05 Chapter 6

Chapter 6

The ESPAR Antenna

6.1 Introduction

The E lectronically S teerable P assive Array Radiator, or ESPAR antenna is a

loaded N port array currently under development at the Advanced Telecommu

nications Research Institute (ATR) of Kyoto, Japan [11]. In its simplest form,

a single active element is surrounded by multiple parasitic elements loaded with

variable reactances. The controlled reactances regulate current on the parasitic

elements, inuencing spatial radiation sensitivity and thus providing the adaptive

trait.

Specically, the ESPAR antenna is being developed for application in wire

less ad hoc networks [96]. Autonomous to cabling and base-station infrastructure,

wireless ad hoc networks are a cheap, simple and dynamic alternative to their

wired, static counter-parts. However, wireless systems are susceptible to signal er

rors arising from multi-path propagation and interference signals from unsolicited

nodes. As data is multi-hopped, signal errors between just a few intermediate

nodes can have a potentially devastating eect on the entire network performance.

In addition, wireless transmission can be a signicant drain on the nodes stored

energy. Node battery life is shortened considerably if high transmission powers

are required for ecient communication. As the ESPAR antenna can direct radia

tion at intended recipients and steer radiation nulls toward the interfering signals,

91

92 CHAPTER 6. THE ESPAR ANTENNA

such problems are signicantly reduced. The radiation nulls and main lobe gains

complement each other to maximize the system signal to interference noise ra

tio. Furthermore, the antenna main lobe gain dramatically decreases the required

transmission power for a set range.

The acronym ESPAR allows an arbitrary radiating structure (patch, wire, aper

ture etc.), and is thus synonymous with the N port systems described by Harrington

and Mautz [26, 20, 27, 28]. Their early analysis on radar scattering of generalized

N port loaded networks lead to the formation of a reactively loaded dipole array

[12]. This generated research into equivalent patch and monopole arrays by Dinger

[29, 30, 23], Sibille [31, 32] and Ohira [33, 34].

This existing literature primarily focuses on general loaded N port network an

tenna theory. To a lesser extent, some experimental results of prototype antennas

have been presented. In contrast, the ESPAR antenna is consciously being devel

oped for mass consumer application. Therefore, with general theory understood,

questions regarding the ESPAR antennas practicality for such application can be

addressed. As such, the Adaptive Communications Research Laboratory (ACR)

of ATR is actively involved in the research of practical beam forming algorithms

[35, 97], and, in the authors case, the design of ecient, robust antenna structures

[73, 98].

An ad hoc network would generally comprise mobile terminals (e.g. notebook

computers). It is envisioned the ESPAR antenna will be external to the mobile ter

minal, with design evolution eventually realizing an integrated solution. Regardless

of its position however, the antenna design must inherit similar criteria to the mo

bile terminal. Of particular signicance are the restrictions of power consumption

and physical volume. The volume criterion limits the ground plane, disallowing

Harringtons analytical procedure of the dipole array in [12]. Chapter 5 described

the analytical diculties in dealing with monopole arrays on nite ground struc

tures, leaving simulation the only viable option (excluding experiment) to predict

antenna characteristics.

Such an antenna has hitherto not been considered. It is unknown whether its

6.2. THE PHYSICAL ESPAR ANTENNA 93

performance will allow useful communication. For instance, if the ESPAR antenna

has high frequency sensitivity then only small communication bandwidths will be

possible. Therefore, a base ESPAR structure was analyzed through simulation.

Both the antenna structure and loading reactances eect electrical response in the

frequency domain. Accordingly, the antenna frequency sensitivity was measured

to ensure utility. A robust frequency response will additionally translate to sim

ilarly stout electrical characteristics when reactance manufacturing and assembly

tolerances are included.

Once the ESPAR structure was deemed practicable, it was optimized for max

imum azimuthal gain. Consequently, radiation sensitivity at side angles, required

transmitter power and antenna impedance mismatch were inherently reduced. In

creases in principal lobe gain are even more pronounced in a homogeneous ad hoc

network. As both communicating node antenna responses combine to dene system

performance, any design improvement made in the antenna gain will potentially

have double the eect in a system.

This chapter commences with an introduction to the ESPAR antenna structure.

Practical loading methods and considerations are then detailed before presenting

the antenna frequency analysis and optimization procedures.

6.2 The physical ESPAR antenna

The antenna conguration is similar to that of Harringtons dipole array [12].

A single active monopole element (0) is surrounded by six equidistant, parasitic,

monopole elements (1-6) of constant radius from the centre. Each parasitic element

is base loaded with some variable reactance, while the entire array ideally rests

upon an innite ground expanse. The antenna is illustrated in Figure 6.1.

