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Thermo-Structural Effects on a Cavity Filter
Introduction
This example investigates the electrical performance of a cascaded cavity filter operating in the millimeter-wave 5G band, including temperature changes. The thermal variations result in structural deformations of the filter geometry. Thus, the resonant frequencies of the filter elements (cavities) are affected by the thermo-structural phenomena. S-parameters are computed for different thermal expansion configurations.
Figure 1: Cascaded cavity filter with 2.92 mm (K) connectors. The front panel is removed to show the interior parts.
Model Definition
This example consists of three modeling parts:
•
Cascaded cavity filter covering two millimeter-wave 5G bands separately using two different parameter input files. One frequency band is 26.5–29.5 GHz for Japan, Korea, and the United States, whereas the other band, for the European Union and China, is 24.25–27.5 GHz.
•
Thermal deformation with the prescribed uniform temperature distribution and its impact on the bandpass filter performance.
•
Thermal deformation with the computed nonuniform temperature distribution and its impact on the bandpass filter performance.
In all cases, the properties of the dielectric are assumed to be independent of the temperature. Of course, one could add a temperature dependency as in the RF Heating waveguide example (Ref. 1).
Cavity Filters For the US and EU Millimeter-wave 5G Bands
The filter includes six rectangular cavities and two 2.92 mm (K) connectors. The first series of cavities are combined through irises that are considered as inductive due to the polarization excited from the coaxial pin and the orientation of the irises. The housing body and connector volume are quite thick with respect to the simulation frequencies, and no wave penetration is expected. Thus, only the cavity and connector walls are part of the model domain. All metallic boundaries are considered to be lossy with finite conductivity and modeled using an impedance boundary condition. The dielectric part of the coaxial connectors is defined as lossless. The two connectors are excited and terminated using the coaxial type of lumped ports with 50 Ω reference impedance, respectively.
The material labeled as Coated Surfaces is added for the impedance boundary condition feature. The electrical property of the high-conductivity coating of the exposed surfaces is a function of the temperature. See Ref. 2 for details. The frequency domain study is run for the US 5G band (26.5–29.5 GHz) first. The second study is using a different parameter input file, which updates the geometry to be resonant for the EU 5G band (24.25–27.5 GHz).
Thermal Deformation with the prescribed uniform temperature distribution
To include thermal deformation effects in the model, material properties are updated. The dielectric material in the coaxial connectors is modified to include the coefficient of thermal expansion (CTE) Young modulus, Poisson ratio, density, thermal conductivity, and specific heat. The values are chosen to be similar to those of FR4 material. The thermal deformation analysis requires to include the entire body of filter and connectors. So, the Aluminum material is added from the library. Brass material is added, with representative properties. Adhesive Layer material is also defined.
The model incorporates the effect of temperature variations on device performance with two cases:
•
The part operating at different (but uniform) ambient temperatures.
•
What happens when there is a temperature difference across the part. This can occur when a nearby electrical component has a thermal excursion due to overheating, for example.
Several effects can be considered. The solid structure itself will expand and contract in response to temperature increases and decreases. This will lead to a change in the sizes of the air cavities, irises, and dielectric materials within the filter. Both the deformations of the solid and the air domains need to be considered. Next, the material properties, most notably the electric conductivity of the coating, will change with temperature. The relative permittivity as well as the structural and thermal properties, can also be functions of temperature. However, in this model, they are assumed to be constant.
For the structural deformation is concerned, one must make a few assumptions about the attachments of the filter to the surroundings. One can assume that the structure is firmly attached to the flexible surrounding supporting structure, which would require that a structural model of the surroundings also need to be considered. One can also assume that the surroundings are perfectly rigid and that there is a small layer of adhesive attaching the filter to the rigid substrate structure. The latter assumption is simpler, and the one that will be used here. For modeling the connection between the deformed filter to the rigid substrate, the Spring Foundation feature is used. The deformations are initially negligible and the connection will gradually relax into its deformed state.
On two faces at which the lumped port boundary conditions are applied, it is assumed that these faces remain planar and that the cross-section is still an annulus under the thermal variations. These faces are modeled via the two Rigid Connector features, which enforce that the faces do not change shape or size, but can move or rotate due to the deformation of the filter itself.
The filter itself is simply modeled at three different isothermal conditions, -40°C, 20°C, and 120°C (that are -60 K, 0 K, and 100 K deviations in temperature about 20°C). See Parameters 2 node. The effect of the thermal expansion is considered by adding the Thermal Expansion subfeature to the Linear Elastic Material feature within Solid Mechanics interface.
A Moving Mesh feature is added under Definitions node to define the deformation of the air domain. The deformation settings follow the example Microwave Filter on PCB with Stress (Ref. 3).
The study uses a parametric sweep to update the temperature variation. The parametric sweep solves for the deformation of the structure and the air domains for three different operating temperatures. For each temperature, a frequency sweep is performed.
Thermal Deformation with the computed nonuniform temperature distribution
This part is meant to address the case of a 5G filter with a nonuniform temperature distribution that needs to be computed, rather than an imposed fixed uniform temperature deviation. The assumption of the analysis here is that the plate upon which the device sits experiences nonuniform heating due to some outside (nonmodeled) source. This nonuniform heating, linearly increasing to the positive x direction, imposes a temperature variation across the bottom face that will nonuniformly heat and distort the filter and affect its performance.
