field calculator operations -...

Ansoft High Frequency Structure Simulator v9 UserAnsoft High Frequency Structure Simulator v9 UserAnsoft High Frequency Structure Simulator v9 UserAnsoft High Frequency Structure Simulator v9 User’’’’s Guide s Guide s Guide s Guide

3.1Field Calculator Operations

3.1-1

IntroductionThis chapter provides advanced details and support regarding usage of the Field Field Field Field CalculatorCalculatorCalculatorCalculator in HFSS v9.x.

The HFSS Field CalculatorField CalculatorField CalculatorField Calculator is a feature of the simulation program which permits full user access and mathematical manipulation of the volumetric phasor field data generated from the finite element analysis. The field calculator permits scalar, vector, and complex operations, integrations and derivatives, and can generate graphical and tabular output data in conjunction with Field OverlayField OverlayField OverlayField Overlay or with the Report EditorReport EditorReport EditorReport Editor.

Some possible applications of the Field CalculatorField CalculatorField CalculatorField Calculator include:

Exportation of raw field data for manipulation outside of HFSS

Generation of specific E, H, J, or Poynting data plots along user-designated paths or locations

Power, loss, and breakdown computations

Frequency-selective surface (FSS) or Electromagnetic Bandgap (EBG) reflection magnitude and phase computations

Voltage or Current computations from line integrals

Wave impedance computations

Geometric operations and mathematics

Field Overlay EnhancementsUsers of the calculator from prior versions of HFSS will find that in general the calculator panel is unchanged. What has changed is the relationship of the calculator to the generation of Field OverlayField OverlayField OverlayField Overlay plots and output graphs, both of which the Field Calculator used to output directly but which are now handled by the unified Field OverlayField OverlayField OverlayField Overlay generation or by the Report EditorReport EditorReport EditorReport Editor, appropriately

Several field displays which were previously available only from the calculator are now generated directly by the Field OverlayField OverlayField OverlayField Overlay engine without user computations. These include:

Plots of field magnitudes or vectors along a line

Plots of vector fields throughout a volume

Plots of field isosurface contours in volumes

Plots of volumetric loss quantities such as Specific Absorption Rate (SAR) and Volume Loss Density



3.1-2

Usage RecommendationsProject convergence is generally achieved by evaluation of a summary criterion like Max DeltaMax DeltaMax DeltaMax Delta----S S S S or DeltaDeltaDeltaDelta----EEEE. In order to obtain high accuracy results from calculations on field data, it is advised that the user take extra precautions to assure that the model’s field data is dependable. These extra precautions might include:

Running the project to a tighter than usual convergence value

Providing Mesh OperationsMesh OperationsMesh OperationsMesh Operations in the areas to be used for calculations

Running parametric variations to isolate sensitivity to modeling parameters such as adaptation frequency or circular structure Surface ApproximationsSurface ApproximationsSurface ApproximationsSurface Approximations

Although the Field CalculatorField CalculatorField CalculatorField Calculator can be used on field data obtained at any frequency from a Fast Fast Fast Fast frequency sweep, this data may be of decreasing accuracy for lossyor dispersive media as the extreme band edges of the sweep are reached. For higher accuracy computations are recommended on a full matrix solution at the desired frequency for analysis.

Since materials assigned as part of a Perfectly Matched LayerPerfectly Matched LayerPerfectly Matched LayerPerfectly Matched Layer (PML) model termination are anisotropic and highly lossy, performing field calculations interior to objects designated as PMLs is not recommended.

Units and StandardsAll field outputs from HFSS are in MKS units, regardless of Design and Project variables, defaults, dimensions, and units.

Raw field data accessed by the Field CalculatorField CalculatorField CalculatorField Calculator are Peak Phasor quantities, and do reflect the total magnitude and phases of source excitations specified by the Edit SourcesEdit SourcesEdit SourcesEdit Sources window. The source excitations should be set to the desired value(s) before engaging the Field CalculatorField CalculatorField CalculatorField Calculator.

Field data from EigensolutionEigensolutionEigensolutionEigensolution designs are normalized to a peak value of 1.0

For all Trigonometry functions, the units are radians by default.



3.1-3

Opening the CalculatorThe Field Calculator is available from the menu, Design Tree, and Toolbar of HFSS

Open the Field Calculator using the menu selection HFSS > Fields > HFSS > Fields > HFSS > Fields > HFSS > Fields > CalculatorCalculatorCalculatorCalculator

From the Project Manager window, right-click the Field OverlayField OverlayField OverlayField Overlay entry and select Calculator.Calculator.Calculator.Calculator.

