A perfect electric conductor (PEC) boundary (also called Electric Wall) is a surface on which the tangential component of the vector electric field (_t) vanishes. Use boundary (DOF) constraints to define PEC boundary conditions on the solid model or finite element model entities. You can remove a neighboring conductor from the model and replace it with a PEC boundary condition, if the losses of the metallic conductor can be ignored. In many applications, a thin metallic object (for example, a metallic strip of a microstrip structure) simplifies to an infinitesimally thin metallic sheet with a PEC boundary condition.

To reduce your model size, you can also apply PEC boundary conditions to symmetry planes that have a zero tangential component of the vector electric field. You must know the electric field distribution before you can take advantage of the symmetry.

To specify PEC boundary conditions, you can use the DL or DA command to set the AX DOFs to zero on the surface of the model or you can use the D command to set the AX DOFs to zero on the nodes of the finite element model. Alternatively, you can specify a PEC boundary condition from the GUI, which will impose AX = 0.

A perfect magnetic conductor (PMC) boundary (also called Magnetic Wall) is a surface on which the tangential component of the vector magnetic field (_t) vanishes. You can remove a highly permeable magnetic medium from the model and replace it with a PMC, if the losses of the magnetic medium can be ignored.

To reduce your model size, you can also apply PMC boundary conditions to symmetry planes that have a zero tangential component of the vector magnetic field. You must know the magnetic field distribution before you can take advantage of the symmetry.

Table 4.4: "Surface Impedance Boundary Conditions" shows surface impedance boundary conditions available for a high-frequency electromagnetic analysis. You can use surface impedance boundary conditions to approximate a radiation boundary and an electrically small lossy/dielectric layer where a very fine mesh would usually be required. See the detailed explanations of these impedance boundary conditions below.

Table 4.4  Surface Impedance Boundary Conditions

Boundary Condition	SIBC Approximations	Equation [1] [2]	SF or SFA Command Label
Far-Field Radiation Boundary			INF
Air-dielectric Interface			IMPD
Dielectric Coating on PEC			IMPD
Non-perfect Electric Conductor			SHLD

You can apply surface impedance to the nodes of the finite element model or the areas of a solid model using the following commands and GUI menu paths with Lab = INF, IMPD, or SHLD:

For the impedance surface load label (Lab = IMPD), VALUE and VALUE2 are the real and imaginary components of the impedance, respectively.

When explicit values of impedance are not known or when a harmonic solution over a wide frequency range is required, it is more convenient to specify the surface impedance in terms of the conductivity (COND) and relative permeability (MUR) of the non-perfect conductor. You can apply surface shielding properties using one of the following commands or menu paths (Lab = SHLD):

You can flag any exterior boundary and assign it as an infinite boundary using one of the following commands or menu paths (Lab = INF):

For modeling a far-field radiating boundary, you need to flag the exterior nodes or exterior areas where the propagating wave is treated as a plane wave. When such an infinite far-field radiation boundary is close to the objects and the scattering wave is not a plane wave or a spherical wave, numerical error will occur. Using perfectly matched layers (PML) is a more accurate method for modeling the far-field radiation boundary (see the next section).

Applying boundary conditions to the solid model offers the advantage that they are independent of the underlying finite element mesh. This allows you to make mesh modifications without having to reapply the loads.

The purpose of an absorbing boundary condition is to absorb the outgoing electromagnetic wave so that there are no reflections back into the FEA computational domain. Perfectly matched layers (PML) are the layers of electromagnetic wave absorbing elements designed for the mesh truncation of an open FEA domain in a harmonic or modal analysis. It is an artificial anisotropic material that is transparent and heavily lossy to incoming electromagnetic waves. PML can reduce the size of the computational domain significantly with very small numerical reflections. A PML region is backed by a PEC boundary condition.

If the electromagnetic wave needs to be absorbed in only one direction, as in the case of a traditional waveguide port, you construct a 1-D PML region in the global Cartesian coordinate system or a local Cartesian coordinate system as shown in the following figure.

A 3-D PML region consists of layers of elements extending from the interior volume towards the open domain as shown in the following figure. You construct a block about the origin of the global Cartesian coordinate system or a local Cartesian coordinate system. You align the edges of the 3-D PML region with the axes of the Cartesian coordinate system.