The Heat Transfer in Solids interface is added and is applied to all solid domains. This means that the heat flux inside of the cavities due to conduction and convection through the air is neglected. This a reasonable assumption for such small cavities, as air is a good insulator. Furthermore, radiation within the cavities and to the surrounding is also neglected. This is reasonable since the conductive heat path to the baseplate is the most significant. The thermal effects of the thin high-conductivity coatings, added for improved electromagnetic performance, are neglected, as they are thermally insignificant.
The temperature variation of the baseplate is modeled via the Heat Flux boundary condition. The baseplate is assumed to be a relatively large plate of metal with a known temperature variation across it with an external temperature distribution.
Within the settings for the Heat Transfer in Solids, the Discretization is set to Linear. This is necessary as the discretization of the thermal problem should be one order lower than the Solid Mechanics problem. The latter is Quadratic by default. When starting from the Thermal Stress entry point within the Add Physics wizard, this combination of discretizations is set automatically; otherwise, it needs to be set manually. The Solid Mechanics is identical to the previous model configuration.
In the Impedance Boundary Condition, the Model Input setting has the Temperature set to Temperature (ht), the computed temperature distribution. This physics interface is otherwise identical to the previous model.
The Multiphysics branch has a Thermal Expansion feature that applies the computed temperature distribution as a thermal expansion within the Solid Mechanics interface. This combines two physics interfaces for bidirectional coupling of multiple physical phenomena.
Step 1 first solves the thermo-structural problem, and then the electromagnetic problem is solved on the deformed state.
Results and Discussion
Total four studies are run and some of the default plots are modified. Since the front surfaces are removed from the physics view, the plots of the stress and heat distribution on the aluminum housing do not show the results for the boundaries removed from the view. These can be retrieved by deleting/disabling the Hide for Physics under the View node.
Cavity filters without thermal deformation
The default multislice plot is adjusted to show the electric field norm inside each series of cavities. The field pattern indicates that the basic TE101 cavity mode is excited around the center frequency. The field strength is also sustained from the input port 1 to output port 2; see Figure 2. The volume of the aluminum housing, connector body, and interior part of the coaxial pin are not included in the simulation and results analysis.
Figure 2: Electric field norm inside the cavities. The dominant TE resonance at each cavity is observed when the plotting frequency is close to the center of the millimeter-wave 5G band for Japan, Korea, and the US.
The S-parameter plot shows the impedance matching properties (S11) with respect to the reference impedance 50 Ω and insertion loss (S21) in dB scale. The first parameter input file shapes the cavities, irises, and coaxial pins to comply with the millimeter-wave 5G band from 26.5 to 29.5 GHz. The insertion loss S21 is better than 0.25 dB, and S11 is below -17.5 dB in the given bandwidth (Figure 3).
Figure 3: S-parameter plot for the millimeter-wave 5G band for Japan, Korea, and the US.
The simulation is repeated with the updated geometry to satisfy the EU millimeter-wave 5G band. The generated results show reasonably acceptable performance similar to that of the geometry for the US band. The factional bandwidth of the EU band (from 24.25 to 27.5 GHz) is wider than the US bandwidth. With the same number of cavity elements, the wider bandwidth results in degraded S11, overall below -13 dB, and 0.3 dB of insertion loss in Figure 5.
Figure 4: Electric field norm inside the cavities. The dominant mode TE resonance at each cavity is observed when the plotting frequency is close to the center of the millimeter-wave 5G band for the EU and China.
Figure 5: S-parameter plot for the millimeter-wave 5G band for EU and China.
Thermal Deformation
The structural mechanics analysis is added in the study, and the default plot includes a thermal expansion, von Mises stress (Figure 8) plot.
Figure 6: Electric field norm around the center frequency of the EU millimeter-wave 5G band when the temperature is -40°C. The thermal-structural deformation did not distort the dominant TE resonant modes in the cavities.
The default plot of the electromagnetics simulation is modified to show the cavity resonances in Figure 6. By looking at the field plot, the impact from the thermal expansion does not distort the dominant TE cavity modes at the center frequency. When the temperature is decreased, the thermal-structural deformation induces smaller cavities, and the S-parameters are shifted toward the higher frequencies. On the other hand, with the increased temperature, frequency responses are downshifted. The overall filter performance in terms of S-parameters (Figure 7) is not severely affected by the thermal expansion of the filter geometry. The frequency shift of -3 dB insertion loss S21 or -10 dB S11 is less than 100 MHz when the ambient temperature changes from -40 to 120°C.
Figure 7: S-parameters are slightly shifted as a function of ambient temperature.
Figure 8: Thermal expansion at 120°C that is 100K above the reference temperature.
Thermal Deformation with Computed Temperature
The last study is a combination of electromagnetics, structural mechanics, and heat transfer. The default plots include the electric field norm distribution, S-parameters, von Mises stress, and heat distribution. The top multislice plot in the Figure 9 is the electric field norm plot outside the passband. The plotted field strength indicates the input signal at port 1 does not propagate to the output port 2. The bottom multislice plot describes the electric field distribution at the passband.