Use the Toolbar Icon:



3.1-4

Field Calculator Layout

Named Expression List:Named Expression List:Named Expression List:Named Expression List:Pre-created retrievable computations

Context Selection Fields:Context Selection Fields:Context Selection Fields:Context Selection Fields:Solution setup, frequency,

and starting phase assumptions

Change Variable Button:Change Variable Button:Change Variable Button:Change Variable Button:Access to Design

variations

Calculator Stack:Calculator Stack:Calculator Stack:Calculator Stack:Buffer for results and

operations in progress

Input Operations:Input Operations:Input Operations:Input Operations:Operations loading new

inputs into the Stack

General Operations:General Operations:General Operations:General Operations:Functions and Operations

which work on multiple data types

Scalar Operations:Scalar Operations:Scalar Operations:Scalar Operations:Functions and Operations which work on Scalar data

only

Vector Operations:Vector Operations:Vector Operations:Vector Operations:Functions and Operations which work on Vector data

only

Output Operations:Output Operations:Output Operations:Output Operations:Functions and Operations which result in final values,

generate output plots, or export data beyond HFSS.

Calculator Stack Calculator Stack Calculator Stack Calculator Stack Operations:Operations:Operations:Operations:

Operations which manipulate the stack

contents to add, delete, or rearrange entries.



3.1-5

Calculator Stack RegisterCalculator stack registers add to the stack display above preceding entries. Therefore, the entry at the top of the stack represents the last register filled.

Note: Note: Note: Note: This convention is opposite to that which many users may be familiar with from the use of hand-held multi-line calculators, which often build their stacks from the bottom up.

Stack ManipulationStack registers are re-ordered and otherwise manipulated with the stack operations buttons across its bottom edge. Their behavior is for the most-part self-explanatory.

PushPushPushPush duplicates the top stack register

PopPopPopPop deletes the top stack register

RlupRlupRlupRlup and RldnRldnRldnRldn will ‘roll up’ or ‘roll down’ the stack register entries, in effect rotating the stack order

ExchExchExchExch will ‘exchange’ the top two stack entries, reversing only their order

ClearClearClearClear empties the stack completely

UndoUndoUndoUndo performs an ‘undo’ operation on the top stack register, attempting to remove the last operation performed upon it. This may result inregeneration of additional stack entries which were present before the prior operation

Note:Note:Note:Note: Simple numerical results cannot be ‘undone’. Only stack entry values which represent some step of an operation can be reverse-parsed.

Newest EntryNewest EntryNewest EntryNewest Entry

Oldest EntryOldest EntryOldest EntryOldest Entry



3.1-6

Named Expressions ListThis listing contains pre-fetchable operation sequences used by HFSS to generate Field OverlayField OverlayField OverlayField Overlay plots. Additional computations can be stored here by the user for a given project

The Add Add Add Add button will add the stack top entry into the list and query for a user name. The Copy to StackCopy to StackCopy to StackCopy to Stack button will copy a selected entry into the stack register.Delete Delete Delete Delete permits selected-entry deletion, while Clear AllClear AllClear AllClear All removes all entries.

Note:Note:Note:Note: only user-created Named Expressions can be deleted or cleared.

Context FieldsThis section indicates the selected Model and solution file for which field calculation will be performed.

SolutionSolutionSolutionSolution selection (sweep or adaptive) determines what options if any are available in the FrequencyFrequencyFrequencyFrequency field.PhasePhasePhasePhase is a net starting phase default value to apply to all phasor entries belowChange Variable ValuesChange Variable ValuesChange Variable ValuesChange Variable Values allows access to model variables in the case of multiple design instances being solved (Optimetrics™)



3.1-7

Input OperationsThe Input ColumnInput ColumnInput ColumnInput Column contains all the calculator functions which place new values into the stack. These values include field data, geometry data, and numerical quantities. Field data (e.g. E-field, H-field, and Poynting vector) for the current project solution is input from the QtyQtyQtyQty (quantity) dropdown menu button .

All field entries are Peak Phasor values in MKS units

All field entries use the current source excitation setup (Edit SourcesEdit SourcesEdit SourcesEdit Sources) at the time the final computation is performed.

Note: Note: Note: Note: There is no context in the stack entities themselves which show for what source settings the computation is appropriate!

EEEE and HHHH are self explanatory

JvolJvolJvolJvol is Volume Current Density, computed as

therefore containing both Conduction and Displacement current

JsurfJsurfJsurfJsurf is Net Surface Current Density, computed as

where nnnn is the surface normal. ‘top’ and ‘bottom’ denote volume domains in the tetrahedra above and below the surface upon which Jsurf is being plotted

Note: Note: Note: Note: As Jsurf requires geometric operations, this value cannot be exported on a grid surface (See Export OperationsExport OperationsExport OperationsExport Operations)

−×

bottomtopHHn��

ˆ

( )Ej�

εωσ ′′+



3.1-8

Input Operations, cont.PoyntingPoyntingPoyntingPoynting is the Poynting vector, computed as

Note: Note: Note: Note: Only the Real part of the PoyntingPoyntingPoyntingPoynting vector is available as an automatic output to a Field OverlayField OverlayField OverlayField Overlay. However the calculator PoyntingPoyntingPoyntingPoynting output is complex to include both power flow and storage information.