The reactive loads alter the antenna currents through equation (2.15), inuenc

ing its radiation characteristics (2.10). Thus control of the reactive loading allows

radiation beam and null steering. Capacitive varactor diodes have been typically

suggested for the reactances [34]. By applying a reverse dc bias, a depletion region


X2 X3

X5

X4 X6

X1 V1

2 3

4 56

0 RF

Figure 6.1: Ideal monopole ESPAR antenna upon innite ground.

is formed over the diodes PN junction. The depletion region size is determined

by the bias magnitude, and hence the capacitance is controlled. With an applied

reverse bias Vr , capacitance of a PN junction is [16]

C = kV r 1 2 (6.1)

where k is a constant derived from the junctions doping charge densities. The only

additional circuitry on the parasitic elements are RF chokes to isolate the parasitic

elements microwave signal from the dc control lines. The cost savings of passive

components like varactors and RF chokes (inductors or resistors) are apparent

when compared to the active phased array alternatives. A typical varactor control

circuit is presented in Figure 6.2.

The monopole array of Figure 6.1 obviously derives from the complementary

free space dipole array. However, the monopole arrays ground allows shielding

(electrically and physically) of the control circuitry which can reside below the

plane. It is for this very reason that the original dipole ESPAR antenna [12] has

been reduced to its monopole equivalent. Practically however, the antenna cannot

utilize such a ground. For integration in mobile terminals, the horizontal ground

needs to be strictly limited. Chapter 5 discusses the implications of reducing

the ground size on a monopole array. Typically, radiation is redirected above

95 6.2. THE PHYSICAL ESPAR ANTENNA

l l

itic le

DC ControVo tage

Parasmonopo

RF Choke

RF Choke

Varactor

Figure 6.2: Typical varactor control circuit.

the horizon, reducing communication eciency in the azimuth. A solution in

the form of a conductive sleeve or skirt on the perimeter of the lateral ground

is suggested to compensate for the nite ground eects. Figure 6.3 depicts the

practical array while Table 6.1 denes ground radius rg , parasitic element radius

rp, active element height ha, parasitic element height hp and skirt height hs. The

dimensions of Table 6.1 represent those that might be used as an initial 2.5GHz

design. The quarter wavelength monopole heights ensure resonance while their

close spacing guarantees strong mutual coupling. In addition the array is bounded

by a conductive skirt to accommodate a small lateral ground area. When measured

however, it was found resonance of the antenna was at 2.4GHz and therefore all

results and dimensions herein are given for 2.4GHz.

Length Structural Dimensions

rg rp ha hp hs mm 60 30 30 30 30 0.48 0.224 0.224 0.224 0.24

Table 6.1: Initial dimensions of the ESPAR antenna in Figure 6.3 at 2.4GHz.

To obtain a specic radiation pattern, all reactive loads need to be set to some

X4X5


1

X3

V

1

2

1

2

1

2

4 56

3

ha

hp

rp

hs

rg

RF

=90, =0

Ground Skirt

=0

Figure 6.3: Practical ESPAR antenna structure with conductive skirt.

value. The term loading case or loading configuration shall be used henceforth to

describe the set of reactive loads used simultaneously on the antenna.

6.3 Reactance considerations

Employing varactors as the reactive loads raises questions regarding their practi

cality. Firstly, it is important to consider their transmission capabilities. Harmonic

distortion would potentially limit the transmission power they could accommodate.

Antenna elements typically display resonance at higher order modes resulting in

spectrum pollution. Secondly, the reactance range varactors oer can restrict the

adaptive possibilities. As variable capacitors they would produce a limited negative

reactance range.

97 6.3. REACTANCE CONSIDERATIONS

6.3.1 Harmonic distortion

Surface mount varactors are not necessarily designed for high power application.

In transmitting mode, the antenna may drive the varactors into non-linearity, cre

ating harmonic distortion. With no lters between the varactors and transmission

medium to counter the eect, unlicensed spectrum will be polluted. A suggested

solution is to distribute the power over multiple varactors [98]. An anti-series var

actor pair conguration is shown in Figure 6.4 with the single varactor alternative.

C

CC

CC

(a) (b)

Figure 6.4: (a) Single varactor and its (b) anti-series varactor pair equivalent.

The varactor pairs create a parallel capacitance twice that of the individual.

In series with an equivalent pair, the total capacitance reduces back to that of the

single varactor equivalent. However, the RF power is divided over the 4 varactors,

exposing each to less and therefore mitigating the harmonic production relative to

the single varactor case. It is analytically shown in [98] that the anti-series varactor

pairs can extinguish second order distortion and boast a third order suppression

ratio (compared to the single varactor) of

HD3 ASV P HD3 SV

= 1

4 3C

2 1

8C0C2 (6.2)

where HD3 ASV P and HD3 SV are the third order harmonic distortion magnitudes of

of the anti-series and single varactor congurations. C0, C1 and C2 are coecients

of the Taylor series expanded, non-linear total capacitance that is a function of


input ac signal v [99]

C = C0 + C1v + C2v 2 . (6.3)

Under varying bias conditions, it was experimentally found [98] that replacing

a single varactor with four can reduce second and third order harmonic distortion

by a worst case average of 18dB and 12dB respectively. Considering the varac

tor under test exhibited a maximum second order harmonic magnitude of -38dBc,

these reductions are not trivial. The measurements were carried out in a compact

anechoic box designed for convenient near-eld measurement [100, 101]. The au-

thors contribution to this research ([100, 101, 98]) was only 10-20% and therefore

extensive results will not be shown.

