single-element radiator analysis...

Single‐Element Radiator Analysis Validation

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CHAPTER 5

SINGLE-ELEMENT RADIATOR ANALYSIS VALIDATION

The problem formulation and analysis of the proposed radiator based on the Method-

of-Moments developed in the preceding chapters has been utilized to arrive at a

prototype single-element radiator design for operating at C-Band. In the last chapter,

the computer program based on this formulation has been utilized for a series of

parametric studies to assess the effect of varying the different design parameters

involved. Some of the parameter values obtained ab initio using previously published

guidelines or empirical data have been refined using the present analysis algorithms to

yield a more optimum radiator design. The radiator input characteristics as well as the

radiation patterns have been computed for the selected parameter set of the prototype.

In this chapter, we have attempted to validate the developed analysis using an

alternate, commercially-proven e.m. analysis tool (Ansoft® HFSS®.) In this process,

the relative merits / demerits of the present analysis are brought out vis-à-vis this

commercial tool. Also, further analysis has been carried out on the prototype radiator

to arrive at a design that may be fabricated for experimental purposes subsequently.

This chapter is organized as follows. For the sake of completeness, a brief

introduction is first given to FEM which is its underlying analytical method and to

Ansoft® HFSS®, the proven commercial e.m.-analysis tool used for the analysis

validation. Next we consider an FEM analysis of the proposed waveguide shunt-slot

fed microstrip patch antenna radiator using this simulation tool. A description is given

of the HFSS®-simulation model used for the analysis of the C-Band prototype,

highlighting some features that are especially incorporated to ensure an accurate


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prediction by HFSS®. This is followed by simulated results obtained from the

analysis. These predictions are compared to the MOM-simulations of Chapter 4. In

addition to the baseline simulation model (Case-1), two other cases that were

analyzed are also described. Case-2 uses an extended ground plane to assess the

impact of its size on the radiator performance. Finally, Case-3 includes the effects of

radiation from fold-over currents towards the rear of the ground plane, particularly on

the backlobe. Finally, the requirements of the HFSS®-analysis w.r.t. memory and

execution time are compared to the developed M-o-M-based theoretical analysis and

computer program for the present geometry.

5.1 A Brief Introduction to FEM and Ansoft® HFSS®.

The Finite Element Method (FEM) is one of the two key frequency-domain

computational electromagnetic techniques, the other being the Method of Moments

(M-o-M.) FEM is one of the most robust formulations suited for the analysis of

arbitrarily-shaped electromagnetic structures both in enclosed or open (radiating)

configurations. This method solves Maxwell’s equations by solving the vector wave

equation. The containing structures for the field may be perfectly conducting or lossy

and the intervening medium anisotropic and/or inhomogeneous with regard to both

permittivity and permeability. The vector wave equation is a second-order partial

differential equation for which the solution yields the field inside the problem space.

It is customary to specify a weak form of this equation and to either minimize a

functional or to apply the Rayleigh-Ritz method [50]. In the second case, a vector

function is used as a testing function (usually local.) The scalar expression obtained is

integrated over the testing function domain. Boundary conditions may be specified for

the problem; the source is also treated as a particular case of this.


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A basic feature of FEM is the segmentation of the problem space into small elements

– hence the term finite element. For a one-dimensional problem like a wire or a

stratified medium, these elements are linear e.g. straight-line segments between node

points. For two-dimensional problems, these would be rectangles, parallelograms or

triangles depending on the geometry to be meshed. Finally, for a three-dimensional

problem; the brick (cuboid), the right prism or the tetrahedron are most popular. Jin

[51] has addressed these three types of FEM formulations in detail, particularly

addressing the optimum aspect ratios of these geometries. For the interested reader, a

large number of references may be found in [50, 51] or on-line. Of the three solid

elements mentioned above, the tetrahedron is the most popular meshing approach

because of its flexibility and ability to approximate arbitrarily-shaped geometries.

The simplest and most widely-employed expansion functions are the lowest mixed-

order edge elements. Higher-order expansion functions and hierarchical functions

have also been used. Apart from the choice of an expansion function, the versatility of

the FEM depends strongly on a robust mesh generator. It is seen that a great amount

of effort has been put by researchers into the development of an efficient meshing

algorithm. The efficacy of the mesh determines the accuracy of the final solution and

the number and type of mesh refinements needed to achieve convergence.

The termination condition of the mesh is another significant aspect, particularly for

radiation-type of problems. Since the entire problem space is meshed in this

formulation, the termination condition limits the problem- (and thus the matrix-) size.