Local SARLocal SARLocal SARLocal SAR and Average SARAverage SARAverage SARAverage SAR are Specific Absorption Rates, computed as

where ρ is mass density.

LocalLocalLocalLocal is derived from raw field data, while AverageAverageAverageAverage is averaged over a small volume around each point dependent on the SAR settings in Menu option HFSS > Fields > SAR SettingHFSS > Fields > SAR SettingHFSS > Fields > SAR SettingHFSS > Fields > SAR Setting…………

Surface Loss DensitySurface Loss DensitySurface Loss DensitySurface Loss Density and Volume Loss DensityVolume Loss DensityVolume Loss DensityVolume Loss Density are export operations for the Ansoft add-on product ePhysics™ to perform thermal analysis. The VolumeVolumeVolumeVolume term is computed as

Note: Surface Loss Density Note: Surface Loss Density Note: Surface Loss Density Note: Surface Loss Density is handled specially, as assumptions of superficial losses on planar surfaces must be done with caution. It is related to the normal component of the real part of the PoyntingPoyntingPoyntingPoynting vector on the respective surface. As with JsurfJsurfJsurfJsurf, this entry cannot be exported on a grid (See Output OperationsOutput OperationsOutput OperationsOutput Operations).

( )∗× HE��

21

ρσ2

2E⋅

( )∗• volJE��

Re21



3.1-9

Input Operations, cont.GeometryGeometryGeometryGeometry loads mathematical placeholders of geometric objects for operation into the stack. The type of object or entity selected influences the stack content type as well.

ConstantConstantConstantConstant loads a value from a list of constants, dimensioned in the MKS units, such as the speed of light, permittivity and permeability of free space, etc.NumberNumberNumberNumber opens a dialog for user entry of a numerical value. The value can be scalar, complex, vector, or any appropriate combination (e.g. a complex vector).

FunctionFunctionFunctionFunction permits entry of a standard function like position (XXXX, YYYY, and ZZZZ) or PhasePhasePhasePhase. These function entries can be used as placeholder operations to perform later steps which will desire a ‘variable’ capability. For example, using PhasePhasePhasePhase will enter a stack placeholder that can permit a later Complex >Complex >Complex >Complex > AtPhaseAtPhaseAtPhaseAtPhase operation (Scalar column) resulting in an output which can still be displayed at variable phase.The Geometry SettingsGeometry SettingsGeometry SettingsGeometry Settings button accesses a discretization setting for all line-type plotting behavior.



3.1-10

Calculator Stack Data TypesDepending on the InputInputInputInput operation selected or the subsequent operation(s) performed on them, stack quantities can be of different data types.Each entry in the Stack Register has its type denoted to the left of the quantity itself by an abbreviation followed by a colon (:).

Data types fall in to three primary categories: Quantity types, Geometry types, and Combination types.

Note:Note:Note:Note: The same indication can be used for a ‘single-point’ value (a single complex vector) or for field data from the entire current field solution (complex vector E field through the entire geometry).

Quantity types are usually for field or user-entered data, or the results of prior operations

CscCscCscCsc denotes a “complex, scalar” couplet (Re, Im).CvcCvcCvcCvc denotes a “complex, vector” entity (Vx, Vy, Vz), where Vx = (Re, Im), etc. Field Phasors are CvcCvcCvcCvc values in most cases.VecVecVecVec denotes a vector triplet (Vx, Vy, Vz) where Vx is a scalar, etc.SclSclSclScl denotes a scalar value

Geometry data types represent pure geometric entries. VolVolVolVol indicates the stack contents is a mathematic volume, usually an object nameSrfSrfSrfSrf indicates the contents is a surface designation, either a Sheet object name, List of faces of geometric objects, or a mathematical PlanedesignationLinLinLinLin indicates any ‘line’ quantity. The line can be open or closed. The second value indicates the current discretization attribute from Geometry Geometry Geometry Geometry Settings Settings Settings Settings which provides a sampling point count along the linePntPntPntPnt indicates a single-point location quantity

Combination entries indicate a particular Quantity restricted to a particular Geometry, e.g. SclSrfSclSrfSclSrfSclSrf indicates scalar data restricted to a surface geometry.



3.1-11

Data Type ConversionData Types are automatically converted by appropriate operations.

Operation-dependent, such as taking the DotDotDotDot product of two vectors

Combination type generation, e.g. taking the ValueValueValueValue of a VecVecVecVec quantity on a SrfSrfSrfSrf surface geometry will result in VecSrfVecSrfVecSrfVecSrf data.

Geometry data types can generally not be ‘converted’

Most operations in the calculator can only be performed on certain data types, which is reflected by the organization of operations into Columns.

General General General General operations can be performed on several different data types, assuming consistency. These operations can but do not always alter the data type of the result.