6.3.2 Reactance range

The reactance of varactors placed at the base of monopole elements will translate

directly to the base reactance of the monopole. Being purely capacitive loads, only

negative reactances can be generated as reactance is dened from capacitance C

jX = 1

jC = j

C 1

X = C

. (6.4)

Varactors considered for prototype ESPAR antennas exhibit capacitive ranges of

0.7pF to 9pF, which from (6.4) at 2.4GHz is a j6.9 to j91.5 reactance range. Therefore, the beam shape possibilities are potentially limited. To improve the

reactance range, and hence the beam-forming ability of the antenna, transmission

lines would have to be included. This is illustrated with fundamental transmission

line theory.

A transmission line of length l and characteristic impedance Z0 terminated with

a lumped impedance ZL will have an input impedance [80]

ZL + Z0 tanh l Zi = Z0 (6.5)

Z0 + ZL tanh l


where the propagation constant of the line contained wave

= + j (6.6)

comprises real and imaginary components and representing the attenuation

constant (Np/m) and phase constant (rad/m) respectively.

More specically, if we assume a lossless transmission line (=0, Z0 = Re(Z0) = R0) and utilize the trigonometric relation

tanh jx = j tan x, (6.7)

Zthen (6.5) becomes

L + jR0 tan l Zi = R0 . (6.8)

R0 + jZL tan l

Lossless varactors will produce a purely imaginary load impedance (ZL = jXL),

so (6.8) can be written

jXL + jR0 tan l Zi = R0

R0 XL tan l ( XL + R0 tan l

) Zi = j R0 . (6.9)

R0 XL tan l

Equation (6.9) states a reactively loaded transmission line will have a purely re

active input impedance whose magnitude depends on the line length l. In other

words, a varactor loaded transmission line will create a load at the monopole base

with dierent reactance range to that of just the varactor.

Multiple loads can then extend the possible reactance range. As an example,

consider three parallel varactor loaded 50 transmission lines meeting at point A

in Figure 6.5, where A can be connected to the monopole base. Each varactor has

a reactance range of j0 to j100. Inserting this range into (6.9) with three transmission line lengths of l1 = 0, l2 = 0.176, and l3 = 0.352 give normalized


345

3476

3

48

9;:

FHG

FJI

FJK

:

=@? ABC


grounded lumped loads (ZL = RL + jXL). Signal induced in the parasitic element

is guided down the transmission line and reected with some phase shift. The total

phase shift (at the monopole base) directly inuences the currents on the monopole

and is determined by the reactive load ZL, the transmission lines characteristic

impedance (Z0) and the transmission lines length. Elementary transmission line

theory states that the reection coecient () of a loaded transmission line is [102]

Z = r + ji =

ZL Z0 (6.10)

L + Z0

where subscripts r and i designate the real and imaginary components of the re

ection coecient. Normalizing with respect to Z0 and assuming no loss in the

transmission line or load (RL = 0 = 1), (6.10) can be rearranged to nd | | the angular component of the reection

i 2xL = arctan = arctan 2 . (6.11)r xL 1

Here xL is the load reactance normalized to the transmission line characteristic

impedance. This relationship is well known and best visualized on a Smith Chart.

When xL increases, its inuence on reduces (d/dxL is small). Therefore, for | | large values of xL , small perturbations will result in minimal phase dierence and | |hence an insignicant eect on the antenna. Conversely, for small xL, equivalent

perturbations will see signicant changes in and hence antenna response.

Equation (6.11) is important when considering the frequency response of a

lumped element (L or C) load. The capacitor reactance relationship (6.4) and

inductor reactance relationship

jXL = jL (6.12)

are linear. Any change in frequency will produce a corresponding change in reac

tance (though inverted for C). If we consider an example operating bandwidth of

10%, all reactances in the loading conguration will vary by 5% of the resonant


frequency. If the loading case comprises capacitive and inductive loads, capacitive

reactances will decrease as frequency increases over the range while inductive reac

tances increase. The antenna response over frequency would normally be solely a

function of structure. However, with the controlling reactances also being frequency

dependent, radiation pattern and antenna match might vary beyond practicality

over a required frequency bandwidth. This eect will be seen to a greater extent

for smaller reactive loads, where changes in XL produce a greater change in .

The second consequence of (6.11) relates to reactance optimization. To real

ize a radiation pattern with particular characteristics (null, lobe locations), the

reactances must be optimized. Therefore, s relationship with reactance (6.11)

inuences our optimization procedure. Clearly, a ne, linear reactance resolution

for large |XL| will be an unnecessary burden on the optimizer. Larger stepping to alleviate this would adversely eect the resolution for small XL values where | | changes in are signicant. In addition, the theoretical reactance range is un

bounded (j j), so a standard search could not include all possibilities. It is consequently more logical to step linearly with respect to . The reactances

can then be calculated from rearranging (6.11):

sin XL = Z0. (6.13)

1 cos

As is naturally bounded between 0 and 2pi, a small, nite set of reactances can

be chosen which represent all possible reactance values that would signicantly

change the characteristics of the antenna.