To optimize the absorbing efficiency of the PML, you must properly construct the PML regions and appropriately choose the following PML parameters:

Use the ET command to define PML elements. Set KEYOPT(4) = 1 for HF119 or HF120 and then mesh the PML region. Use any element shape to mesh the PML block.

More than one 1-D PML region may exist in a finite element model. The element coordinate system (ESYS command) uniquely identifies each PML region. Use the LOCAL command to define a Cartesian coordinate system, and then assign this coordinate system to the elements in the PML region (VATT or ESYS command prior to meshing or the EMODIF command after meshing).

The attenuation from the PML interface to the PML exterior surface is a parabolic distribution that minimizes numerical reflections from the PML elements. The numerical reflections are caused by the discretization of a continuous distribution of material from element to element. To obtain satisfactory numerical accuracy, you should use at least four layers of PML elements. At lower operating frequencies (< 1 GHz), the PML thickness may need to be greater than a quarter wavelength.

Since PML acts as an infinite open domain, any boundary conditions and material properties need to be carried over into the PML region. Material properties such as permittivity, permeability, and conductivity in the PML region must be the same as the adjacent interior region. For example, in the model of a microstrip structure with PML regions, you should carry over the dielectric and air properties to the adjacent PML layers (see Figure 4.6: "Microstrip Structure with PML Regions").

A PEC boundary condition must back all exterior surfaces of the PML region, except for symmetric surfaces with a PMC boundary condition. To specify a PEC boundary condition on the outer surfaces of the PML region, use the D command for a finite element model or the DL or DA command for a solid model. PEC or PMC boundary conditions can be applied on the symmetric surfaces of a PML region. For a high frequency structure that has a matching load, rather than an open domain, the PML region plays the role of the matching load.

You should include some buffer elements (at least four) between the PML region and a discontinuity or object in the interior domain. The PML will then absorb the outgoing wave effectively and minimize numerical reflections.

Since PML is an artificial anisotropic material, excitation sources are prohibited in the PML region.

The attenuation of the electromagnetic wave in a PML region may be controlled. You can specify the normal reflection coefficient (harmonic) for propagating waves by using one of the following:

The direction designations are Xminus, Yminus, Zminus, Xplus, Yplus, and Zplus. The minus and plus refer to the negative and positive directions along the Cartesian coordinate axes, respectively. If the propagating wave is only absorbed in one direction, you define a 1-D PML region (Lab = ONE). You only need to specify the Xminus argument for a 1-D PML region. For a 3-D PML region, you can define a different normal reflection coefficient for each direction (Xminus, Yminus, Zminus, Xplus, Yplus, and Zplus). The normal reflection coefficients default to 1.E-3 (-60 dB) for a harmonic analysis. Normal reflection coefficients should be less than 1.0. If only a few PML layers are used (for example, four layers), specifying a very small normal reflection coefficient (such as -100 dB) may lead to significant numerical reflection. Increase the number of layers before specifying a very small reflection coefficient. Repeat the PMLOPT command for additional PML regions. Refer to the PMLOPT and PMLSIZE commands in the Commands Reference and Perfectly Matched Layers in the Theory Reference for ANSYS and ANSYS Workbench for more information.

The number of PML layers dominates the absorbing efficiency of PML. However, an excessive number of PML elements will significantly increase the computational requirements. The number of PML layers (n) for acceptable numerical accuracy can be determined by one of the following:

where: DMIN, DMAX, and THICK are shown in the following figure.

If n is less than 5, the number of layers is set to 5 in order to reduce the numerical reflection. If n is greater than 20, the number of layers is set to 20 to avoid having an excessive number of PML elements.

The PMLSIZE macro must be issued before you mesh your model. If the thickness of the PML region is known, it specifies an element edge length. If the thickness of the PML region is unknown, it species the number of layers (n).

Refer to the PMLOPT and PMLSIZE commands in the Commands Reference and Perfectly Matched Layers in the Theory Reference for ANSYS and ANSYS Workbench for more information.