VectorVectorVectorVector operations can only be performed on vector data, while ScalarScalarScalarScalar operations can only be performed on scalar data. Specific details regarding each such operation are denoted in following sections.

A summary table of operations primarily for data restriction or type conversion is below for reference.

CvcCvcCvcCvc CscCscCscCsc VecVecVecVec SclSclSclScl

CvcCvcCvcCvcMagMagMagMag (vector

mag) or Sc al? Sc al? Sc al? Sc al? > X, Y, > X, Y, > X, Y, > X, Y, or Z Z Z Z

Complex > Complex > Complex > Complex > Real, Imag, Real, Imag, Real, Imag, Real, Imag, CmplxMag, CmplxMag, CmplxMag, CmplxMag,

CmplxPhase, CmplxPhase, CmplxPhase, CmplxPhase, or AtPhase AtPhase AtPhase AtPhase

(No Single Operation)

CscCscCscCsc Vec ? > X, Y, Vec ? > X, Y, Vec ? > X, Y, Vec ? > X, Y, or Z Z Z Z


Complex > Complex > Complex > Complex > Real, Imag, Real, Imag, Real, Imag, Real, Imag, CmplxMag, CmplxMag, CmplxMag, CmplxMag,

CmplxPhase, CmplxPhase, CmplxPhase, CmplxPhase, or AtPhaseAtPhaseAtPhaseAtPhase

VecVecVecVec

Complex > Complex > Complex > Complex > ComplexReal ComplexReal ComplexReal ComplexReal

or ComplexImagComplexImagComplexImagComplexImag


MagMagMagMag (vector mag) or Scal? > X, Scal? > X, Scal? > X, Scal? > X,

Y, Y, Y, Y, or Z Z Z Z

SclSclSclScl(No Single Operation)

Complex > Complex > Complex > Complex > ComplexReal ComplexReal ComplexReal ComplexReal

or ComplexImagComplexImagComplexImagComplexImag

Vec ? > X, Y, Vec ? > X, Y, Vec ? > X, Y, Vec ? > X, Y, or Z Z Z Z

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Fro

m…

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Fro

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Fro

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Co nve rt T o….Co nve rt T o….Co nve rt T o….Co nve rt T o….DAT A DAT A DAT A DAT A CONVERSIONCONVERSIONCONVERSIONCONVERSION



3.1-12

General OperationsGeneralGeneralGeneralGeneral operations are those possible on different data types. All require some consistency or expected restriction on the entry (or entries) being operated upon.

+ (plus)+ (plus)+ (plus)+ (plus) adds the top two stack entries. Both quantities may be vector or scalar, complex or real-only, but must be consistent.---- (minus) (minus) (minus) (minus) subtracts the top stack entry from the prior one. As with + + + + above vector, complex, or scalar subtraction is possible but both quantities must be consistent.x (multiply)x (multiply)x (multiply)x (multiply) performs the product of the top two stack entries. This is a scalar multiple only: one entry must be a scalar, the other can be vector, or scalar, but must be real only./ (divide)/ (divide)/ (divide)/ (divide) divides the second stack entry by the latest. As with xxxx above only a scalar division of other scalars or real-only vectors is permitted.NegNegNegNeg takes the negative (mutiply by -1) of the top stack entry. Vector, complex, or scalar allowed.AbsAbsAbsAbs takes the absolute product of the top stack entry. Complex, vector, or scalar allowed.SmoothSmoothSmoothSmooth performs a data smoothing operation on the top stack entry to assure data continuity. This operation is performed automatically on all pre-created field Named ExpressionsNamed ExpressionsNamed ExpressionsNamed Expressions for Field Overlay Field Overlay Field Overlay Field Overlay plotting. All data types allowed.ComplexComplexComplexComplex is a submenu with all complex operations

RealRealRealReal and ImagImagImagImag takes the appropriate part of any Complex (vector or scalar) entry.CmplxMagCmplxMagCmplxMagCmplxMag takes the magnitude of any Complex (vector or scalar) entry.Similarly, CmplxPhaseCmplxPhaseCmplxPhaseCmplxPhase takes the phase.ConjConjConjConj takes the Complex Conjugate of any Complex (vector or scalar) entryAtPhaseAtPhaseAtPhaseAtPhase evaluates the top two stack entries, the earlier of which must be a Complex Vector field quantity, and the last of which must be a scalar number. The scalar value is taken as the phase in radians at which the field phasor is evaluated.CmplxRealCmplxRealCmplxRealCmplxReal and CmplxImagCmplxImagCmplxImagCmplxImag converts a Scalar (vector or not) top

entry and applies it to the real or imaginary part of a complex value, appropriately. Used to convert real-only numbers in order to permit operations with complex ones.

Domain Domain Domain Domain restricts the second-stack entry field quanity (complex or real, scalar or vector) to the volume defined by the top stack entry (Volume only)



3.1-13

Scalar OperationsScalarScalarScalarScalar operations are those executable only on Scalar data. In some cases a combination of data types and more than one stack entry is required.