Three types mesh termination conditions are popular: a) Absorbing Boundary

Conditions (ABCs); b) Perfectly Matched Layer (PML); and c) Boundary Integral

(BI). ABCs are the most convenient boundary termination owing to their simplicity.


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However, for radiation problems, the boundary location must be defined at a certain

(relatively large) distance from the radiating structures. This ensures that the presence

of the ABC does not perturb the near-field and coupled field regions of the actual

problem and also depends on the angle of incidence. The PML requires much lesser

stand-off distance from the actual structure being analyzed. It is a local truncation

technique but needs user-defined parameters to be specified. The BI method is a

global truncation by contrast. It needs no stand-off distance but the obtained matrix is

partially full leading to larger memory requirements and execution time.

The strength of the FEM lies in the problem matrix being sparse. Due to this, the

solution is obtained relatively fast even though the mesh discretization is fine. In

commercial programs, as in the Ansoft® HFSS®, a feature of adaptive meshing is

implemented that makes the method highly versatile. In regions of fast field variation,

the analyzer iteratively introduces finer meshing to better approximate the field

behaviour. Thus, at the expense of minimum incremental matrix elements, a more

accurate solution may be obtained.

With this, the key aspects of the FEM method have been introduced. Features specific

to HFSS® will be briefly addressed in the following section.

5.1.1 The Ansoft® HFSS® Electromagnetic Analysis Software

The HFSS® module from Ansoft® is an FEM-based full-wave electromagnetic

simulator for analyzing passive devices of arbitrary three-dimensional geometry [52].

The basic mesh element used by HFSS® is the tetrahedron. The type of elements used

is termed tangential vector finite elements. Adaptive meshing, as mentioned earlier,


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allows this simulator to obtain fast, accurate simulations for the specified geometry.

The program also allows mesh seeding. This term means that on selected geometries,

a user-specified density of meshing may be applied even before the first iterative

solution is available. Such a requirement is determined by the user based on an a

priori knowledge of fast field variation across certain types of regions e.g. dielectrics

or thin slots. This expedient can cut down a number of iterations that may otherwise

be needed to reach the correct level of mesh refinement solely by adaptive meshing.

After evaluating fields at the tetrahedral nodes, HFSS® computes the field variation at

all points within the problem geometry. The program uses this information to

compute the device network parameters. The solver integrates the far-field

contributions of the field computed across the outer surface of the ABCs (volume

enclosing the problem) to obtain this. The computed fields can be post-processed to

obtain parameters like directivity, gain, etc. also.

Other features of HFSS® relevant for the problem under analysis will be addressed in

the subsequent sections of this chapter (for a single-element radiator.) For more

details of HFSS®, the User’s Guide [52] may be referred.

5.2 Analysis of the Proposed Single-Element Waveguide Shunt-Slot Fed Microstrip Patch Radiator using Ansoft® HFSS® (Case-1)

The C-Band prototype microstrip radiator described in the previous chapter is

analyzed using the FEM-based solver, Ansoft® HFSS®. This is expected to serve as an

alternate analysis for the validation of the results obtained from the M-o-M

formulation developed in this thesis. In this section we will address the baseline case

(Case-1) as per the final optimized parameter set given in Section 4.9.3 (simulated

input parameters as in Fig. 4.12.) and which uses a reduced ground plane of size


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100mm X 100mm. By contrast, the M-o-M formulation inherently assumes an infinite

ground in the basic Green’s function derivation (see Chapter 2.) The other features of

the HFSS®-simulation model will be described below, highlighting the aspects

necessary to obtain a convergent solution with reasonable memory and execution-time

requirements. This will be followed by sample simulated results.

5.2.1 The HFSS®-Simulation Model for Baseline (Case-1) Antenna Element

The simulation model of the prototype single-element microstrip patch radiator for the

baseline case is illustrated in Fig. 5.1. Both the feeding waveguide and the dielectric

substrate of the patch radiator are modelled as hollow Box entities. The coupling slot

and patch are modelled as Sheet objects. The slot length is parallel to the waveguide

axis and it is imparted a transverse offset as per the design. The coordinate system is

centred at the slot and the patch is placed above it to the other side of the substrate.

The boundary condition for radiation pattern computation is chosen as ABC; also

modelled as a Box entity.

The material definition for the waveguide and ABC is specified as vacuum from the

HFSS® system library. This has εr = μr = 1 but no other loss factors and is equivalent

to free space for computational purposes. For the substrate, the particular material

chosen (see Section 4.1.3) is available in the system library as Rogers RO3003 (tm)

with the correct parameters. The patch is assigned Perfect E and the slot Perfect H.