Periodic boundary conditions enable you to model time-harmonic electromagnetic scattering, radiation, and absorption characteristics of doubly periodic array structures. A periodic array is assumed to extend infinitely as shown in the following figure. The direction normal to the periodic plane is selected as the Z direction of the global Cartesian coordinate system.

For scattering problems, an arbitrarily polarized plane wave impinges on the periodic structure at some arbitrary oblique arrival angle with respect to the Z direction. The reflection, transmission, absorption, and polarization characteristics of the periodic structure are simulated. For most scattering problems, the periodic structure will not include internal excitation sources. For radiation problems, an electromagnetic current source or other excitation source will exist inside the periodic structure.

The infinite extension assumption allows you to investigate a single periodic unit cell as shown in the following figure. The electromagnetic fields on the cell sidewalls exhibit a dependency described by the theorem of Floquet. Refer to High-Frequency Electromagnetic Field Simulation in the Theory Reference for ANSYS and ANSYS Workbench for more information on this theorem.

The cell sidewalls are assigned as master and slave boundaries, and they are bound together by the periodic boundary conditions. The electromagnetic wave in the periodic volume radiates into infinity or is absorbed in the z direction. You must use PML to truncate the open space because Floquet's electromagnetic wave propagates in the periodic structure. You should also use PML or a matched impedance port to terminate a traditional waveguide port, if it exists inside the periodic structure.

To impose periodic boundary conditions, the mesh pattern on the master boundary must be identical to the mesh pattern on the slave boundary. You must mesh the master boundary using the AMESH command. You then use the AGEN or MSHCOPY command to generate the mesh on the slave boundary prior to meshing the cell volume. Matching the nodes on the master boundary to the nodes on the slave boundary imposes the periodic boundary conditions. You use the CPCYC or CP command to generate the coupled nodes.

As an example, the following command input listing creates periodic boundary conditions for a unit cell of a infinite rectangular waveguide periodic array:

/batch,list
/title, S11 of JRM Array, E plane scan, 9.25 GHz
/com, Problem: Compute S11 of JRM Array for E-Plane scan at 9.25 GHz
/com, Numerical Model: Waveguide + Radiation Space + PML
/com,                  Waveguide: 0.9"x0.4"x0.75"
/com,                  Radiation Space: 1.0"x0.5"x0.75"
/com,                  PML: 1.0"x0.5"x0.75"
/com,
/nopr
/prep7
freq=9.25e9
lamda=3.e8/freq
scal=25.4e-3
a1=scal*0.9/2.
b1=scal*0.4/2.
a2=scal*1.0/2.
b2=scal*0.5/2
c1=scal*0.75
c2=scal*0.5
c3=scal*0.75
c4=scal*1.5
rmin=c3
rmax=sqrt(2.)*c3
dpml=c4-c3

h=lamda/5
tiny=1.e-5
ang=30
angmax=60.

et,11,200,5
et,1,119,1,,,0
et,2,119,1,,,1                              ! cycle element
mp,murx,1,1.
mp,perx,1,1.

local,11
wpcsys,,11
block,-a1,a1,-b1,b1,0,-c1
!block,-a2,a2,-b2,b2,0,c2
block,-a2,a2,-b2,b2,0,c3
block,-a2,a2,-b2,b2,c3,c4
vglue,all
type,11
esize,h
asel,s,loc,x,-a2
asel,a,loc,y,-b2
asel,r,loc,z,0,c3
amesh,all
PMLSIZE,9e9,9.5e9,rmin,rmax,dpml,angmax
asel,s,loc,x,-a2
asel,a,loc,y,-b2
asel,r,loc,z,c3,c4
amesh,all
alls
asel,s,loc,x,-a2
agen,2,all,,,2*a2
asel,s,loc,y,-b2
agen,2,all,,,0,2*b2
alls
nummrg,all

mat,1
type,1                                       ! create normal element
vsel,s,loc,z,-c1,c3
esize,h
vmesh,all
type,2                                       ! create PML element
PMLSIZE,9e9,9.5e9,rmin,rmax,dpml,angmax
vsel,s,loc,z,c3,c4
vmesh,all
alls
aclear,all
etdel,11
alls

nsel,s,loc,x,-a2
nsel,a,loc,x,a2
cpcyc,ax,,,2*a2,0,0,1
nsel,s,loc,y,-b2
nsel,a,loc,y,b2
cpcyc,ax,,,0,2*b2,0,1
alls
finish

The finite element models created are shown in the following figure.