VecVecVecVec? > X? > X? > X? > X, YYYY, or ZZZZ takes the scalar or complex-scalar top stack entry and makes it the selected component of a vector quantity (which will then be either vector or complex-vector, appropriately)

1/x1/x1/x1/x inverts the top stack entry. The entry may be complex or real-only.

PowPowPowPow takes two scalar (complex or real only) entries and raises the earlier entry to the ‘power’ of the later entry.

√√√√ takes the square root of the top stack entry, which may be complex

TrigTrigTrigTrig is a submenu containing Trigonometric functions sinsinsinsin, coscoscoscos, tantantantan, asinasinasinasin,acosacosacosacos, atanatanatanatan, and atan2atan2atan2atan2. All operate on the top stack entry only which must be scalar and real-only, and is assumed to be in radians. . . . AtanAtanAtanAtan is used for angles ranging from -90 to 90 degrees, while atan2atan2atan2atan2 is usable over a -180 to 180 range.

d/dd/dd/dd/d? > X? > X? > X? > X, YYYY, or ZZZZ takes the derivative of the top stack entry value in the specified direction. Stack quantity may be complex.

∫∫∫∫ takes the integration of the top stack entry, which must be both scalar and non-complex.

Note: Note: Note: Note: To take the integration of complex values, use integration by parts to perform the integration of the Real and Imaginary portions separately and then use the ComplexRealComplexRealComplexRealComplexReal and ComplexImagComplexImagComplexImagComplexImagoperations to facilitate recombining the results.

MinMinMinMin and MaxMaxMaxMax each have suboptions of Value Value Value Value and PositionPositionPositionPosition. Will return either the value or the location of the min or max point of the top stack quantity, which must be a non-complex scalar quantity limited by some geometry operation (using Domain Domain Domain Domain or ValueValueValueValue), e.g. a SclLinSclLinSclLinSclLin, SclSrfSclSrfSclSrfSclSrf or SclVolSclVolSclVolSclVolquantity.

∇∇∇∇ is the Gradient operator. Takes the Gradient of the top stack entry, which may be complex. Result of operation becomes a vector quantity (preserving complex status if applicable)

LnLnLnLn and LogLogLogLog are natural and base-10 logarithms. Both operate on real, positive-only scalar values. (E.g. if taking the log of a field quantity, be sure to take the AbsAbsAbsAbs absolute value to assure no negative numbers.)



3.1-14

Vector OperationsVectorVectorVectorVector operations are those executable only on Vector data. In some cases a combination of data types and more than one stack entry is required.

ScalScalScalScal? > X? > X? > X? > X, YYYY, or ZZZZ takes the vector or complex-vector top stack entry and extracts the selected component to form a scalar or complex-scalar entry, appropriately)MatlMatlMatlMatl………… performs a vector operation on the top stack entry using material data from the project geometry.

Available material quantities are PermeabilityPermeabilityPermeabilityPermeability, PermittivityPermittivityPermittivityPermittivity,ConductivityConductivityConductivityConductivity, and Omega and Omega and Omega and Omega (2πƒ). The stack quantity can be multiplied or divided by these values.The stack quantity may be a complex or real-only vector. The resultant will be a complex vector.

Note: Note: Note: Note: The material value will be accurate at each location in the model for designs containing different material characteristics in different solids. The ConductivityConductivityConductivityConductivityselection actually multiplies the stack quantity by (σ + jωε″), not simply σ

MagMagMagMag takes the vector magnitude of a real-only or complex vector. It does not influence the complex status of the stack entry.DotDotDotDot and Cross Cross Cross Cross take the named vector algebra operation on the top two stack entries. Both may be performed on real-only or complex vectors, or combinations thereof. DotDotDotDot will result in a scalar (real-only or complex, depending on the type of vector quantities operated upon).DivgDivgDivgDivg (Divergence) and Curl Curl Curl Curl take the appropriate operation on the top stack entry which may be a real-only or complex vector quantity. DivgDivgDivgDivgresults in a conversion of vector to scalar status.TangentTangentTangentTangent requires the top two stack entries to be a real-only Vector followed by a Line entity. This operation will take the component of the Vector data tangential to the line. The line may be a curve or other multipoint entity. The result of the operation will be a SclLinSclLinSclLinSclLin data entity.NormalNormalNormalNormal requires the top two stack entries to be a real-only Vector followed by a Surface entity. The operation takes the Normal component of the vector quantity to the specified surface. The surface may be non-planar. The result of the operation will be a SclSrfSclSrfSclSrfSclSrf data entity.Unit Unit Unit Unit VecVecVecVec > Tangent > Tangent > Tangent > Tangent and NormalNormalNormalNormal require geometry, not vector entries, and produce vector data as outputs. TangentTangentTangentTangent produces the unit vector data tangential to a Line, while NormalNormalNormalNormal produces unit vector data distributed on a Surface, similar to the two prior operations described.