Figure 9: The electric field norm beyond the passband is presented at the top, with the input signal failing to reach the output port. Conversely, the electric field emanating from the excited port was detected with minimal attenuation at the center of the passband, as illustrated at the bottom.
The filter is deformed by the uneven heat source on the baseplate. However, as shown in Figure 10, the S-parameters are not significantly distorted. The level of deformation in Figure 11 is less compared to the results of the ambient temperature change in Figure 8. The temperature distribution plots (Figure 12 and Figure 13) give an idea intuitively on which part of the aluminum housing and coaxial structures are hotter and suffer more from the thermo-structural effects.
Figure 10: S-parameters affected by the uneven heat source from the baseplate.
Figure 11: Deformed aluminum housing due to the heat expansion.
Figure 12: Surface plot of the temperature field.
Figure 13: Isosurface plot of the temperature field.
References
1.  www.comsol.com/model/rf-heating-6078
2.  www.comsol.com/video-training/getting-started/use-functions-define-material-property
3.  www.comsol.com/model/microwave-filter-on-pcb-with-stress-47501
Application Library path: RF_Module/Filters/cavity_filter_5g
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Radio Frequency > Electromagnetic Waves, Frequency Domain (emw).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Frequency Domain.
6
Click  Done.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file cavity_filter_5g_us.txt.
The loaded parameters will be used to build the filter geometry providing reasonable performance such as low insertion loss and impedance matching for the millimeter-wave 5G band in Japan, Korea, and the United States.
Parameters 2
1
In the Home toolbar, click  Parameters and choose Add > Parameters.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
dT
0
0
 
T0
20[degC]
293.15 K
 
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
Block 1 (blk1)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type a0.
4
In the Depth text field, type a0.
5
In the Height text field, type h0.
6
Locate the Position section. In the x text field, type -a0/2.
7
In the y text field, type -a0/2.
8
In the z text field, type -h0-w0/2.
Array 1 (arr1)
1
In the Geometry toolbar, click  Transforms and choose Array.
2
Select the object blk1 only.
3
In the Settings window for Array, locate the Size section.
4
In the x size text field, type 3.
5
Locate the Displacement section. In the x text field, type a0+w0.
6
Click  Build Selected.
7
Click the  Zoom Extents button in the Graphics toolbar.
Block 2 (blk2)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type w0.
4
In the Depth text field, type i0.
5
In the Height text field, type h0.
6
Locate the Position section. In the x text field, type a0/2.
7
In the y text field, type -i0/2.
8
In the z text field, type -h0-w0/2.
9
Click  Build Selected.
10
Click the  Wireframe Rendering button in the Graphics toolbar.
Block 3 (blk3)
1
Right-click Block 2 (blk2) and choose Duplicate.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Depth text field, type i1.
4
Locate the Position section. In the x text field, type a0*1.5+w0.
5
In the y text field, type -i1/2.
6
Click  Build Selected.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 2.92[mm]/2.
4
In the Height text field, type c0.
5
Locate the Position section. In the z text field, type -8.5[mm].
Cylinder 2 (cyl2)
1
Right-click Cylinder 1 (cyl1) and choose Duplicate.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 0.435[mm].
4
In the Height text field, type p0.
5
Click  Build Selected.
Union 1 (uni1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
Click the  Select All button in the Graphics toolbar.
Rotate 1 (rot1)
1
In the Geometry toolbar, click  Transforms and choose Rotate.
2
Select the object uni1 only.
3
In the Settings window for Rotate, locate the Input section.
4
Select the Keep input objects checkbox.
5
Locate the Rotation section. From the Axis type list, choose x-axis.
6
In the Angle text field, type 180.
7
Click  Build Selected.
8
Click the  Zoom Extents button in the Graphics toolbar.
Cylinder 3 (cyl3)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 0.4[mm].
4
In the Height text field, type p1.
5
Locate the Position section. In the x text field, type 2*(w0+a0).
6
In the z text field, type -p1/2.
Cylinder 4 (cyl4)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type r1.
4
In the Height text field, type w0.
5
Locate the Position section. In the x text field, type 2*(w0+a0).
6
In the z text field, type -w0/2.
7
Click  Build Selected.
Import 1 (imp1)
1
In the Geometry toolbar, click  Import.
2
In the Settings window for Import, locate the Source section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file cavity_filter_5g_case.mphbin.
5
Click  Import.
6
Click  Build All Objects.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane type list, choose Face parallel.
4
On the object imp1, select Boundary 21 only.
Work Plane 1 (wp1) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 16.
4
In the Height text field, type 9.
5
Locate the Position section. In the xw text field, type -8.
6
In the yw text field, type -22.
Work Plane 1 (wp1) > Mirror 1 (mir1)
1
In the Work Plane toolbar, click  Transforms and choose Mirror.
2
Select the object r1 only.
3
In the Settings window for Mirror, locate the Input section.
4
Select the Keep input objects checkbox.
5
Locate the Normal Vector to Line of Reflection section. In the xw text field, type 0.
6
In the yw text field, type 1.
7
Click  Build Selected.
8
Click the  Zoom Extents button in the Graphics toolbar.
Extrude 1 (ext1)
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, locate the Distances section.