The SPSCAN macro can perform a harmonic analysis of the unit cell and extract the S-parameter at the port over a specified scanning angle range. You can then use the PLSYZ command to plot the S-parameter over the scanning angle range.

You can use the HFPA command to specify the scan angle for a harmonic analysis. In POST1, you can issue the HFARRAY command to define the antenna array. You can then use PRHFFAR or PLHFFAR to obtain the radiation pattern and the directive gain of the phased array antenna, based on the solution for the unit cell.

Excitation port refers to a plane where an excitation source is defined by the HFPORT command. Excitation ports include traditional waveguide ports, arbitrary modal ports, uniform lumped gap ports, and plane wave ports. The port plane can be an interior surface that is inside the computational domain or an exterior surface that truncates the computational domain. For traditional waveguides, you may launch a modal electromagnetic field for a coaxial waveguide, rectangular waveguide, circular waveguide or parallel plate waveguide. A waveguide port can be either interior or exterior with respect to the matching condition. A modal port automatically uses the electromagnetic field of an ANSYS Emag - High Frequency modal analysis for the excitation. The modal port can be either an interior port or an exterior port. The lumped gap port is a simplified interior port with an assumed uniform electromagnetic field. A plane wave port is an interior port that is only used for a scattering analysis of a periodic structure.

Specifying the excitation port option is a two-step process. First you select the solid model area (or nodes) to define the port location and assign a port number. The port number assigned must be between 1 and 50. For an exterior port, you choose the areas or nodes and then use one of the following to assign a port number and apply a surface load:

For an interior port, you would use one of the following to assign a port number and apply a body load:

Next, you need to identify the port type: coaxial waveguide, rectangular waveguide, circular waveguide, parallel-plate waveguide, modal, lumped gap, or plane wave. You also need to specify the attributes of the port (geometric properties and excitation conditions). You may define geometric properties of a waveguide with respect to a local coordinate system. For a waveguide port, the origin of the local coordinate system must be centered about the face of the port without considering symmetry. For waveguide, modal, and lumped gap ports, the z direction must correspond with the wave propagation direction. For a plane wave port, the z direction of either the global Cartesian or a local coordinate system must be perpendicular to the periodic plane (see Figure 4.11: "Arbitrary Infinite Periodic Structure").

To define a local coordinate system, use one of the following:

To identify the port, use the command or menu path shown below.

The Porttype argument defines the port type. The Opt1 argument defines the mode type for a waveguide port or the required mode number for a modal port. To view the electromagnetic field at a modal port, issue /PSF for an exterior port or /PBF for an interior port after you have issued HFMODPRT or SPSWP.

The VAL1 - VAL8 arguments specify inputs such as geometric properties and excitation conditions. See the HFPORT command for additional information.

As shown in the following figure, a port may exist on the exterior surface or interior surface of a modeled domain. An exterior port allows you to launch an incident wave and the port absorbs the reflected wave for the launched mode. An interior port allows you to launch a bidirectional incident wave. All reflected modes will pass through the interior port and will be absorbed by a PML absorbing boundary condition if the interior port is assigned as a matched port. The Opt2 argument controls the ability to launch a wave and to pass reflected waves.

When launching a fundamental mode using the exterior port option (Opt2 = EXT), you should locate the port at least half of a wavelength away from any discontinuity or structure to ensure that other reflected higher order modes are damped out. You may extract S-parameters at this port for the single mode.

An interior port (Opt2 = INT) has the advantage that it supports launching of a wave and passing of all reflected waves. Hence, you can place an interior port very close to a structure or discontinuity with no loss in accuracy. An interior port can only be defined in the normal element region (KEYOPT(4) = 0), and not at the interface between the normal region and the PML region or in the PML region.

A PML region can be located behind the interior port to absorb the reflected and incident waves as shown in the following figure. If higher order modes are a concern, you can use interior ports and PML absorption. The S-parameters of the specified single mode can be extracted at the ports.