6.4 Frequency sensitivity

The electrical sensitivity of the antenna is an important measure gauging its prac

ticality. Typically, an antenna will be required to operate linearly over some

frequency bandwidth. While the antenna structure would normally dictate the

electrical sensitivity around resonance, the ESPAR antennas reactive loads bring

additional frequency dependence. Section 6.3.3 discussed how changes in frequency

103 6.4. FREQUENCY SENSITIVITY

can cause the reactance to eect the antenna in a non-linear fashion (6.11). There

fore it is important to conrm that the characteristics of the antenna will not

degrade beyond practical limits.

It would be impossible to test every reactance combination, most of which

would not produce practical antenna characteristics anyway. Therefore a sample

of loading cases that produced potentially useful radiation patterns were tested over

a frequency bandwidth. However, in order to nd the loads required to generate

these patterns an optimization of the reactance values needed to be performed.

6.4.1 Reactive optimization

Optimization was required to determine a set of load values that would produce

directional radiation patterns and acceptable reection responses. Computer sim

ulation determined antenna electrical characteristics for a given load conguration.

The three packages available were XFDTD v5.1, HFSS v7.0 and NEC. Of the three,

XFDTD and HFSS were the most accurate with their capability to simulate the

skirted ground plane. However, these packages had simulation times in excess of

1.5 hours. In comparison, NEC considered the antenna on innite ground, but

its simulation term was only several seconds. This made it the ideal choice for

optimization purposes.

The genetic algorithm discussed in Chapter 3 employed NEC as the solver from

which a tness value could be determined. The cost function tness included min

imizing the antenna S11 and maximizing front to null (radiation minimum) ratio

of a = 0 30 primary lobe and = 90 270 null. Antenna symmetry allowed such patterns to be repeated with 60 steps through the horizontal.

Mathematically, the tness was calculated using

f = FNRmn S11. [dB] (6.14)

where FNRmn is the front to null ratio between a main lobe directed along m

and null at n. The negative sign for S11 enabled minimization of the negative


Case 1

Load Reactance (j) 2 3 4 5 6

Main lobe angle ()

Null angle ()

S11 (dB)

-10dB BW (MHz)

1 -150 250 78 26 78 250 0 180 -9.1 -2 184 -97 89 46 89 -97 0 180 -12.4 217 3 -183 226 103 81 59 125 15 245 -12.0 206 4 212 -156 87 56 85 144 30 170 -12.3 217 5 -246 -225 179 43 87 125 30 210 -11.9 201

Table 6.2: Five loading congurations with dierent H-plane radiation characteristics (main lobe and null locations). Reection summary is calculated with XFDTD.

logarithmic value in a maximizing function.

Five dierent loading cases for a 2.4GHz ESPAR antenna were optimized. Each

case represented dierent radiation characteristics that might be desirable in the

nal design. The main goal of the optimization was simply to nd loading con

gurations that produced dierent, directional radiation patterns. Whether they

were completely optimal with respect to (6.14) was not critical. Table 6.2 describes

the dierent loading cases, their corresponding principal lobe and null directions,

and reection responses. While cases 1 and 2 appear equivalent, the main lobe

beamwidth of case 2 was considerably larger than case 1 and was thus included.

The S11 results in Table 6.2 were computed with XFDTD so the nite ground

structure could be accounted for and are shown in Figure 6.6. The resonant depths

range from -9.1dB to -12.4dB. Those under -10dB manage an impedance bandwidth

of better than 200MHz (8.3%). The resonant frequencies ranged between 2.355GHz

and 2.402GHz. This 47MHz change represents a 2.2% shift for the dierent reactive

loading cases, although each S11 did not degrade by more than 0.52dB over this

range. With such wide impedance bandwidths, it was concluded that the antenna

reection response was practical.

XFDTD, HFSS and NEC were used to calculate and compare radiation patterns

of the dierent cases at 2.4GHz. Both E-plane and H-plane cases were considered

and are presented in Figures 6.7 and 6.8. As NEC simulated the structure on an

innite ground plane, it was expected some error between it and the remaining


2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

12

10

8

6

4

2

0

Frequency [GHz]

S11

[dB]

Case 1 Case 2 Case 3 Case 4 Case 5

Figure 6.6: Reection response of the loading congurations from Table 6.2 calculated with XFDTD.

packages would be present.

Excellent agreement between XFDTD and HFSS was observed for all cases, the

independence of the packages suggesting the results shown were a likely prediction

of the experimental case. As expected, NEC results showed the most dierence,

however lobe and null locations remained constant and thus its use for optimizing

the beam shapes was validated. The ground limitation of NEC is apparent in

Figure 6.8 where maximum radiation is not elevated. Conversely, both XFDTD and

HFSS predict elevation. Monopoles on nite ground structures typically exhibit

elevated radiation (see Chapter 5). While ground sleeves in Chapter 5 were shown

to control this elevation, the hs dimension in Table 6.1 was merely an initial guess

and not optimized.