3.1-15

Output Operation ColumnThe OutputOutputOutputOutput column contains operations which result in finalizing computations, exporting data from the Field Calculator or exporting from HFSS itself.

ValueValueValueValue applies the ‘value’ of the next-to-last stack entry (a field quantity) to the geometry of the top stack entry. For example, entries can be the vector Real(<Ex, Ey, Ez>) and a Surface entity, resulting in a a VecSrfVecSrfVecSrfVecSrfquantity. The second stack entry can be scalar or vector but must be real-only. The top stack entry may be any geometry (point, surface, line, or volume).

EvalEvalEvalEval is used to finalize computations, to convert the text-string indicating the computation being performed to an actual numerical value. Units will not be provided. The stack entry must be reduced to a single-value entry which can be a scalar, complex, or vector output.

WriteWriteWriteWrite………… will ‘write’ the top calculator stack entry to a file for use outside of HFSS. The filename will be prompted. Usable on any quantity.

ExportExportExportExport………… has suboptions of To FileTo FileTo FileTo File or On Grid.On Grid.On Grid.On Grid. This is used to export field values on a large set of points which are either on a pre-defined set of cartesian (x, y, z) points (To FileTo FileTo FileTo File) or on a regular grid of (x, y, z) points in response to a prompt (On GridOn GridOn GridOn Grid).

The format for the To FileTo FileTo FileTo File export requires a ‘points’ file be provided. The points file format is simply xxxxxxxxxxxxx

On GridOn GridOn GridOn Grid requests specification of the locations for export by start, stop, and step values in x, y, and z. For ‘planar’ exports use the same start and stop point in one of the three axes and any nonzero value for the step.



3.1-16

Graphing Calculator ResultsCalculator operations resulting in single-number outputs (per Design Instance) or in linear graph outputs can be plotted using the Report Editor, the same as plotting Matrix Results.

The basic procedure is:

1. Generate a computation in the Field Calculator and save it as a NamedNamedNamedNamedExpressionExpressionExpressionExpression

2. Draw a line in the design (model or non-model)

3. Use the Report Editor to plot the Named Expression on the Line

Create a Report of type FieldsFieldsFieldsFields

Note: Note: Note: Note: Computations which do not require a line will still need one to permit the Report Editor to activate the Calculator ExpressionsCalculator ExpressionsCalculator ExpressionsCalculator Expressions output Category. Without any Lines in the geometry, the TracesTracesTracesTraces window will not permit the setting of Category Category Category Category to view Calculator ExpressionsCalculator ExpressionsCalculator ExpressionsCalculator Expressions, even if the Field Calculator result being plotted is independent of ‘location’ (e.g. integral of some quantity throughout a volume).



3.1-17

Graphing Calculator Results, cont.In the TracesTracesTracesTraces dialog, define the Solution Context (including a Line, even if not needed). Following step-by-step instructions assume a Rectangular PlotRectangular PlotRectangular PlotRectangular Plotformat.

In the SweepsSweepsSweepsSweeps tab, define the appropriate variable and sweep values

For computations which use the defined Geometry Geometry Geometry Geometry Line, leave the Primary Sweep as NormalizedDistanceNormalizedDistanceNormalizedDistanceNormalizedDistance

Note:Note:Note:Note: NormalizedDistance allows graph overlaying even in cases where the line length changes, perhaps as a result of Parametric or Optimization variations (OptimetricsOptimetricsOptimetricsOptimetrics™)

For single-result quantities plotted vs. Phase or some Design Parameter, select the appropriate alternate Primary Sweep type

Leave the XXXX tab set to “Use Primary Sweep”

In the YYYY tab select Category Calculator ExpressionsCalculator ExpressionsCalculator ExpressionsCalculator Expressions. The user-created Named ExpressionNamed ExpressionNamed ExpressionNamed Expression will be at the bottom of the Quantity Quantity Quantity Quantity list beneath the auto-created Field Output types. In the Function column, select NoneNoneNoneNone

Note: Note: Note: Note: It is not required to select NoneNoneNoneNone for the Function column. It is assumed, however, that the Named Expression Named Expression Named Expression Named Expression already includes all operations desired upon it.

Click the Add TraceAdd TraceAdd TraceAdd Trace and then DoneDoneDoneDone to generate the Report.



3.1-18

Calculator Outputs as Field OverlaysAny Field Calculator stack entry saved as a Named ExpressionNamed ExpressionNamed ExpressionNamed Expression can be plotted as a Field OverlayField OverlayField OverlayField Overlay in the same manner as standard field outputs

Generate the expression in the calculator and save it by using the AddAddAddAdd…………button beneath the Named Expression Named Expression Named Expression Named Expression listing.

