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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009 1171

Investigation Into the Relationship BetweenMicrostrip Patch Width and Efficiency

Siwen Yong and Jennifer T. Bernhard, Senior Member, IEEE

AbstractThe equation W = = 2 ( "r

+ 1 ) , which determinesthebest length for an efficient slot radiator, is frequently used to de-termine the best width for patch antenna efficiency. Even thoughno proof exists that efficient slot radiators yield the most efficientpatch antenna, this equation is still widely used in patch antennadesign. The goal of this investigation is to determine if patch an-tennas designed using the above-mentioned equation are indeedmost efficient. This is achieved by means of a parametric study in-corporating both simulation and measurement. Finally, it is shownthat efficiency is affected by both patch width and probe locationand the aforementioned equation doesnot determine the bestwidthfor efficiency.

Index TermsEfficiency, microstrip antennas.

I. INTRODUCTION

THE equation

(1)

is frequently used to determine the best width for patch antenna

efficiency [1][5]. This equation is derived from Schroeders

paper that uses (1) as a good physical length for a resonant slot

[6]. However, even though patch antennas are frequently mod-

eled as a transmission line sandwiched between two slots [7], no

proof exists that applying this approach yields the most efficient

antenna.

In the following section, the equations required to determine

total, radiation, and mismatch efficiency are presented. The var-

ious sources of loss in patch antennas are examined, along with

a discussion on the importance of microstrip patch width on effi-

ciency. Section III provides simulated radiation, mismatch, andtotal efficiencies for patches built on both high- and low-per-

mittivity substrates, while the effects of probe placement on ef-

ficiency are considered in Section IV. Finally, the results from

simulation are validated by comparing them to measurements in

Section V and a method is proposed to determine the best width

for efficiency in Section VI.

Manuscript received June 09, 2009; revised July 28, 2009. First publishedOctober 13, 2009; current version published November 10, 2009.

The authors are with the Electromagnetics Laboratory, Department of Elec-trical and Computer Engineering, University of Illinois at Urbana-Champaign,Urbana, IL 61801 USA (e-mail: jbernhar@illinois.edu).

Digital Object Identifier 10.1109/LAWP.2009.2034477

II. TOTAL, RADIATION, AND MISMATCH EFFICIENCY

The total efficiency of an antenna, which is defined as the

amount of power radiated by the antenna as a fraction of the

power available from the feed network, can be found by [2]

(2)

Therefore, in order to ascertain if an antenna is efficient, it is

necessary to determine both its radiation and mismatch efficien-

cies separately. A discussion of these efficiencies is in order and

is included below.

Typically, radiation, conductor, dielectric, and surface wave

losses exist in microstrip patch antennas. Therefore, radiation

efficiency is expressed as

where is the radiated power, is the surface wave power,

is the power loss in the dielectric, and is the power loss

in the conductors. In order to simplify the calculation of radi-

ation efficiency, several authors [8][10] assumed that surface

wave losses are dominant. Consequently, dielectric and con-

ductor losses were neglected and radiation efficiency was found

as , which is frequently referred toas surface wave efficiency. Subsequently, it was suggested that

radiation efficiency of patch antennas is independent of width

[8][11]. However, for the thin substrates used in this study, sur-

face wave losses are less significant [2], [10], and radiation ef-

ficiency was determined using the equation [10]

(3)

where is the radiation resistance and is the loss resis-

tance at the input terminals. Both and are found to be

dependent on width [12], [13].Finally, others [8][11] claim that the radiation efficiencies of

patch antennas are primarily dependent on dielectric thickness

and not patch width. Pozar [10] proposes that for a given power

level, fields are more concentrated for thin substrates than thick

substrates and more power is lost due to dielectric heating in thin

substrates, resulting in poorer radiation efficiency. However, the

same analysis must hold when comparing a wider patch antenna

to a narrower one, and patch width should affect radiation effi-

ciency significantly.

In addition to the losses present in the antenna structure itself,

power may be lost if the feeding network and the antenna are

not conjugate-matched. The fraction of incident power that is

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1172 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009

transmitted to the antenna is defined as the mismatch efficiency

and may be determined by the equation

(4)

Finally, once both mismatch and radiation efficiencies have beenfound, the total efficiency of an antenna can be calculated by

employing (2).

III. SIMULATED RESULTS

In this section, simulation data from patches built on Rogers

Duroid 6010 substrate and Rogers Duroid 5880 substrate are

presented. Patches built on Duroid 6010 substrate had

, a thickness of 2.54 mm, a loss tangent of 0.023, and were

designed to operate at 750 MHz. Patches built on Duroid 5880

substrate had , a thickness of 3.175 mm, a loss tangent

of 0.009, and were designed to operate at 1.62 GHz. The sub-

strates were chosen to determine if (1) predicts the best width forefficiency for low- or high-permittivity substrates. In addition,

the frequencies were chosen to keep approximately constant

in both experiments.