3
In the table, enter the following settings:
Distances (mm)
2
4
Click  Build All Objects.
Next, the model utilizes virtual geometry operations and selections. The Form Composite Domains feature is used four times to simplify the geometry by reducing the number of different distinct domains within the model. They are labeled to represent their materials.
Form Composite Domains (Cavity Air)
1
In the Geometry toolbar, click  Virtual Operations and choose Form Composite Domains.
2
In the Settings window for Form Composite Domains, type Form Composite Domains (Cavity Air) in the Label text field.
3
Locate the Input section. Click the  Paste Selection button for Domains to composite.
4
In the Paste Selection dialog, type 6, 7, 26-33 in the Selection text field.
5
Click OK.
Form Composite Domains (Coax Brass)
1
In the Geometry toolbar, click  Virtual Operations and choose Form Composite Domains.
2
In the Settings window for Form Composite Domains, type Form Composite Domains (Coax Brass) in the Label text field.
3
Locate the Input section. Click the  Paste Selection button for Domains to composite.
4
In the Paste Selection dialog, type 4, 5, 8-11, 18-25, 27, 29 in the Selection text field.
5
Click OK.
Form Composite Domains (Aluminum Housing)
1
In the Geometry toolbar, click  Virtual Operations and choose Form Composite Domains.
2
In the Settings window for Form Composite Domains, type Form Composite Domains (Aluminum Housing) in the Label text field.
3
On the object cmd2, select Domains 2, 3, and 20 only.
Form Composite Domains (Coax Dielectric)
1
In the Geometry toolbar, click  Virtual Operations and choose Form Composite Domains.
2
In the Settings window for Form Composite Domains, type Form Composite Domains (Coax Dielectric) in the Label text field.
3
On the object cmd3, select Domains 7–12 and 15 only.
Define selections that are useful for configuring physics settings and material properties later on. Selections are defined for the various materials, as well as the surfaces that need to be coated with a high-conductivity material.
Definitions
Lumped Port 1
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Lumped Port 1 in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 80 only.
Lumped Port 2
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Lumped Port 2 in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 89 only.
Air Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Air Domains in the Label text field.
3
Select Domains 5 and 6 only.
Dielectric Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Dielectric Domains in the Label text field.
3
Select Domains 7, 8, and 11 only.
Surfaces of Electromagnetic Domains
1
In the Definitions toolbar, click  Adjacent.
2
In the Settings window for Adjacent, type Surfaces of Electromagnetic Domains in the Label text field.
3
Locate the Input Entities section. Under Input selections, click  Add.
4
In the Add dialog, select Air Domains in the Input selections list.
5
Click OK.
6
In the Settings window for Adjacent, locate the Input Entities section.
7
Under Input selections, click  Add.
8
In the Add dialog, select Dielectric Domains in the Input selections list.
9
Click OK.
Surfaces of Domains for Coating
1
In the Definitions toolbar, click  Difference.
2
In the Settings window for Difference, type Surfaces of Domains for Coating in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Input Entities section. Under Selections to add, click  Add.
5
In the Add dialog, select Surfaces of Electromagnetic Domains in the Selections to add list.
6
Click OK.
7
In the Settings window for Difference, locate the Input Entities section.
8
Under Selections to subtract, click  Add.
9
In the Add dialog, select Lumped Port 1 in the Selections to subtract list.
10
Click OK.
11
In the Settings window for Difference, locate the Input Entities section.
12
Under Selections to subtract, click  Add.
13
In the Add dialog, select Lumped Port 2 in the Selections to subtract list.
14
Click OK.
Electromagnetic Domains
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type Electromagnetic Domains in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog, in the Selections to add list, choose Air Domains and Dielectric Domains.
5
Click OK.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Air.
4
Click the Add to Component button in the window toolbar.
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Air (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Air Domains.
Coax Dielectric
1
In the Model Builder window, right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Coax Dielectric in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Dielectric Domains.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
2.1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Electromagnetic Waves, Frequency Domain (emw)
1
In the Model Builder window, under Component 1 (comp1) click Electromagnetic Waves, Frequency Domain (emw).
2
In the Settings window for Electromagnetic Waves, Frequency Domain, locate the Domain Selection section.
3
From the Selection list, choose Electromagnetic Domains.
Lumped Port 1
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
In the Settings window for Lumped Port, locate the Boundary Selection section.
3
From the Selection list, choose Lumped Port 1.
4
Locate the Lumped Port Properties section. From the Type of lumped port list, choose Coaxial.
Lumped Port 2
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
In the Settings window for Lumped Port, locate the Boundary Selection section.
3
From the Selection list, choose Lumped Port 2.
4
Locate the Lumped Port Properties section. From the Type of lumped port list, choose Coaxial.
Impedance Boundary Condition 1
1
In the Physics toolbar, click  Boundaries and choose Impedance Boundary Condition.
2
In the Settings window for Impedance Boundary Condition, locate the Boundary Selection section.
3
From the Selection list, choose Surfaces of Domains for Coating.
4
Click to expand the Model Input section. In the T text field, type T0+dT.
In the Impedance Boundary Condition feature, the Model Input for Temperature is defined as T0+dT where T0 is the reference ambient temperature and dT is the temperature deviation. This is used to evaluate the conductivity of the coating at the specified temperature.