In the image below, the saved quantity is a scalar representing the value of the H field x-component only relative to a Phase function

Plot this to an overlay directly by selecting a geometry and making menu selection HFSS > Fields > HFSS > Fields > HFSS > Fields > HFSS > Fields > Plot Calculated ExpressionPlot Calculated ExpressionPlot Calculated ExpressionPlot Calculated Expression

Alternately, generate any standard Field Overlay as a placeholder. Use the Modify PlotModify PlotModify PlotModify Plot………… dialog to select Calculator Calculator Calculator Calculator for the plot Category and highlight the user expressionby name. (See following page

for example.)



3.1-19

Calculator Outputs as Field Overlays, cont.The example below shows a ‘standard’ Vector_H plot and the plot of the Named ExpressionNamed ExpressionNamed ExpressionNamed Expression ScalarY(AtPhase(<Hx, Hy, Hz>, Phase)).

Observe that the scalar custom plot has a data range of positive to negative values, as the computation did not take a MagMagMagMag or AbsAbsAbsAbs function as with standard magnitude output plots. Note also that its values match the locations where the Vector plot shows strong Y-directed Hlines.



3.1-20

Field Calculator “Cookbook”The following pages outline specific operations of potential interest in the Field Field Field Field CalculatorCalculatorCalculatorCalculator. They may be thought of as providing sample numerical recipes demonstrating example calculator usage. By no means do these examples represent the full limit of what the Field CalculatorField CalculatorField CalculatorField Calculator can be used for, however.

OrganizationSequences show one at a time, with the Stack contents displayed for each step.

Each sequence will be identified as to the type of output it produces:

Computations resulting in custom Field OverlaysField OverlaysField OverlaysField Overlays

Computations usable as Calculator ExpressionsCalculator ExpressionsCalculator ExpressionsCalculator Expressions in the ReportReportReportReport EditorEditorEditorEditor for line graph report outputs (variation in fields vs. position along a line entity)

Computations resulting in single-value (NumericNumericNumericNumeric) outputs

Note:Note:Note:Note: Numeric outputs can also be used in the Report EditorReport EditorReport EditorReport Editor, if the report requested is the plot of these outputs with respect to some changing design variable (geometry, frequency, material parameter, etc.)

An Example of the type of output each computation provides will be shown

Cautionary notes for each computation will be provided

Variations of each computation will be mentioned



3.1-21

Plotting Field Magnitude Normal to a Surface

Output Type: Field OverlayUsage Example: Displaying the coupling field through an aperture (e.g. in a Bethe hole coupler)

Steps:1. Select QuantityQuantityQuantityQuantity (e.g HHHH field)

2. Select FunctionFunctionFunctionFunction > ScalarScalarScalarScalar List > ”PhasePhasePhasePhase”

3. Select ComplexComplexComplexComplex > AtPhaseAtPhaseAtPhaseAtPhase

4. Select GeometryGeometryGeometryGeometry > SurfaceSurfaceSurfaceSurface List > Select an entity(e.g. Facelist1Facelist1Facelist1Facelist1)

5. Select Unit Unit Unit Unit VecVecVecVec > NormalNormalNormalNormal

6. Select DotDotDotDot

7. Click the AddAddAddAdd………… button to place this in the Named Expressions list, and give it an identifying name (e.g. H_norm_to_listH_norm_to_listH_norm_to_listH_norm_to_list)

8. Close Calculator.

9. Select face entity used in Step 4 above and plot using one of the methods described in Calculator Outputs as Field OverlaysCalculator Outputs as Field OverlaysCalculator Outputs as Field OverlaysCalculator Outputs as Field Overlays



3.1-22

Plotting Field Magnitude Normal to a Surface, cont.Example:

The image below left shows the complete vector H field on an aperture between two rectangular waveguides oriented at 90 degrees to oneanother. The image below right shows the magnitude of the surface normal component of this field only, as generated with the preceding calculator routine.

Cautions:If performed on surface entities created from sheet object(s) only, surface normals for all tetrahedral faces are not rigorously enforced (‘up’ vs. ‘down’confusion is possible on a per-triangle basis). Therefore an error message to that effect may appear. (In the above example image, a cylindrical virtual body was used to generate the circular end face used as the aperture.)Selecting a different ‘face’ entity than that used for generation of the surface normal in Step 5 may result in meaningless output

Variations:This same technique can be used with any surface quantity, be it a Facelist, Plane definition, or Sheet objectUse of the “Phase” function in Step 2 can be replaced with entry of a single NumberNumberNumberNumber phase value if the user does not wish to permit varying the output graphics relative to excitation phase.The field complex phasor can also be made a real-only vector by taking the Complex Magnitude or Phase, or Real or Imaginary parts to replace Steps 2 and 3.A similar computation can be performed by user entry of a numerical Vector (rather than obtaining a normal vector from a surface entity) to permit plotting only the field components normal to this vector anywhere in the model space. A user entered Number > VectorNumber > VectorNumber > VectorNumber > Vector replaces Steps 4 and 5.