6.4.2 Experimental verification

To ensure the simulation procedures were correct, the antenna and loading cases

were physically built and measured. An existing solid metal ground structure was


90 90

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HFSS Gain: 5.84dBi NEC Gain: 10.71dBi XFDTD Gain: 6.14dBi

0dB

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90

0dB

3

6

9

12 0

30

60120

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Figure 6.7: Normalized H-plane radiation pattern comparison between HFSS, XFDTD and NEC. Cases 1 to 5 from top left to right to bottom (refer to Table 6.2).


0 0

0dB

6

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0dB

6

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0 0

0dB

6

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0dB

6

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0

0dB

6

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Figure 6.8: Normalized E-plane radiation pattern comparison between HFSS, XFDTD and NEC. Cases 1 to 5 from top left to right to bottom (refer to Table 6.2). Case 1,2: = 0, case 3: = 15, case 4,5: = 30.


employed. Each monopole element was fed with an SMA panel mount connector,

axed to the bottom of the ground plane. While varactor diodes would typically

be used to produce electrically controlled reactances, their use was inappropriate

for conrming the simulated results. To do so would initially require circuitry to

be designed for varactor mounting and control. Moreover, varactors would require

extensive calibration to conrm the exact reactance they were creating at the

monopole base. Even then, any production variation between units, or asymmetry

in board assembly would potentially degrade results.

Instead, combinations of SMA adapters terminated with either open circuits,

short circuits or surface mount capacitors were used to create the dierent reactive

loads. Existing connectors were measured and all permutations were calculated

from which the case reactances could be selected. Figure 6.9 shows an example

load. At point B, the exact reection phase length (BLoad ) could be measured

with a network analyzer. When added to the ground and panel connector thickness

(AB), the precise reactance at A could be calculated from (6.13). Reactances

were created to within 2 of the required . Detailed information on the load

construction is given in Appendix B. With this procedure, a test antenna with

reactive loads was constructed at a cost incorporating only the panel mount SMA

connectors used as physical mounts for the loading capacitors (see Figure 6.9).

This loading conguration however has a signicant section of transmission line.

A transmission line of physical length L has a of

2L 4pif L = 2pi = radians (6.15)

u

where is the electromagnetic wavelength in the transmission line at frequency

f propagating with velocity u. Thus, the transmission lines change with fre

quency is d 4piL

= radians Hz1 . (6.16)df u

Equation (6.16) shows the change in with respect to frequency is not constant

when L is variable (as is the case with dierent reactances). Therefore, as each


i

itic le

Ri le le

l l

( ialB

A Ground Cross-Sect on

ParasMonopo

ght AngSMA MaAdapter

Pane mount SMA fema e connector part cross-sect

Surface Mount Capac

ions)

itor

Total 50 transmission line length (L)

Figure 6.9: Example SMA loading. The monopole is loaded by a transmission line that provides a reactance at A.

reactance changes at a dierent rate with frequency, the experimental results can

only be compared to their simulated counterparts at the reactance design frequency.

This however, is sucient to validate simulation procedure.

The loss of the SMA loading structures was no greater than 0.3dB. Larger

structures incorporating electrically long phase shifters had losses in excess of 2dB

and as such, the results they produced had signicant error. It was additionally

hoped the relatively low prole SMA loads would have negligible eect on the

antenna radiation characteristics. Figure 6.10 displays the underside of the antenna

when fully loaded. The centre SMA mount would be connected to the RF signal

in operation. The reactances in Figure 6.10 are typical of the loading cases where

some loads are over twice as long as others. Clearly then, (6.16) is signicant

and large experimental frequency sweeps of the antenna would produce misleading

results.

All ve loading cases were constructed and antenna S11, H-plane radiation

patterns, and primary lobe gains were measured for comparison with simulation.


Figure 6.10: Photo of an example loading conguration underneath the ESPAR antenna. Loads of dierent length comprising various SMA adapters are seen. Capacitors terminating the panel mount SMA connectors provide additional phase reection diversity.


S

Measurement procedure is given in Appendix A. Due to (6.16), experimental

11 was only measured at the designed antenna resonance (2.4GHz). All cases

were within 1dB of XFDTDs prediction (Figure 6.6) ranging from -9.7dB to -

12.8dB. The measured radiation patterns and primary lobe gains further veried

simulation accuracy with excellent agreement. Figure 6.11 displays a comparison

of H-plane simulation with experiment. Primary lobe gains were within 1dB of

those predicted and pattern shape was consistent. The similarity of simulation

and experiment simultaneously validates the simulation procedure, and the use of

SMA transmission line loads for accurate reactance creation.