All five sides of the ABC (apart from the base under substrate) are defined as a

Radiation Boundary. The four long faces of the waveguide are assigned PerfE. Since

the substrate is completely enclosed in the ABC box volume, no specific boundary


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Fig. 5.1: Ansoft® HFSS® Simulation Model of Proposed Single-Element Radiator (Case-1)

ABC

Patch

Slot

Waveguide

Substrate

Fig. 5.2: Zoomed View near Coupling Region showing Shunt Slot under Patch Radiator


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assignment is needed. It is important to observe the order of boundary definition.

Previously defined boundaries are overwritten by the later ones e.g. the slot definition

must be the last one made to ensure the waveguide wall does not “seal off” the

coupling region. A boundary display feature allows verification of the boundaries

before proceeding further. The two ends of the waveguide are defined as Excitations

and the type is WavePort.

An initial execution of the defined geometry led to a problem. The solution

converged within four passes with a very good return loss. However, the field plots

indicated a very low coupling. Upon examining the solution in detail, we found that

the slot had only two triangle elements at convergence; the patch only a few. Since the

absence of a coupling aperture in the top-wall turns the problem into a small length of

waveguide, the solver found it convenient to short out the slot and achieve

convergence quickly.

Hence, it became necessary to apply Mesh Operations which allows selected entities

of the problem definition to be “seeded” before the solver is invoked. A tetrahedron

length of 5mm was specified on the substrate. The patch and slot being planar entities,

triangle size was specified – as 1.5mm and 0.25mm respectively. Fig. 5.3 shows the

mesh plots for these three entities upon convergence of the problem. We observe that

the solver adapts to a finer mesh in the part of the substrate underlying the patch

radiator. The mesh on the slot is very dense, justifying the fine discretization specified

while seeding.

An adaptive solution was specified at 5.8 GHz which is the resonant frequency

observed in Section 4.6.2 for the identical parameter set.


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(a)

Fig. 5.3: Mesh Plots on Selected Entities at Convergence a) Substrate; b) Patch; and c) Slot

(b)

(c)


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A frequency sweep of the type Discrete is specified over the range 5.0 to 6.0 GHz

with a LinearStep of 0.01 GHz. This sweep type does not save the fields at each

frequency point thus reducing the memory storage requirements. A second sweep of

the type SinglePoints that saves the fields is specified for 5.59 GHz which is the

resonance observed in the HFSS® analysis – details of this are discussed in the next

subsection. Other options for sweep are also available that may be more suitable for

other types of problems [52].

5.2.2 The HFSS®-Simulated Results for Baseline (Case-1) Antenna Element

The simulator proceeds with an initial mesh to arrive at a solution for all the node

points. The mesh is adaptively refined at the adapt frequency till the network

parameters show that the specified convergence criterion is met. After this the swept

frequency response of the antenna is computed for the relevant sweep(s). For the

present problem, as there are two ports; the parameters s11 and s21 are of interest.

Since the presence of the slot only slightly disturbs the current in the waveguide top-

wall, neither of these two parameters is expected to be particularly sensitive. For this

reason, a derived parameter 1 is used to represent

the power coupling out from the waveguide (see Eqn. 2.104.) This is defined in

HFSS® using an auxillary window called Output Variables where a user-defined

variable derived from the basic computed network parameters may be specified.

Upon executing the proposed antenna geometry, it was found that a very low value of

Pout is predicted. Also, the response increases monotonically with frequency, without

exhibiting any resonant behaviour. The simulation was repeated by tweaking the slot

length to either side of the obtained prototype value of 4.0mm followed by


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intermediate lengths. Finally, it was found that a slot size of 3.75mm X 0.5mm

exhibits the optimum coupling response. Figs. 5.4 & 5.5 show the computed swept

frequency response for the VSWR and the coupled power.