Materials
Coated Surfaces
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Coated Surfaces in the Label text field.
3
Locate the Geometric Entity Selection section. From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Surfaces of Domains for Coating.
This is the same boundary selection as you specified the Impedance Boundary Condition.
5
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
rho(T)
S/m
Basic
6
In the Model Builder window, expand the Component 1 (comp1) > Materials > Coated Surfaces (mat3) node, then click Basic (def).
7
In the Settings window for Basic, locate the Model Inputs section.
8
Click  Select Quantity.
9
In the Physical Quantity dialog, select General > Temperature (K) in the tree.
10
Click OK.
Analytic 1 (an1)
1
Right-click Component 1 (comp1) > Materials > Coated Surfaces (mat3) > Basic (def) and choose Functions > Analytic.
2
In the Settings window for Analytic, type rho in the Function name text field.
3
Locate the Definition section. In the Expression text field, type 1/(2e-8[ohm*m]*(1+0.004[1/K]*(T-293.15[K]))).
4
In the Arguments text field, type T.
5
Locate the Units section. In the table, enter the following settings:
Argument
Unit
T
K
6
In the Function text field, type S/m.
7
Locate the Plot Parameters section. In the table, enter the following settings:
Plot
Argument
Lower limit
Upper limit
Fixed value
Unit
√
T
100
1000
0
K
8
Click  Plot.
These settings are for the electrical property used in the Impedance Boundary Condition representing the high conductivity coating of the exposed surfaces.
Study 1 - US Band
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study 1 - US Band in the Label text field.
Step 1: Frequency Domain
Define the study frequency ahead of performing any frequency-dependent operation such as building mesh. The physics-controlled mesh uses the highest frequency value in the specified range.
1
In the Model Builder window, under Study 1 - US Band click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type range(25.5,0.1,30.5).
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All.
Definitions
Hide for Physics 1
1
In the Model Builder window, right-click View 1 and choose Hide for Physics.
2
In the Settings window for Hide for Physics, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 37, 39, 43, 157, 159, 173, and 175 only.
Mesh 1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
Study 1 - US Band
In the Study toolbar, click  Compute.
Results
Electric Field (emw)
1
In the Settings window for 3D Plot Group, locate the Data section.
2
From the Parameter value (freq (GHz)) list, choose 28.1.
Multislice 1
1
In the Model Builder window, expand the Electric Field (emw) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the X-planes subsection. In the Planes text field, type 0.
4
Find the Y-planes subsection. In the Planes text field, type 0.
5
Find the Z-planes subsection. From the Entry method list, choose Coordinates.
6
In the Coordinates text field, type -2.6 2.6.
7
In the Electric Field (emw) toolbar, click  Plot.
Surface 1
In the Model Builder window, right-click Electric Field (emw) and choose Surface.
Transparency 1
1
In the Model Builder window, right-click Surface 1 and choose Transparency.
2
In the Settings window for Transparency, locate the Transparency section.
3
Find the Transparency subsection. Set the Transparency value to 0.85.
Surface 1
1
In the Model Builder window, click Surface 1.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose Thermal.
4
Clear the Color legend checkbox.
S-Parameter (emw)
In the Model Builder window, under Results click S-Parameter (emw).
The following instruction shows how to use the Graph Marker subfeature to analyze 1D plots. When plotting transmittivity properties of a bandpass filter, the half-power bandwidth of the passband can be computed through a graph marker.
Passband with Graph Marker
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Passband with Graph Marker in the Label text field.
Global 1
1
Right-click Passband with Graph Marker and choose Global.
2
In the Settings window for Global, click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Electromagnetic Waves, Frequency Domain > Ports > S-parameter, dB - dB > emw.S21dB - S21.
Graph Marker 1
1
Right-click Global 1 and choose Graph Marker.
2
In the Settings window for Graph Marker, locate the Display section.
3
From the Display mode list, choose Bandwidth.
4
Locate the Text Format section. In the Precision text field, type 3.
5
Select the Include unit checkbox.
6
Click to expand the Coloring and Style section. Select the Show frame checkbox.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Clear Table.
4
Click  Load from File.
5
Browse to the model’s Application Libraries folder and double-click the file cavity_filter_5g_eu.txt.
This parameters will update the geometry for the millimeter-wave 5G band in the European Union and China.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies > Frequency Domain.
4
Click the Add Study button in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2 - EU Band
In the Settings window for Study, type Study 2 - EU Band in the Label text field.
Step 1: Frequency Domain
1
In the Model Builder window, under Study 2 - EU Band click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type range(23.25,0.1,28.5).
4
In the Study toolbar, click  Compute.
Results
Electric Field (emw) 1
1
In the Settings window for 3D Plot Group, locate the Data section.
2
From the Parameter value (freq (GHz)) list, choose 25.75.
Multislice 1
1
In the Model Builder window, expand the Electric Field (emw) 1 node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the X-planes subsection. In the Planes text field, type 0.
4
Find the Y-planes subsection. In the Planes text field, type 0.
5
Find the Z-planes subsection. From the Entry method list, choose Coordinates.
6
In the Coordinates text field, type -2.6 2.6.