6.4.3 Frequency variation

With condence in the simulation procedure, XFDTD and HFSS were used to

vary the operating frequency of the antenna from 2.3GHz to 2.5GHz (8.3%). Both

packages use lumped circuit elements for the reactive load so similarity with a

varactor response can be expected. From Figure 6.6, the worst reection response

over this range was case 1 at -7.5dB. The remaining cases did not rise above -

9.6dB. The variation in H-plane and E-plane radiation for case 1 can be seen in

Figure 6.12. While Figure 6.12 displays some variation in ancillary lobes, the

main lobe beamwidth, gain and position remain relatively constant. Table 6.3

summarizes these results and those for the remaining cases.

Case Gain ( = 0) (dB) FNR (dB) 3dB Beamwidth () 1 0.02 -3.80 0 2 0.23 -0.49 0 3 0.44 -1.01 +10 4 0.42 -1.20 +5 5 0.32 -1.29 +20

Table 6.3: Variation in ESPAR radiation characteristics from 2.3GHz to 2.5GHz. Results shown are averaged between XFDTD and HFSS.

Critical characteristics of the radiation such as gain, front to null ratio and 3dB

beamwidth varied at worst by 0.44dB, -3.8dB and 20 respectively. As a result, it


Figure 6.11: Comparison between measured (green), HFSS (red) and XFDTD (blue) H-plane radiation patterns. Cases 1 to 5 from top left to right to bottom (refer to Table 6.2).


90 90

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(a) (b) 0 0

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7dBi

2

3

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180 180

(c) (d)

Figure 6.12: Case 1 H-plane patterns at (a) 2.3GHz and (b) 2.5GHz and E-plane patterns at (c)2.3GHz and (d) 2.5GHz. Results for both HFSS (red) and XFDTD (blue) shown.


was concluded that the radiation characteristics remained relatively constant over

the frequency span.

While only a small sample of loading congurations were considered, the fact

that none had signicant variation over the 8.3% frequency bandwidth is a good in

dication that other congurations will be similarly robust. Signicantly, the sample

loading congurations are relatively important cases due to their practical radia

tion features. The frequency insensitivity also suggests the antenna characteristics

would be equally robust to small assembly related reactance errors.

6.5 ESPAR optimization

The analysis performed in the previous section was critical to the condence in

a practical implementation of the ESPAR antenna. However, consideration of

the ve loading conguration results concluded the antenna dimensions were not

optimal. E-plane radiation in Figure 6.8 displayed elevations of up to 25 resulting

in a gain reduction at the horizontal of 1.55dB. In addition, it is not known what

the true potential for main lobe gain is. The gain of an antenna is a dening feature

in the performance of an ad hoc wireless network. Thus the optimization goal was

simply to maximize directional gain in a single azimuth direction. Antenna gain is

dened as the product of its directivity D and eciency e [9]

G = eD. (6.17)

Conductor ohmic losses are considered negligible, thus only the antenna impedance

mismatch is considered in the eciency. Equation (6.17) can then be rewritten [9]:

( ) G = 1 S11|2 D (6.18)|

which shows optimizing the gain simultaneously optimizes the return loss and

antenna directivity.

Considering the ESPAR conguration, there are two main areas requiring opti

115 6.5. ESPAR OPTIMIZATION

mization; the structural dimensions and reactive loads. Both structure and loading

reactances couple to determine the radiation characteristics of the antenna, and

as such, an optimum set of reactance values is unique to a single structure only.

Therefore, it was desirable to optimize both reactance values and structure. As

this presented a very large solution space, the optimization was partitioned into

several consecutive stages that alternated optimization of reactive loads and struc

ture. At each successive stage, optimization variables underwent an increase in

resolution with a decrease in range. The genetic algorithm technique of Chapter

3 was used as the optimization method. Its cost function employed HFSS to solve

each structure to ensure the returned tness would be an accurate representation

of reality.

6.5.1 Reactance optimization

With an expensive cost function (HFSS), the optimization process needs to be as

ecient as possible. Referring to Figure 6.3, there are six dierent reactance values

that require attention. However, because the optimization goal is to maximize gain

in a single azimuth direction, the problem can be simplied by selecting either

= 0 or = 30 as the direction of gain optimization. Reactance symmetry

around this angular axis can then be used. The two axes reduce the required

optimization variables to four and three respectively. It was not known which

case would provide a higher gain, but it was suspected the = 0 case might as

radiation was along the elemental axis.

The second method to reduce the optimization time of the reactances was that

outlined in Section 6.3.3. was discretized between 0 and 2pi from which reactance

was calculated using (6.13). During the initial optimization stage, each reactance

was discretized into 64 levels (5 bits) separated by 5.6 in . In the later stages

of optimization, stepping was reduced to less that 1.


6.5.2 Structural optimization

To reduce optimization time, the limited set of antenna dimensions in Table 6.1

were optimized. Monopole radius (1mm) and skirt sheet thickness (0mm; a 2-D

sheet) were kept constant. It was thought the time cost involved to include these

dimensions in the optimization, would outweigh the marginal performance increase

they would net.