5.00 5.20 5.40 5.60 5.80 6.00Frequency [GHz]

1.00026

1.00028

1.00030

1.00032

1.00034

1.00036

1.00038

VO

LT

AG

E S

TA

ND

ING

WA

VE

RA

TIO

Ansoft Corporation HFSSDesign1VSWR Quick Report

Curve Info

VSWR(WavePort1)Setup1 : Sw eep1


VSWR(WavePort1)_1Setup1 : Sw eep2


Fig. 5.4: HFSS®-Computed VSWR of Proposed Single-Element Radiator (Case-1)

5.00 5.20 5.40 5.60 5.80 6.00Frequency [GHz]

6.00E-007

8.00E-007

1.00E-006

1.20E-006

1.40E-006

1.60E-006

1.80E-006

2.00E-006

Po

ut

Ansoft Corporation HFSSDesign1XY Plot 3

m1

Curve Info

PoutSetup1 : Sw eep1Name X Y

m1 5.5900E+000 1.7050E-006

Fig. 5.5: HFSS®-Computed Coupled-Power, Pout for Proposed Single-Element Radiator (Case-1)


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The frequency at which Pout exhibits a peak is inferred as the resonant frequency. This

peak value is 1.7050 X 10-6 and occurs at 5.59 GHz (see Fig. 5.5.) As a result, the

fields are recalculated at this frequency in a separate SinglePoints sweep as mentioned

earlier, for field visualization and pattern calculation.

The problem execution was carried out using Ansoft® HFSS® 11.1.1 on a DELL

E8400 with a 2.99GHz-CPU having a 2 GB RAM and an Intel Core-2 Duo Processor.

The convergence behaviour of the input VSWR with number of iterative passes is

illustrated in Fig. 5.6 below. The total CPU-time for the solution was 2h 47m with the

RAM usage of 1.67GB. A total of seven passes were necessary for convergence with

77045 tetrahedra in the final mesh.

The powerful visualization feature of HFSS® allows one to observe the field plots

inside selected geometries. Fig. 5.7 shows E-field contours in two orthogonal

sections of the problem through the slot centre. Several other plots are possible [52].

1 2 3 4 5 6 7Iterative Pass Number

1.000

1.002

1.004

1.006

1.008

1.010

1.012

1.014

1.016

1.018

VS

WR

Co

nv

erg

en

ce

Ansoft Corporation HFSSDesign1VSWR Quick Report1

Curve Info

VSWR(WavePort1)Setup1 : AdaptivePassFreq='5.6GHz'

Fig. 5.6: VSWR Convergence Behaviour for Proposed Single-Element Radiator (Case-1)


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(a)

(b)

Fig. 5.7: Electric Field Contour Plots through the HFSS®-Solved Problem Geometry (Case-1) a) parallel to waveguide longitudinal section; b) parallel to waveguide cross-section


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The contour plots indicate a definite coupling mechanism from the waveguide

through the coupling slot to the patch radiator. The fields are confined under the patch

metallization and guided to the ends of the patch. Radiation is seen to occur as the

field couples to the surrounding space. Some energy is seen confined near the

substrate (outside patch margin) which is associated with the surface wave along the

air-dielectric surface.

Pattern cuts are computed in HFSS® by integrating the far-field contributions of the

fields across the specified radiation boundaries. The pattern cuts obtained in the two

principal planes are close to those expected for the dominant TM01 mode on the patch

geometry (see Fig. 5.8.) The 3-dB beamwidths in the principal planes are obtained as

141 X 84. This compares favourably with the predicted pattern beamwidths using

the developed M-o-M code – these are 118 X 84 at 5.8 GHz (see Figs. 4.39, 5.9 &

10.) The change in E-plane beamwidth may be partly on account of frequency

difference, but there is another factor evident in the pattern plot in Fig. 5.8. It is

possible to discern undulations in the E-plane plot that are ascribed to the presence of

a finite ground plane (M-o-M assumes an infinite ground plane by contrast.) Kraus

[53] has treated this aspect in detail and radiation from the ends of the finite ground

plane causes periodic undulations in the E-plane pattern of a slot. The angular

frequency of these undulations is related to the ground plane size. In addition to the

beam broadening, this effect, incidentally, introduces a boresight dip with the peaks in

E-plane occurring at approximately + 45 instead. The null observed in H-plane by

the MOM-simulation is also missing in the FEM prediction (Fig. 5.9); the finite

ground plane is felt to be the reason. The peak directivity obtained is 5.313 dBi which

is expected for such a geometry. A backlobe of -14.55 dB is observed – this is the far-


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field contribution of the sidewalls of the radiation surface. Significantly, field

predictions in the rear half-space are available (Figs. 5.9 & 10 – note that boresight is

denoted as 90 in these figures) that were not possible with MOM due to the

assumption of an infinite ground plane inherent in the Green’s functions used.

Overall, there is excellent agreement of the pattern predictions by the developed

formulation with the HFSS® results (in the forward half-space).