3.1-23

Plotting Phase of a Field Component as a Graphical Overlay

Output Type: Field OverlayUsage Example: Displaying variations in propagation velocity across material or mode transitions.

Steps:1. Select QuantityQuantityQuantityQuantity (e.g EEEE field)

2. Select appropriate polarization, e.g. with ScalScalScalScal???? > ScalarZScalarZScalarZScalarZ (See CautionsCautionsCautionsCautions, below.)

3. Select ComplexComplexComplexComplex > CmplxPhaseCmplxPhaseCmplxPhaseCmplxPhase

4. [Option] Convert to degrees.

1. Select ConstantConstantConstantConstant > PiPiPiPi

2. Select “////” (Divide)

3. Select NumberNumberNumberNumber > ScalarScalarScalarScalar to enter “180180180180”

4. Select “****” (Multiply)

5. Click the AddAddAddAdd………… button to place this in the Named Expressions list, and give it an identifying name (e.g. Phase_Ez_degPhase_Ez_degPhase_Ez_degPhase_Ez_deg)


7. Select face entity used in Step 4 above and plot using one of the methods described in Calculator Outputs as Field OverlaysCalculator Outputs as Field OverlaysCalculator Outputs as Field OverlaysCalculator Outputs as Field Overlays



3.1-24

Plotting Phase of a Field Component as Overlay, cont.

Example:The images below are of a length of rectangular waveguide with a wedge-shaped insert of εr = 4 in the middle. The top image is the Vector E field distribution (with the broadwall in the XY plane, the fields are predominately Z directed) plotted on a cutplane down the waveguide center. The bottom image is the Phase of Ez on the same surface, clearly showing the different phase spacing in the higher dielectric material. Excitation is from the right.

Cautions:Remember the “phase” of a zero-magnitude vector is essentially indeterminate. So if you have a predominately single-component field and do not isolate the appropriate component before computing the phase (instead simply taking the ‘magnitude’ of a 3-component phase ‘vector’), you can expect a much noisier output. In the above example the X and Y directed components of the E field were discarded before taking the phase for this reason.

Expect also some ‘noise’ in the transition from -180 to +180 due to attempted interpolation of data that has been modulus-restricted. This effect is visible in the example above.

Variations:The same fundamental sequence could be used with different methods of isolating a polarization of interest for which the phase was desired, such as taking the DotDotDotDot product with a manually entered vector or a Unit Unit Unit Unit VecVecVecVec > NormalNormalNormalNormal.

For output in Radians simply omit the Step 4 marked [Optional].



3.1-25

Plotting Phase of a Field Component Tangential to a Path

Output Type: Report Editor PlotUsage Example: Displaying the Phase change along a periodic transmission medium, through a filter structure, or within a given path in a cavity for accelerator uses.

Steps:1. Select QuantityQuantityQuantityQuantity (e.g EEEE field)

2. Select GeometryGeometryGeometryGeometry > LineLineLineLine List > Select the line entity (e.g. Polyline2Polyline2Polyline2Polyline2)

3. Select Unit Unit Unit Unit VecVecVecVec > TangentTangentTangentTangent

4. Select ComplexComplexComplexComplex > CmplxRealCmplxRealCmplxRealCmplxReal(making the unit vector the ‘real’ part of a complex vector with imaginary and therefore phase of zero)

5. Select DotDotDotDot

6. Select ComplexComplexComplexComplex > CmplxPhaseCmplxPhaseCmplxPhaseCmplxPhaseto extract the phase of the complex Dot product

7. Use AddAddAddAdd………….... to add this quantity to the Named Expressions list, e.g. as “Phase_E_tanPhase_E_tanPhase_E_tanPhase_E_tan”


9. Use the Report EditorReport EditorReport EditorReport Editor to request a report of type “FieldsFieldsFieldsFields”, selecting the line used in Step 2 above and selecting the quantity to plot from the Calculator Calculator Calculator Calculator ExpressionsExpressionsExpressionsExpressions listing



3.1-26

Plotting Phase of a Field Component Tangential to a Path, cont.Example:

A curved length of periodically changing circular waveguide is modeled below, with a polyline drawn down the center of the waveguide along which the tangential field phase is plotted. Note that for plots along lines the horizontal axis is “NormalizedLength” so if geometric variations are being analyzed with OptimetricsOptimetricsOptimetricsOptimetrics™ the output can be extracted and overlaid for all variations.

Cautions:Using a different line entity to produce the Report than was used in the creation of the Named Expression will result in either garbage outputs or an error messageSmoothing of the Field data prior to performing further computations in the calculator can result in cleaner traces, as can converging beyond simply that required for good S-parameter outputs..

Variations:The phase can also be generated in Degrees by adding linear multiplication by NumberNumberNumberNumber > “180180180180” and division by ConstantConstantConstantConstant > PiPiPiPi, as was done in the prior example.

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