7
In the Electric Field (emw) 1 toolbar, click  Plot.
Surface 1
In the Model Builder window, right-click Electric Field (emw) 1 and choose Surface.
Transparency 1
1
In the Model Builder window, right-click Surface 1 and choose Transparency.
2
In the Settings window for Transparency, locate the Transparency section.
3
Find the Transparency subsection. Set the Transparency value to 0.85.
Surface 1
1
In the Model Builder window, click Surface 1.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose Thermal.
4
Clear the Color legend checkbox.
S-Parameter (emw) 1
In the Model Builder window, under Results click S-Parameter (emw) 1.
Thermal Deformation with the Prescribed Uniform Temperature Distribution
Definitions
Aluminum Domain
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Aluminum Domain in the Label text field.
3
Select Domains 1, 2, and 15 only.
Brass Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Brass Domains in the Label text field.
3
Select Domains 3, 4, 9, 10, and 12–14 only.
Enclosure Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Enclosure Domains in the Label text field.
3
Select Domain 2 only.
Solid Domains
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type Solid Domains in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog, in the Selections to add list, choose Dielectric Domains, Brass Domains, and Enclosure Domains.
5
Click OK.
Nonuniform Heat Domains
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type Nonuniform Heat Domains in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog, in the Selections to add list, choose Dielectric Domains, Aluminum Domain, Brass Domains, and Enclosure Domains.
5
Click OK.
Surfaces of Air Domains
1
In the Definitions toolbar, click  Adjacent.
2
In the Settings window for Adjacent, type Surfaces of Air Domains in the Label text field.
3
Locate the Input Entities section. Under Input selections, click  Add.
4
In the Add dialog, select Air Domains in the Input selections list.
5
Click OK.
Component 1 (comp1)
Deforming Domain 1
1
In the Physics toolbar, click  Moving Mesh and choose Free Deformation.
2
In the Settings window for Deforming Domain, locate the Domain Selection section.
3
From the Selection list, choose Air Domains.
The air domain is the deforming domain.
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Structural Mechanics > Solid Mechanics (solid).
4
Find the Physics interfaces in study subsection. In the table, clear the Solve checkboxes for Study 1 - US Band and Study 2 - EU Band.
5
Click the Add to Component 1 button in the window toolbar.
6
In the Home toolbar, click  Add Physics to close the Add Physics window.
Solid Mechanics (solid)
1
In the Settings window for Solid Mechanics, locate the Domain Selection section.
2
From the Selection list, choose Solid Domains.
Linear Elastic Material 1
In the Model Builder window, under Component 1 (comp1) > Solid Mechanics (solid) click Linear Elastic Material 1.
Thermal Expansion 1
1
In the Physics toolbar, click  Attributes and choose Thermal Expansion.
2
In the Settings window for Thermal Expansion, locate the Model Input section.
3
From the Tref list, choose User defined. In the associated text field, type T0.
4
From the T list, choose User defined. In the associated text field, type T0+dT.
Spring Foundation 1
1
In the Physics toolbar, click  Boundaries and choose Spring Foundation.
2
Select Boundaries 10 and 210 only.
3
In the Settings window for Spring Foundation, locate the Spring section.
4
From the Spring type list, choose Use material data.
5
In the ds text field, type 0.1[mm].
This represents a thin, 0.1[mm], adhesive layer connecting the filter body to a rigid substrate.
Rigid Connector 1
1
In the Physics toolbar, click  Boundaries and choose Rigid Connector.
2
Select Boundaries 77 and 89 only.
This feature enforces the deformation effects from the thermal variations only within the filter itself excluding the connector port boundaries. So, the lumped port boundaries remain planar during the simulation.
Rigid Connector 2
1
In the Physics toolbar, click  Boundaries and choose Rigid Connector.
2
Select Boundaries 74 and 80 only.
Materials
Coax Dielectric (mat2)
1
In the Model Builder window, under Component 1 (comp1) > Materials click Coax Dielectric (mat2).
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Young’s modulus
E
25[GPa]
Pa
Young’s modulus and Poisson’s ratio
Poisson’s ratio
nu
0.2
1
Young’s modulus and Poisson’s ratio
Density
rho
2000[kg/m^3]
kg/m³
Basic
Coefficient of thermal expansion
alpha_iso ; alphaii = alpha_iso, alphaij = 0
18e-6[1/K]
1/K
Basic
The material properties are modified to include the thermal deformation analysis. These properties may not represent low-loss material for millimeter-wave applications, but they are used to show the basic modeling workflow.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Aluminum.
4
Click the Add to Component button in the window toolbar.
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Aluminum (mat4)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Aluminum Domain.
Brass
1
In the Model Builder window, right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Brass in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Brass Domains.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Young’s modulus
E
110[GPa]
Pa
Young’s modulus and Poisson’s ratio
Poisson’s ratio
nu
0.33
1
Young’s modulus and Poisson’s ratio
Density
rho
8700[kg/m^3]
kg/m³
Basic
Coefficient of thermal expansion
alpha_iso ; alphaii = alpha_iso, alphaij = 0
19e-6[1/K]
1/K
Basic
Adhesive Layer
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Adhesive Layer in the Label text field.
3
Locate the Geometric Entity Selection section. From the Geometric entity level list, choose Boundary.