Fig. 5.8: HFSS®-Computed Radiation Pattern Cuts for Proposed Single-Element Radiator (Case-1)

red H-Plane; and brown E-Plane

-30.00

-20.00

-10.00

90

60

30

0

-30

-60

-90

-120

-150

-180

150

120

Polar Plot

Curve Info

dB10normalize(DirL3Y)Setup1 : Sw eep2Freq='5.59GHz' Phi='0deg'



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Fig. 5.9: Comparison of Computed Radiation Patterns for Prototype Antenna Element: HFSS® vs. MOM (H-Plane)

-60

-50

-40

-30

-20

-10

00

30

60

90

120

150

180

-150

-120

-90

-60

-30

MOM

HFSS

Relative Power, dB

Off-Axis Angle, deg


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Fig. 5.10: Comparison of Computed Radiation Patterns for Prototype Antenna Element: HFSS® vs. MOM (E-Plane)

-60

-50

-40

-30

-20

-10

00

30

60

90

120

150

180

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MOM

HFSS

Relative Power, dB

Off-Axis Angle, deg


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5.2.3 Observations for Baseline (Case-1) Antenna Element Analysis

In this subsection, an HFSS®-analysis of a single-element radiator based on the

proposed geometry has been completed. We close this section with the following

observations.

a) The results of the HFSS®-analysis broadly validate the analysis based on M-o-

M developed in Chapters 2 to 4 of this thesis with the C-band prototype design

parameters as an example.

b) The dimensions frozen with the help of the M-o-M analysis could be used

directly except for the slot length. This needs some tweaking to arrive at the

dimension where resonance may be observed in the HFSS® simulation.

c) The radiation patterns obtained from HFSS® are in close agreement to those

obtained from the developed code except for the effect of the finite ground

plane.

d) Radiation from the ends of the finite ground plane is found to add undulations

to the E-plane pattern of the radiator and to cause beam broadening in both

planes.

e) The directivity and beamwidths obtained are close to the expected values for a

rectangular microstrip antenna excited in its dominant TM01 mode.

As mentioned at the beginning of this chapter, we shall investigate two other cases for

this prototype radiator the first by increasing the ground plane dimensions and the

second by including the effect of currents induced to the rear of the ground plane. The

former is taken up in the next section.


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5.3 Ansoft® HFSS® Analysis of the Proposed Single-Element Radiator using Extended Ground Plane (Case-2)

It is conventional to use a large ground plane relative to patch size behind the

microstrip patch radiator. This has the advantage of allowing the surface waves to

attenuate before being scattered from the edges of the substrate. Also fringing fields

from the radiating element are shielded from the rear half of the ground plane. This

property may be useful, for instance, when active elements are placed to the rear;

hence the arrangement eliminates the possibility of spurious feedback and oscillation.

Further, the single-radiator is expected to be used as a building block for an array of

patches. Hence, it would be useful to examine its radiation characteristics with a

larger ground plane. As a final consideration, an experimental model has been

implemented for the proposed geometry for which the actual dimensions chosen for

the extended ground are used in this section for analysis.

The proposed radiator geometry analyzed in the previous section is analyzed with a

ground plane of size 180 X 180 and is designated as Case-2. The geometry is

discussed in the following.

5.3.1 The HFSS®-Simulation for Antenna Element with Extended Ground-Plane

(Case-2)

The dimensions and parameters for the Case-2 simulation model are identical to the

previous case except for the ground plane size of 180 X 180 (see Fig. 5.11.) The ABC

is extended 5mm beyond this but the height is retained as previously. This implies a

change in ABC volume by a ratio of 3.24 : 1. Meshing operations similar to the

previous case were applied to the substrate, patch and slot. Boundary conditions and

port excitations are maintained identical.


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A total CPU-time of 10h 40m was needed for obtaining convergence by the solver for

this version of the problem. The final number of tetrahedra in the adaptive mesh was

132,072. The simulated results obtained for this problem are presented.

5.3.2 The HFSS®-Simulation Results for Single-Element Radiator with Extended

Ground-Plane (Case-2)

The HFSS®-computed VSWR characteristics of the radiating element (Case-2) are

illustrated in Fig. 5.12. These are seen to be in close agreement with those of the

previous case with the smaller ground plane (see Fig. 5.4.) This is expected because

the exciting waveguide and slot region are unchanged and only the ground size and

ABC have been altered.