In contrast to the reactive optimization, the optimization of structural dimen

sions had to be performed over a restricted range of values. A maximum of 0.2

variation from the initial dimensions was chosen as the optimization range for the

dimensions hs, rp and rg . Monopole heights ha and hp were only varied by 0.06

(7.5mm) during optimization1 .

The antenna electrical characteristics were not uniformly sensitive to all struc

tural dimensions. For instance, variation in ha or hp would produce greater changes

than the same variation in rg . Consequently, the optimization resolutions were set

empirically for each dimension. During the initial optimization stages, the resolu

tion of rg was 2mm, rp and hs were stepped by 1.5mm and the element heights ha

and hp were resolved to 1mm. The resolutions of ha and hp were rened to 0.5mm

when the optimization was in its nal stages.

6.5.3 Optimization result and analysis

The antenna solution was attained through four stages of optimization. Each phase

adopted a smaller optimization variable range with an increase in resolution. The

optimum chromosome in the nal population of each stage seeded the ranges and

resolutions of the following stage. Employing a dual PIII 850 with 1Gb RAM, the

total optimization involving 3799 unique cost function computations took close to

4 weeks. Table 6.4 and Table 6.5 present the reactances and structural dimen

sions of the antenna at termination of the optimization. The predicted antenna

characteristics are given in Section 6.5.4.

1This work was performed before Chapter 5, thus it was not thought to reduce rg to rp


X1 X2 X3 X4 X5 X6 -14 -65 39 17 39 -65

Table 6.4: Optimized reactances (j) for the ESPAR antenna.

Length Structureal Dimensions

rg rp ha hp hs mm 60 38.5 27 27 34.5 0.48 0.308 0.216 0.216 0.276

Table 6.5: Optimized structure of the ESPAR antenna at 2.4GHz.

Comparing the dimensions of Table 6.5 and Table 6.1, the most signicant

change is the parasitic radius rp , which increased by 9.5mm to almost a third of

a wavelength. Similar to Section 5.4.2, all unique solutions (chromosomes) were

recorded so a sensitivity analysis could be made. Figures 6.13 and 6.14 show the

sensitivity plots of all optimization variables. The reactances are replaced with

their equivalent reection phase for illustrative purposes.

The tness was not sensitive to variables hs and rg in Figure 6.13. As such,

after the second stage of optimization, the skirt height and ground radius were kept

constant to reduce the solution space. It is for this reason, their sensitivity plots

do not exhibit tness of equal magnitude to the remaining variables. Conversely,

the parasitic elemental radius and element heights had signicant eect on tness.

These sensitivity results validate the dierent resolutions used between variables

mentioned in Section 6.5.2.

Figure 6.14 conrms the solution space does not have a single well dened opti

mum but is rather populated with multiple sub-optimum solutions. Each reactance

plot shows two to three signicant solutions. The sensitivity plots suggest the so

lution obtained was not necessarily the best possible. In addition, the stochastic

basis of the genetic algorithm requires multiple optimization runs be performed for

increased accuracy. However, with a single optimization taking 4 weeks, this was

not deemed appropriate for the few tenths of a dB likely to be gained.


1 0 1 2 3 4 5 6 7 850

55

60

65

70

r g [m

m]

1 0 1 2 3 4 5 6 7 835

30

25

20

h s [m

m]

1 0 1 2 3 4 5 6 7 820

25

30

35

h a [m

m]

1 0 1 2 3 4 5 6 7 820

25

30

35

h p [m

m]

1 0 1 2 3 4 5 6 7 820

25

30

35

Fitness

r p [m

m]

Figure 6.13: Sensitivity plots of the ESPAR antenna dimensions.

6.5. ESPAR OPTIMIZATION 119

1 0 1 2 3 4 5 6 7 8200

100

0

100

200

1

[]

1 0 1 2 3 4 5 6 7 8200

100

0

100

200

2

[]

1 0 1 2 3 4 5 6 7 8200

100

0

100

200

3

[]

1 0 1 2 3 4 5 6 7 8200

100

0

100

200

Fitness

4

[]

Figure 6.14: Sensitivity plots of the ESPAR antenna reactive loads.


Figure 6.15: Top and bottom view of constructed antenna (Tables 6.4 and 6.5) with xed reactive loading.

6.5.4 Experimental verification

The antenna was built in a similar fashion to that explained in Section 5.5.1. The

only addition was the plated vias through the ground plane. The SMA panel mount

dielectric extended through the PCB that made up the ground. It was then cut

ush with the top ground surface. However, to mitigate loss through the PCB, the

vias were plated with copper sheet. Therefore, a perfect 50 line was produced

from the monopole base through to the load termination. Top and bottom views

of the antenna are presented in Figure 6.15. All solder joins are only signicant

visually. Their discontinuity with the antenna surface was negligible at a maximum

of 0.2mm.

The antenna was tested in a anechoic chamber with its S11, H-plane and E-plane

radiation patterns recorded. The antenna mismatch impedance was poor with a

measured S11 of -7dB at 2.4GHz, within 0.4dB of the computer result. Simulation

results of the S11 bandwidth showed minimal (within 0.5dB) degradation over

100MHz and hence it is clear the S11 is not too localized around resonance. This

could obviously not be shown experimentally due to (6.15) but as simulation was so

close to experiment, it can safely be assumed. If lower levels of S11 are required, the

problem would have to be re-optimized with weights associated to the directivity


and S11 in (6.18).