4
Select Boundaries 10 and 210 only.
5
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Young’s modulus
E
70[GPa]
Pa
Young’s modulus and Poisson’s ratio
Poisson’s ratio
nu
0.35
1
Young’s modulus and Poisson’s ratio
The following study uses a parametric sweep to wrap around the stationary study solving for the deformation of the structure with the three different temperatures.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Physics interfaces in study subsection. In the table, clear the Solve checkbox for Electromagnetic Waves, Frequency Domain (emw).
4
Find the Studies subsection. In the Select Study tree, select General Studies > Stationary.
5
Click the Add Study button in the window toolbar.
6
In the Home toolbar, click  Add Study to close the Add Study window.
Study 3
Step 2: Frequency Domain
1
In the Study toolbar, click  Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
3
In the Solve for column of the table, under Component 1 (comp1), clear the checkboxes for Solid Mechanics (solid) and Moving Mesh.
4
Locate the Study Settings section. From the Frequency unit list, choose GHz.
5
In the Frequencies text field, type range(23.25,0.1,28.5).
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
dT
-60 0 100
 
Set the temperature deviation -60K, 0K, and 100K from the reference temperature 20°C.
5
In the Model Builder window, click Study 3.
6
In the Settings window for Study, type Study 3 - Thermal Deformation, Uniform Temperature Distribution in the Label text field.
7
In the Study toolbar, click  Compute.
Results
Multislice 1
1
In the Model Builder window, expand the Results > Electric Field (emw) 2 node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the x-planes subsection. In the Planes text field, type 0.
4
Find the y-planes subsection. In the Planes text field, type 0.
5
Find the z-planes subsection. From the Entry method list, choose Coordinates.
6
In the Coordinates text field, type -2.6 2.6.
Electric Field (emw) 2
1
In the Model Builder window, click Electric Field (emw) 2.
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (freq (GHz)) list, choose 25.95.
4
From the Parameter value (dT) list, choose -60.
5
In the Electric Field (emw) 2 toolbar, click  Plot.
S-Parameter (emw) 2
1
In the Model Builder window, click S-Parameter (emw) 2.
2
In the Settings window for 1D Plot Group, locate the Legend section.
3
From the Position list, choose Lower right.
Global 1
1
In the Model Builder window, expand the S-Parameter (emw) 2 node, then click Global 1.
2
In the Settings window for Global, locate the x-Axis Data section.
3
From the Axis source data list, choose Inner solutions.
4
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose Cycle.
5
In the S-Parameter (emw) 2 toolbar, click  Plot.
Moving Mesh
1
In the Model Builder window, under Results click Moving Mesh.
2
In the Moving Mesh toolbar, click  Plot.
Thermal Deformation with the Computed Nonuniform Temperature Distribution
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
Find the Physics interfaces in study subsection. In the table, clear the Solve checkboxes for Study 1 - US Band, Study 2 - EU Band, and Study 3 - Thermal Deformation, Uniform Temperature Distribution.
4
In the tree, select Heat Transfer > Heat Transfer in Solids (ht).
5
Click the Add to Component 1 button in the window toolbar.
6
In the Home toolbar, click  Add Physics to close the Add Physics window.
Heat Transfer in Solids (ht)
1
In the Settings window for Heat Transfer in Solids, locate the Domain Selection section.
2
From the Selection list, choose Nonuniform Heat Domains.
3
Click to expand the Discretization section. From the Temperature list, choose Linear.
For the Heat Transfer in Solids, the Discretization is set to Linear, one order lower than that in the Solid Mechanics problem.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 2, 6-9, 21-29, 31, 32, 34-36, 47, 60-63, 72, 73, 75, 76, 102, 103, 120, 121, 142-145, 154, 155, 202, 205-208, 219, 220, 225 in the Selection text field.
5
Click OK.
6
In the Settings window for Heat Flux, locate the Heat Flux section.
7
From the Flux type list, choose Convective heat flux.
8
In the h text field, type 5[W/m/m/K].
9
In the Text text field, type 25[degC].
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundary 226 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type 225[degC].
Thin Layer 1
1
In the Physics toolbar, click  Boundaries and choose Thin Layer.
2
Select Boundaries 10 and 210 only.
3
In the Settings window for Thin Layer, locate the Heat Conduction section.
4
From the k list, choose User defined. In the associated text field, type 0.42[W/m/K].
5
Locate the Thermodynamics section. From the ρ list, choose User defined. In the associated text field, type 1000[kg/m^3].
6
From the Cp list, choose User defined. In the associated text field, type 1500[J/(kg*K)].
Materials
Aluminum (mat4)
1
In the Model Builder window, under Component 1 (comp1) > Materials click Aluminum (mat4).
2
Select Domains 1, 2, and 15 only.
Adhesive Layer (mat6)
1
In the Model Builder window, click Adhesive Layer (mat6).
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thickness
lth
0.1[mm]
m
Shell
Electromagnetic Waves, Frequency Domain (emw)
Impedance Boundary Condition 1
1
In the Model Builder window, under Component 1 (comp1) > Electromagnetic Waves, Frequency Domain (emw) click Impedance Boundary Condition 1.