The plane wave source port (Porttype = PLAN, Opt2 = SOFT) launches a plane wave for a scattering analysis of a periodic structure. Here, you need to define the coupled master and slave surfaces of the solid model or nodes of the finite element model. You must use PML to truncate the open space because Floquet's electromagnetic wave propagates in the periodic structure. The plan wave port must be an interior soft port as illustrated in the following figure. For information on how to define a plane wave, see Plane Wave Source.

The HFPORT arguments VAL1 - VAL8 define the other port inputs.

You can use a current source to excite electromagnetic fields in a high-frequency structure. Current density is input by defining up to three components of a vector quantity (JSX, JSY, and JSZ) and a phase angle. If the current density vector is not aligned with the global Cartesian coordinate system, you may take advantage of either a rotated nodal coordinate system (NROTAT command) or an element coordinate system (ESYS command). If current density is specified at nodes (BF command) or transferred to nodes from a solid model entity (BFA, BFL, or BFK), you can use a rotated nodal coordinate system to align the current density vector. If current density is specified on elements (BFE command) or transferred to elements from a solid model volume (BFV command), you can use an element coordinate system to align the current density vector. To view the current density vectors, use the /PBC,JS,,2 command option.

To define a current density volume source, use one of the following:

For a surface current source, you should specify the current density on at least three nodes on an element face. The surface current source must coincide with the element faces. You can define a current density surface source using one of the following:

For a line current source, you should specify the current density at two nodes connected by an element edge. The line current source must coincide with the element edges. To define a current density line source, use one of the following:

A point current source must be at the element nodes. You can define a current density point source using one of the following:

In general, a current density source launches the electromagnetic wave in all directions. For a propagating or resonant system, you can use a current density source to excite the propagating modes or resonant modes of the structure. Only proper modes can exist in the structure. In order to reduce the parasitic modes, you should choose the distribution of the current density based on the electric field distribution of the excited mode.

The following guidelines apply when a current density source is used to excite a high-frequency propagating structure:

You can also define a radiation source using a current density distribution in terms of a conducting current distribution on the radiator. For example, you can choose a sinusoidal current distribution to model a very thin half-wavelength dipole antenna.

A incident plane wave source is available. You can define a plane wave by component values of an electric polarization vector and the incident angles in a global Cartesian coordinate system:

If a plane wave port is assigned, you can define a plane wave in a local Cartesian coordinate system.

Define a external plane wave (a free-space harmonic incident plane electromagnetic wave) using one of the following:

You need to specify the following plane wave attributes:

When used together with an unbounded domain model (using PML as an absorber), the scattering effects of an incident field on a body can be simulated using the scattering analysis command HFSCAT.

You cannot use the PLWAVE command to define an incident plane wave for a scattering analysis of a periodic structure. Here, a plane wave port must be specified using the HFPORT command. The scattering analysis command HFSCAT is not valid because a total field formulation is used for the scattering analysis of a periodic structure.

You can apply a fixed magnetic field (hard) excitation source on an exterior surface using one of the following:

You should impose a hard surface magnetic field excitation source on the exterior nodes of a computational domain as shown in Figure 4.18: "Exterior Hard Surface Magnetic Field Excitation". Specify a soft excitation source if the surface magnetic field source is on the interior nodes of a computational domain as shown in Figure 4.19: "Soft Interior Surface Magnetic Field Excitation".

For a surface magnetic field source, you should specify the magnetic field at three nodes on an element face, at least. The surface magnetic field source must coincide with the element faces. The magnetic field is input by defining up to three components of a vector quantity (HX, HY, HZ) and a phase angle. If the magnetic field vector does not align with the global Cartesian coordinate system, you may take advantage of a rotated nodal coordinate system (NROTAT command). The magnetic field specified at nodes (BF command) or transferred to nodes from a solid model entity (BFA, BFL, or BFK) may use a rotated nodal coordinate system to align the magnetic field vector. To view the magnetic field vectors, use the /PBC,H,,2 command option.