Fig. 5.11: Ansoft® HFSS® Simulation Model of Proposed Single-Element Radiator with Extended Ground Plane (Case-2)


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5.00 5.20 5.40 5.60 5.80 6.00FREQUENCY [GHz]

6.00E-007

8.00E-007

1.00E-006

1.20E-006

1.40E-006

1.60E-006

1.80E-006

2.00E-006

Po

ut

Ansoft Corporation HFSSDesign1Coupled Power Plot

m1

Curve Info


m1 5.6300E+000 1.8209E-006

Fig. 5.13: HFSS®-Computed Coupled-Power, Pout for Single-Element Radiator (Case-2)

5.00 5.20 5.40 5.60 5.80 6.00FREQUENCY [GHz]

1.00026

1.00028

1.00030

1.00032

1.00034

1.00036

1.00038

1.00040

VS

WR

Ansoft Corporation HFSSDesign1VSWR Plot

Curve Info





Fig. 5.12: HFSS®-Computed VSWR of Single-Element Radiator with Extended Ground Plane (Case-2)


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However, we observe a small shift in the resonance indicated by Pout (Fig. 5.13.) The

maximum power coupling is 1.8209 X 10-6 and takes place at 5.63 GHz now. This is

a relatively small shift and is felt to be as (i) Pout is a difference of two quantities very

close in magnitude, hence minor changes in predicted values will cause greater

impact; and (ii) change in exact meshing in vicinity of the slot / patch entities due to

modified problem definition. The contour plots and radiation patterns presented next

are computed at this new frequency (although the difference is minor.)

The contour plots at the resonant frequency show a clear coupling mechanism from

the waveguide and a field detachment resulting in radiation (see Fig. 5.14.) The H-

plane contours show that the surface wave sustains to a considerable distance from the

patch. This justifies retaining the extended ground plane.

The computed radiation patterns show a scalloped behaviour in both planes (see Fig.

5.15.) The peak directivity is predicted as 6.618 dBi and the half-power beamwidths

in the principal planes are 138 X 104. The E-plane beamwidth is close to the

previous case but H-plane beamwidth is broader. These changes may be ascribed to

the undulations introduced due to the modified ground plane dimensions. It is

interesting to observe that this time the undulations are seen in the H-plane pattern

also.

The predicted backlobe is -14.57 dB which is very close to the number obtained in

Case-1. Thus, even though the pattern variation in the forward half-plane is affected

significantly, the backlobe is affected little. It may be remarked again that the

backlobe is computed from the field across the sidewalls of the radiation boundary.


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(a)

(b)



185

Fig. 5.15: HFSS®-Computed Radiation Pattern Cuts for Single-Element Radiator with Extended Ground Plane (Case-2)


-30.00

-20.00

-10.00

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60

30

0

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Polar Plot

Curve Info




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5.4 Ansoft® HFSS® Analysis of Proposed Single-Element Radiator including Currents on Rear of Ground Plane (Case-3)

In both the previous analysis cases, the backlobe estimation was based on the far-field

contribution of the fields at the side-walls of the radiation box enclosing the problem

geometry. A more rigorous treatment of this aspect would be to include the fold-over

currents from the edges of the ground plane towards its rear surface in the analysis

and add their far-field contribution also to arrive at the backlobe value. An analysis of

the problem geometry has been carried out with a modified HFSS®-model that allows

the computation of the fold-over currents over the rear surface of the ground plane of

the microstrip radiator. This is designated as Case-3 and the analysis considerations

and computed results are discussed in the following.

5.4.1 The HFSS®-Simulation for Antenna Element including Fold-over Currents

to the Rear of the Ground-Plane (Case-3)

The substrate parameters and radiator dimensions for Case-3 simulation model are

identical to the preceding two cases. A moderate ground plane size of 120 X 120 is

selected to reduce the computational burden. The ABC is extended 5mm outside the

substrate dimensions and the height towards above is still retained identical. However,

the ABC is increased to the lower side (see model in Fig. 5.16.) To allow the

waveguide to pass through either end of the ABC, a clone subtraction procedure was

used. The substrate, slot and patch were seeded prior to invoking the solver as

described previously while other boundary conditions are identical.

The problem was solved in a total CPU-time of 8h 55m for obtaining convergence. At

that instant, the final number of tetrahedra in the adaptive mesh was 110,403 with a

peak memory requirement of 1.77GB. Simulated results are discussed next.


187

5.4.2 The HFSS®-Simulation Results for Antenna Element including Fold-over

Currents to the Rear of the Ground-Plane (Case-3)

The VSWR response of the radiating element is nearly unchanged from the previous

two cases (see Fig. 5.17.) The value of Pout (Fig. 5.18) is different from the previous

case and is 1.7644 X 10-6 in this case and the resonant frequency is 5.59GHz.

