)
Integral Equation	MoM / MLFMM	Surface triangles	Electrically large radiators, RCS, reflectors	One point, swept
Asymptotic	SBR ray tracing	Faceted surface	Installed antennas, very large platforms	One point, swept

Common Questions

Frequently Asked Questions

When should I use the time-domain solver versus the frequency-domain solver in CST Studio?

The time-domain (transient) FIT solver computes broadband S-parameters from a single pulsed run on a hexahedral mesh, making it the default for wideband and electrically large structures like antennas, connectors, and packages. The frequency-domain FEM solver works one frequency at a time on a tetrahedral mesh and is more efficient for high-Q resonant filters and periodic unit cells. Rule of thumb: wideband and large goes transient, narrowband and resonant goes frequency-domain.

What mesh cell size does CST Studio require for accurate millimeter-wave simulation?

Target 10 to 20 mesh cells per wavelength at the highest frequency, with local refinement where fields vary fast. At 60 GHz the wavelength is 5 mm, so 15 cells per wavelength means a maximum cell edge near 0.33 mm; in dielectric the wavelength shrinks by √ε_r so cells must shrink too. Resolve thin traces and gaps with 1 to 2 cells minimum, then run adaptive mesh refinement until the S-parameter change per pass drops below about 0.02 linear magnitude.

How do CST Studio results compare with HFSS for the same structure?

Both are full-wave 3D solvers and converge to the same physics when meshed properly, typically within 0.1 dB of insertion loss and a few percent of resonant frequency. HFSS is FEM-only with adaptive tetrahedral meshing, strong on resonant and small geometries, while CST offers both FIT time-domain (great for broadband and large) and FEM frequency-domain. Disagreements almost always trace to insufficient mesh density, mismatched ports, or radiation-boundary placement rather than a solver error.

Related Terms

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