You can also apply a soft excitation source as shown in the following figure. It allows reflection waves to go through the source surface without any reflection. To do so, you define an interior surface magnetic field source using the BF or BFA command. The HF119 or HF120 elements in the region that the reflection wave propagates into must be scattering elements (KEYOPT(4) = 2). However, you still define the elements in the PML region by a KEYOPT(4) = 1 setting.

You can apply a fixed electric field source on an external surface using one of the following:

For a line electric field source, you should specify the electric field at two nodes connected by an element edge. For a surface electric field source, you should at least specify the electric field at three nodes on an element face. The surface electric field source must coincide with the element faces. The line electric field source must coincide with the element edges.

The electric field is input by defining up to three components of a vector quantity (EFX, EFY, and EFZ) and a phase angle. If the electric field vector does not align with the global Cartesian coordinate system, you may take advantage of a rotated nodal coordinate system (NROTAT command). The electric field specified at nodes (BF command) or transferred to nodes from a solid model entity (BFA, BFL, or BFK) may use a rotated nodal coordinate system to align the electric field vector. To view the electric field vectors, use the /PBC,EF,,2 command option.

The electric field source is a fixed hard excitation source, which is equivalent to an unmatched voltage source. The AX DOF updates automatically after the excitation electric field is imposed on the element nodes.

Only the first order HF119 and HF120 elements are available for this excitation.

The near and far fields beyond the FEA domain are of importance in high-frequency electromagnetics. Many design parameters (for example, radar cross-section, antenna pattern, directive gain, and radiation power) are based on the far field values.

The surface equivalence principle enables you to calculate the electromagnetic fields beyond the FEA domain. It states that the electromagnetic field exterior to a given surface can be exactly represented by an equivalent electric and magnetic current placed on that surface and allowed to radiate into the region external to that surface. Refer to the Theory Reference for ANSYS and ANSYS Workbench for more information on this principle.

For problems requiring near-field and far-field computations (for example, antenna parameters, radar cross section, and electromagnetic field values) you must first define an equivalent source surface in the preprocessor as shown in the following figure. The surface must enclose the radiator or scatter, except for symmetry planes. The equivalent electric and magnetic current are computed and stored on the surface. This enables you to quickly calculate near-field and far-field information in the postprocessor.

For radiation and scattering problems, you must use an absorbing boundary condition, either PML or far-field radiation boundary (INF). Since the ideal radiation or scattering plane wave leads to a very large spherical computational domain for an acceptable numerical accuracy, you should use PML to truncate the computational domain. The equivalent source surface should be between the radiator or scatter and the PML region. In principle, the equivalent source surface should be close to the radiator or scatter to obtain good near-field and far-field results. However, because of the lower order element discretization of the computational domain and the numerical integration on the equivalent source surface, you should use half a wavelength or greater separation between the radiator or scatter and the equivalent source surface. You should also place some buffer elements between the equivalent source surface and the PML region.

You define an equivalent source surface using a surface boundary condition with the Maxwell flag MXWF. Exercise care when applying a MXWF surface load to define an equivalent source surface. Do not flag any surface on a symmetry plane (for example, the y-z and x-z planes in Figure 4.20: "Equivalent Source Surface"). The following is one way to flag an equivalent source surface:

The following is another way you can flag an equivalent source surface:

You do not need to define an equivalent source surface when performing a scattering analysis of a periodic structure. The interior plane wave port surface serves as the equivalent source surface.

You can simplify your model and reduce the number of DOFs if fringe effects at discontinuities can be ignored or a passive device can be treated as a lumped circuit. As shown in the following figure, six types of lumped circuits are available.

To utilize this simplification, you apply lumped circuit loads to the mid-nodes of element edges using the BF command with Lab = LUMP. ANSYS Emag - High Frequency imposes the lumped circuit loads on the end nodes of the element edges as well as the mid-nodes.

When applying lumped circuit loads to multiple edges, you must generate equivalent circuit loads whose sum is equal to the given lumped circuit load. For example, consider the 2-port lumped network shown in the following figure.

The following figure shows the equivalent circuit model and impedance values for a FEA mesh with the impedance load shown in Figure 4.22: "2-Port Lumped Network". The 2Z/3 loads are applied to the mid-nodes of the corresponding edges.