The E-field contours through the principal sections of the problem region show

similarity to the previous two cases. Concentration of the field in the substrate is

observed as are the (relatively small) fringing fields in the plane of the substrate

outside its edge (as evident in Fig. 5.19). These fields indicate the presence of fold-

over currents induced at the rear of the ground plane along with scattering from the

edges of the ground plane.

Fig. 5.16: Ansoft® HFSS® Simulation Model of Single-Radiator including Rear Side of Ground Plane (Case-3)


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5.00 5.20 5.40 5.60 5.80 6.00FREQUENCY [GHz]

1.00026

1.00028

1.00030

1.00032

1.00034

1.00036

1.00038V

SW

RAnsoft Corporation HFSSDesign1VSWR Plot

Curve Info





Fig. 5.17: HFSS®-Computed VSWR of Single-Radiator including Rear Side of Ground Plane (Case-3)

5.00 5.20 5.40 5.60 5.80 6.00FREQUENCY [GHz]

6.00E-007

8.00E-007

1.00E-006

1.20E-006

1.40E-006

1.60E-006

1.80E-006

2.00E-006

2.20E-006

Po

ut

Ansoft Corporation HFSSDesign1Power Couped Out

m1

Curve Info


m1 5.5900E+000 1.7644E-006

Fig. 5.18: HFSS®-Computed Coupled-Power, Pout of Single-Radiator including Rear Side of Ground Plane (Case-3)


189

(a)


(b)


190

The computed radiation patterns show lesser undulations compared to the last case on

account of the smaller ground plane size. The H-plane pattern is relatively unaffected

by the scattering from the edges of the ground plane (see Fig. 5.20.) The predicted

peak directivity is 7.096 dBi and the half-power beamwidths are 131 X 61 in the

principal planes. The changes in the beamwidths compared to the previous cases are

small and associated with the size of the ground plane that introduces undulations in

the pattern.

As a notable difference, the predicted backlobe is -18.41 dB which differs from the

result obtained in both the previous cases. This is clearly due to the inclusion of the

fold-over currents in the simulation. For the far-field computation, the fields at the

lower face of the ABC actually are used. This is close to the real condition of the

radiator. It is interesting to observe that even though a relatively small fringing field is

seen at the ground plane edges, the backlobe is significant.


191

Fig. 5.20: HFSS®-Computed Radiation Pattern Cuts for Single-Radiator including Rear Side of Ground Plane (Case-3)


-40.00

-30.00

-20.00

-10.00

90

60

30

0

-30

-60

-90

-120

-150

-180

150

120

Radiation PatternCurve Info




192

5.5 Comparison of the Developed M-o-M Analysis with the Ansoft® HFSS® Analysis

As mentioned earlier, the analysis using Ansoft® HFSS® presented in the preceding

sections was intended to validate the analysis developed using the M-o-M formulation

in the foregoing chapters. Additionally, we have simulated the effect of ground plane

size and its rear aspect that was not possible in the M-o-M analysis. In this section we

will compare the features of the two methods of analysis with regard to 1) the

computational resources needed by the two methods; and 2) the physical details of the

radiating element that may be included in the analysis.

Table 5.1 presents a typical comparison of the computer resources used during the

two analyses. Since the Case-1 described in Section 5.2 is the nominal configuration

in Ansoft® HFSS®; this is selected for comparison. The developed M-o-M based

Table 5.1: Comparison of Computing Resources in Typical Executions of the Developed M-o-M Analysis and the Ansoft® HFSS® Simulation

ANALYSIS COMPUTER

CONFIGURATION

CPU-TIME

(per freq point)

Memory

Requirement

M-o-M (based on

present formulation)

ZENITH PC

1.60GHz, 256MB

RAM,

Intel Pentium-IV

~ 21 s ~ 13MB

Ansoft® HFSS®

(Case-1)

DELL E8400 PC

2.99GHz, 2GB

RAM, Intel®

Core®-2 Duo

~ 159 s ~ 1.7GB


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program was executed on a moderately sized PC with a small RAM. All the HFSS®-

executions were done on a relatively faster machine with a much larger memory. It is

seen that the developed M-o-M program executes nearly eight times faster than

HFSS®. Even the storage requirements for the FORTRAN program are relatively

small. The HFSS® storage is predominantly required during matrix retrieval. It is

further notable that the other two configurations, Case-2 & -3 need still higher

execution time as well as memory compared to the nominal case shown in Table 5.1.

