Free Space
For inductive and capacitive (sometimes resistive) analysis, it is quite common for the fields to extend into the environment of the device in question. It is therefore important not only to model the device itself, but also its (close) surroundings. Typically, this is done by adding a box or sphere around the device’s geometry.
The default Free Space node is used to specify the physical conditions in close proximity to the device — typically in air or vacuum. It adds an Ampère’s Law governing equation with a limited set of material models: the permeability μr and permittivity εr are assumed to be one, and the conductivity is taken from the Stabilization conductivity.
The Free Space feature provides a canvas on top of which the Ampère’s Law feature and other features can be added to locally specify material properties and excitation forms.
Free Space assumes vacuum conditions, hence it does not require any material, but also a material with vacuum properties will be accepted. If the feature is applied on a selection that spans over materials with properties that are found to be inconsistent with that of vacuum, these will be ignored, and a warning is added to the solver. This can be fixed by adding appropriate physics features for the ignored materials. Otherwise, it is possible to disable the consistency check of materials by means of clearing the Check applicability of features in study checkbox in the Check consistency section that is available at the physics level (notice that the section is visible only after clicking the Show More Options button () and selecting Advanced Physics Options in the Show More Options dialog).
Stabilization
For transient and frequency domain modeling of inductive devices, it is desirable to limit the contrast in conductivity. This improves the numerical stability. In reality, the conductivity may vary between 10−14 S/m (dry air) and 6 ⋅ 107 S/m (for copper), but from a numerical viewpoint any material that causes insignificant eddy current or leakage current loss is effectively an insulator. As a result, the “insulator conductivity” is often chosen to be much higher than the true material property (note that this reasoning does not hold for capacitive modeling).
A suitable rule of thumb for choosing the stabilization conductivity is given by the skin depth, as compared to the overall geometry size. The assumption is that if the skin depth in Free Space is around one hundred times the device size, the resulting loss and the impact on lumped device properties are insignificant. At the same time, the model will still be sufficiently stable. What is considered a good value will differ per model, though. It is therefore recommended to double-check the free space loss as compared to other loss terms in the model. If the stabilization conductivity has a negative impact on the overall model accuracy, consider lowering it. If the solver has trouble converging, consider raising it. Alternatively, consider using Gauge Fixing.
Stabilization Conductivity
The Stabilization conductivity allows for five options:
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From material; use the conductivity specified by the material.
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Automatic (default in 3D); set the skin depth δs to be 100 times the geometry size and use that to deduce the appropriate conductivity σstab. The Typical frequency used for this conversion is taken from the solver. If there is no such frequency available — as is the case for a transient analysis — a Fallback frequency is used. The appropriate fallback frequency may differ per model and is best determined manually. Note that in addition to the fallback frequency, a solver-independent (user defined) frequency is an option too. A good value is the typical operating frequency of the modeled device. For more information, see Stabilization.
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From skin depth; very similar to the option Automatic, but with the added advantage that a user defined skin depth can be set.
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Off (default in 2D); disable the stabilization conductivity altogether: σstab = 0. This models a perfect vacuum and is a good approximation for air. In 2D oftentimes only the out-of-plane magnetic vector potential is used, providing sufficient stability.
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User defined; specify a suitable stabilization conductivity directly.
Note that a Fallback frequency that is chosen too low may result in an overly damped model, just like a stabilization conductivity that is chosen too high, or a skin depth that is chosen too small. The device’s typical operating frequency, combined with a skin depth that is at least an order of magnitude larger than the device size, should provide a suitable stabilization conductivity.
When in doubt, it is recommended to check the amount of resistive loss in the insulators and compare this against the overall device loss. Sweeping over the stabilization conductivity (investigating the effect of different amounts of stabilization) or comparing against a Gauge Fixed model with zero stabilization is an option too.