The antenna produced H and E-plane radiation characteristics that can be

seen in Figure 6.16. In the azimuth, the antennas maximum gain reaches 8.08dBi.

Its front-to-back and front-to-null ratios are 10dB and 18.8dB respectively. This

pattern can be reproduced at 60 intervals through the azimuth due to antenna

symmetry. The main lobe is elevated at an angle of 4 above the horizontal. Cross

polarization patterns were measured and found to be below 14dB of the principal

lobe gain.

There is a clear agreement between the simulated and experimental results. Had

the cost function simulated the antenna with inconsistent error, the GA would have

converged on a simulated optimum rather than its true counterpart. The similar

ity between the simulated and experimental results conrm the cost function was

accurate and hence the chance of a single optimization run nding the optimum

solution was maximized. The simulated gain was degraded by 0.7dB when com

pared to experimental testing. However, this error was consistent over a number

of dierent tests and therefore would not have aected the optimization.

When the original antenna (Table 6.1) was optimized with respect to reactance

only, an experimental gain no greater than 6.7dBi was achieved (case 1). In addi

tion, the main lobe was elevated at 25. Conversely, regardless of the nite ground

plane, the optimized antenna has minimal lobe elevation and a gain of 8.08dBi.

This reduction in main-lobe elevation is seen as the likely reason for the increase in

azimuthal gain. To reject the possibility that the reactance-structure combination

uked a suppression of main lobe elevation, a further 10 random, non-optimized

reactance loading cases were tested. Principal lobe elevations were recorded be

tween 0 and 15 with a mean of 9.7. Horizontal gains were no less than 0.5dB of

the elevated gains. This is in contrast to the original antennas average elevation

of 25 with horizontal gains between 1dB and 1.6dB less than the elevated gains.

These results suggest the optimized structure of the antenna reduced the main lobe

elevation independent of the reactive loading.

While the structural optimization netted an increase in gain of approximately


90

8dBi

0

8

16 0

30

60120

150

180

210

240 300

330

270

(a) 0

8dBi

2

4

10

16

30

60

90

120

150210

240

270

300

330

180

(b)

Figure 6.16: Comparison of HFSS simulation (red) and experimental (blue) H-plane (a) and E-plane (b) radiation patterns at 2.4GHz of the antenna dened in Tables 6.4 and 6.5. HFSS Gain: 7.4dBi, experimental gain: 8.08dBi

6.6. SUMMARY 123

1.4dB over the reactive optimization, this could potentially translate to 2.8dB in a

system environment, which is equivalent to a signicant reduction in transmitter

power of approximately 48%. In addition, showing that an accurate structural

simulation works, has laid foundations for immersing the antenna in dielectric to

reduce it to a more practical size as has been proposed previously [103].

6.6 Summary

Loaded N port array theory is well known and documented. However, practical

implementation of the antenna has always been limited; usually only as a means of

theory validation. The ESPAR antenna is being developed specically for consumer

application and therefore its practicality requires consideration. Accordingly, the

ESPAR antennas utility for implementation in a communication system has been

investigated. Practical issues regarding the reactive loads were initially examined.

Varactor harmonic distortion was shown to be reduced by replacing a single var

actor with an anti-series pair. Varactors or their anti-series pair equivalents could

then be combined with dierent transmission lines to encompass the full reactance

range.

Testing and examination of a physical ESPAR structure followed. Simula

tion was used to perform a frequency sensitivity analysis of the ESPAR structure.

It showed that over an 8.1% bandwidth, the antenna had relatively stable gain,

front to null ratio and 3dB H-plane beamwidth possessing a maximum variation of

0.44dB, -3.8dB and 20 respectively for ve separate loading congurations. The

loading congurations were pre-optimized for practical radiation features which

therefore weighted their relative importance. Simulation procedure was validated

with experimental testing at resonance (2.4GHz).

Finally, the design of a horizontal gain optimized ESPAR antenna was pre

sented. The antenna was optimized with respect to gain to reduce interference and

transmission powers in a system. In a homogeneous network, any optimization

in the gain of an antenna will potentially have double the eect in the system.


Situated in a large solution space, a genetic algorithm was used for optimization

because of its robust nature. The GA employed a FEM based cost function in

order to obtain accurate modeling of the antenna. Both physical structure and

loading reactances were optimized. The nal antenna possessed a maximum gain

of 8.08dBi even though S11 was only -7dB at 2.4GHz. Average principal lobe

elevation angles were recorded at 9.7 for 10 random loading cases.

The author was involved in the ASVP testing and was subsequently an ancillary

author in its publication [104, 100, 101, 98]. The frequency sensitivity procedure

and results were presented at [71, 72] and the ESPAR optimized design has been

published [73].

05 Chapter 6

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