One may argue that often, more than the time saved, it is also the accuracy of the

solution as well as the ability to solve a variety of problems (such as different slot and

patch shapes) which are more important. It is true that, as compared to HFSS®, the

developed program executes faster only for a very specific case of rectangular

waveguide feeding a rectangular patch through a rectangular aperture. The

formulation would need modification if other waveguide cross-sections / patch or slot

shapes need to be analyzed. Thus, this is not a limitation of the method-of-moments as

such but of the present formulation since a specific geometry was selected. Also, the

present work may be extended to different slot and patch shapes by appropriately

modifying the basis functions. Hence, given these limitations, the speed of execution

of the developed program is faster as indicated.

Keeping in view the above observations and reasoning, we may enumerate some

points in regard to the two analysis methods.

1) The FORTRAN program based on the developed M-o-M formulation is found

to execute much faster even on a relatively moderate PC than an equivalent

HFSS® analysis (for the specific problem geometry selected).


194

2) The M-o-M formulation inherently assumes an infinite ground plane. This is

implicit in the Green’s functions used for deriving the various moment matrix

terms which are for an infinite grounded dielectric slab. However, the

truncation of the matrix term summations does imply a kind of finite ground

size. A large ground plane would be computationally prohibitive on HFSS®.

3) It is not simple to analyze a finite ground plane using the M-o-M formulation.

It will require a modification of the formulation to include currents across the

ground plane also. Whereas in HFSS®, it is relatively simple to analyze with

differing ground plane sizes (as shown by the three cases analyzed.)

4) The M-o-M formulation, however, is derived for this specific geometry and

will not allow minor modifications in geometry like the small taper in patch or

slot shape while this is comparatively simple in HFSS®. Such variations in

shape may represent fabrication imperfections, for instance, that a designer

may need to estimate the impact of.

5) There is a close agreement in the network parameters as well as radiation

behaviour of the antenna element obtained from the two alternate analysis

methods. Also the dimensions of the patch and slot required to obtain

resonance were found to be in close agreement with only the length of the

latter needing minor tweaking.

6) In this regard, we may consider that the developed M-o-M analysis stands

validated through a theoretical comparison with a proven e.m. analysis tool.

7) In conclusion, the computer program based on the developed formulation may

be used for a quick optimization of the radiating element design

parameters in the initial design phase. This is especially useful if the element

is to be used as a part of a larger array. This may be followed by a more


195

rigorous analysis using Ansoft® HFSS® or a suitable tool to tune the slot

dimensions and to assess the impact of other features like a finite ground plane

& fold-over currents.

5.6 Summary

In this chapter, the results of an analysis of the proposed waveguide shunt-slot fed

microstrip patch antenna using the FEM-based, commercially-available, proven e.m.

analysis tool, the Ansoft® HFSS® have been presented. A brief review of the FEM

technique has been provided, discussing the second-order p.d.e. upon which it is

based, the meshing or segmentation of the problem into ‘finite’ elements, boundary

conditions and adaptive meshing that makes FEM highly flexible. Next, the baseline

case, comprising of the WGMPA with a specified ground-plane size of 100mm X

100mm is first described. Details of basic HFSS® library elements invoked to build up

the problem geometry are described. We observe that default meshing of the problem

space turns out to be inadequate especially in the substrate and on the planar entities –

the slot and patch. This is on account of fast field variations locally on these entities.

How this is resolved by mesh seeding has also been discussed at length.

Subsequently, the simulated results for the baseline case have been presented showing

the input impedance characteristics and the power coupling. A slight tweaking of the

slot dimensions from the M-o-M value became necessary to obtain the expected

resonance. Radiation patterns obtained from the HFSS® analysis are compared to and

found to closely resemble the M-o-M predictions and thus validate the developed

formulation and analysis. The merits and limitations of the developed M-o-M based

formulation for the proposed geometry are also discussed. Two additional analyses

that respectively simulate the presence of a larger ground plane and the effect of fold-


196

over currents on its rear are also presented subsequently. The larger ground-plane

slightly changes the resonant frequency but notably introduces undulations to the

pattern. The inclusion of the fold-over currents is seen to significantly alter the

backlobe prediction. This underscores the importance of considering these currents if

the element is to operate in an array environment sensitive to spurious oscillations e.g.

when integrated with active elements. Finally, a comparison is drawn between the

computing resources required in the developed M-o-M program and HFSS® for the

present WGMPA geometry. The relative advantages in speed / memory storage

requirements of the former are highlighted at the expense of assuming an infinite

ground-plane. The utility of the developed formulation for the design and analysis of

such a radiator are also summarized.

single-element radiator analysis...

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