2
In the Settings window for Impedance Boundary Condition, locate the Model Input section.
3
From the T list, choose Temperature (ht).
Except for the above update in the Impedance Boundary Condition, the settings in this physics interface for simulating electromagnetics are identical to the previous model configurations.
Multiphysics
Thermal Expansion 1 (te1)
1
In the Physics toolbar, click  Multiphysics Couplings and choose Domain > Thermal Expansion.
2
In the Settings window for Thermal Expansion, locate the Domain Selection section.
3
From the Selection list, choose Solid Domains.
Materials
Coax Dielectric (mat2)
1
In the Model Builder window, under Component 1 (comp1) > Materials click Coax Dielectric (mat2).
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
0.25[W/(m*K)]
W/(m·K)
Basic
Heat capacity at constant pressure
Cp
1350[J/kg/K]
J/(kg·K)
Basic
Brass (mat5)
1
In the Model Builder window, click Brass (mat5).
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
105[W/(m*K)]
W/(m·K)
Basic
Heat capacity at constant pressure
Cp
380[J/(kg*K)]
J/(kg·K)
Basic
Next, add a stationary study step for the thermo-structural analysis. A frequency domain study step is also required to solve the electromagnetics problem on the deformed state.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Physics interfaces in study subsection. In the table, clear the Solve checkbox for Electromagnetic Waves, Frequency Domain (emw).
4
Find the Studies subsection. In the Select Study tree, select General Studies > Stationary.
5
Click the Add Study button in the window toolbar.
6
In the Home toolbar, click  Add Study to close the Add Study window.
Study 4
Step 1: Stationary
1
In the Settings window for Stationary, locate the Physics and Variables Selection section.
2
Select the Modify model configuration for study step checkbox.
3
In the tree, select Component 1 (comp1) > Electromagnetic Waves, Frequency Domain (emw).
4
Click  Disable in Model.
5
In the tree, select Component 1 (comp1) > Solid Mechanics (solid), Controls spatial frame > Linear Elastic Material 1 > Thermal Expansion 1.
6
Click  Disable.
Step 2: Frequency Domain
1
In the Study toolbar, click  Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
From the Frequency unit list, choose GHz.
4
In the Frequencies text field, type range(23.25,0.1,28.5).
5
Locate the Physics and Variables Selection section. In the Solve for column of the table, under Component 1 (comp1), clear the checkboxes for Solid Mechanics (solid) and Moving Mesh.
6
In the Solve for column of the table, under Component 1 (comp1) > Multiphysics, clear the checkbox for Thermal Expansion 1 (te1).
7
In the Model Builder window, click Study 4.
8
In the Settings window for Study, type Study 4 - Thermal Deformation, Nonuniform Computed Temperature in the Label text field.
9
In the Study toolbar, click  Compute.
Results
Electric Field (emw) 3
1
In the Settings window for 3D Plot Group, locate the Data section.
2
From the Parameter value (freq (GHz)) list, choose 25.75.
3
In the Electric Field (emw) 3 toolbar, click  Plot.
S-Parameter (emw) 3
1
In the Model Builder window, click S-Parameter (emw) 3.
2
In the Settings window for 1D Plot Group, locate the Legend section.
3
From the Position list, choose Lower right.
Global 2
1
In the Model Builder window, expand the S-Parameter (emw) 3 node.
2
Right-click Results > S-Parameter (emw) 3 > Global 1 and choose Duplicate.
3
In the Settings window for Global, locate the Data section.
4
From the Dataset list, choose Study 2 - EU Band/Solution 2 (sol2).
5
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dotted.
Global 1
1
In the Model Builder window, click Global 1.
2
In the Settings window for Global, click to expand the Legends section.
3
From the Legends list, choose Manual.
4
In the table, enter the following settings:
Legends
S11, Thermal Deformation
S21, Thermal Deformation
Global 2
1
In the Model Builder window, click Global 2.
2
In the Settings window for Global, locate the Legends section.
3
From the Legends list, choose Manual.
4
In the table, enter the following settings:
Legends
S11, No Deformation
S21, No Deformation
Transparency 1
1
In the Model Builder window, expand the Results > Stress (solid) 1 node.
2
Right-click Volume 1 and choose Transparency.
Domain
1
In the Model Builder window, expand the Results > Temperature (ht) node, then click Domain.
2
In the Settings window for Volume, locate the Coloring and Style section.
3
From the Color table transformation list, choose Nonlinear.
4
Set the Color calibration parameter value to -1.4.
5
In the Color calibration parameter text field, type -1.5.
Result Templates
1
In the Results toolbar, click  Result Templates to open the Result Templates window.
2
Go to the Result Templates window.
3
In the tree, select Study 4 - Thermal Deformation, Nonuniform Computed Temperature/Solution 9 (sol9) > Heat Transfer in Solids > Isothermal Contours (ht).
4
Click the Add Result Template button in the window toolbar.
5
In the Results toolbar, click  Result Templates to close the Result Templates window.
Results
Domain
1
In the Model Builder window, expand the Isothermal Contours (ht) node, then click Domain.
2
In the Settings window for Isosurface, locate the Levels section.
3
In the Total levels text field, type 30.
4
In the Isothermal Contours (ht) toolbar, click  Plot.