The variation of radiation, mismatch, and total efficiencies

with patch width was studied using both high- and low-per-

mittivity substrates in order to determine if substrate permit-

tivity had any effect on efficiency. Antennas built on Rogers

Duroid 6010 substrate were designed to operate at 750 MHz

with a width of 84.52 mm as determined from (1). The probe

was placed 20 mm from the edge of the patch along the length.

The patch length was 62.56 mm from [14][17] and remained

unchanged throughout the experiment. To extract the simulatedradiation efficiencies, two sets of simulations were run using

HFSS [18]. The first set of simulations was run using perfect

electric conductors (PECs) with lossless dielectric. This yielded

the radiation resistance referred to the input ( ). The second

set of simulations was run using copper for the patch and ground

plane, and the loss tangent of the substrate was included as well.

The input resistance would be the resistance from both radiation

and loss referred to the input ( ). If , the antenna

may be modeled as a series circuit and

(5)

Conversely, if , the antenna may be modeled as a

parallel circuit and

(6)

[19], [20] where and are the radiation and input con-

ductances referred to the input, respectively. All simulated radi-

ation efficiencies determined using this method fall below unity,

unlike radiation efficiencies determined by HFSS antenna pa-

rameters calculations, which may be nonphysical since they fre-

quently rise above unity.

Finally, mismatch and total efficiencies were calculated using

(4) and (2), respectively. Simulated efficiencies for patch widthsvarying from 50 to 120 mm were determined. The widths were

Fig. 1. Simulated efficiencies for patch antennas of varying widths built onRogers Duroid 6010 substrate with " = 1 0 : 2 and probe placed 20 mm fromthe edge of the patch along the length. All widths are normalized by .

normalized by as determined by [3] and range from 0.371

to 0.911. The efficiencies were extracted at a frequency of

732.9 MHz, which was the frequency of best impedance match

at the nominal width of 84.52 mm, which was normalized to

0.637. The results of the study are presented as Fig. 1.

Fig. 1 indicates that both radiation and mismatch efficien-

cies peak at different widths. In addition, Fig. 1 indicates that

total efficiency peaks at a normalized width of 0.718, while mis-

match efficiency peaks at 0.637, thus illustrating the importance

of considering both radiation and mismatch efficiency in the de-

termination of total efficiency. Furthermore, Fig. 1 indicates that

radiation efficiency peaks at a normalized width of 0.873. There-

fore, (1) fails to predict the best width for radiation or total ef-

ficiency.

Closer examination of Fig. 1 indicates that radiation effi-

ciency fluctuates with increasing widths. An explanation is thatas patch width increases, fringing at the radiating slots decreases

and less power is lost through radiation, resulting in a decrease

in radiation efficiency. However, increasing patch width also

results in less current crowding and less concentrated fields,

yielding decreases in both conductor and dielectric losses and,

consequently, an increase in radiation efficiency. As a result of

these competing processes, radiation efficiency fluctuates with

increasing patch width and does not stay constant as proposed

in [8][11].

The variation of efficiency with patch width was studied using

Rogers Duroid 5880 substrate as well. At a nominal frequency

of 1.62 GHz, the antenna had a length of 59.7 mm, a width of73.2 mm, and the probe was placed 7 mm from the edge of

the patch. Efficiencies were extracted for patches with widths

from 55 to 105 mm at a frequency of 1.6505 GHz, which was

the frequency of best impedance match at the nominal width.

Similar to Fig. 1, the widths in Fig. 2 were normalized by

and range from 0.435 to 0.84. The nominal width of 73.2 mm

was normalized to 0.582.

Similar to Fig. 1, Fig. 2 indicates that mismatch and radiation

efficiencies peak at different widths. However, since mismatch

efficiency is poorer than radiation efficiency at all widths, mis-

match efficiency acts as an envelope for total efficiency. In addi-

tion, Fig. 2 indicates that the best width for radiation efficiency

is at 100 mm, and not the nominal width of 73.2 mm as pre-dicted by (1).

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YONG AND BERNHARD: RELATIONSHIP BETWEEN MICROSTRIP PATCH WIDTH AND EFFICIENCY 1173

Fig. 2. Simulated efficiencies for patch antennas of varying widths built onRogers Duroid 5880 substrate with " = 2 : 2 and probe placed 7 mm from theedge of the patch along the length. All widths are normalized by .

Fig. 3. Simulated radiation, mismatch, and total efficiencies for patch antennasof width 84.52 mm with " = 1 0 : 2 and varying probe placements. All probelocations are normalized by L .

A comparison of Figs. 1 and 2 indicate that radiation efficien-

cies are higher in Fig. 2 than in Fig. 1. The fluctuations in radia-

tion efficiency are also smaller. A possible explanation is due to

the loss tangent of Duroid 5880 being much lower than that for

Duroid 6010. Therefore, dielectric loss is a more significant loss

mechanism in antennas built on Duroid 6010 substrate. Conse-

quently, radiation efficiencies should be higher in antennas builton Duroid 5880 and experience less fluctuation. In addition, it

is unlikely that these fluctuations are due to changes in surface

wave power since Perlmutter et al. investigated the relationship

between surface wave efficiency and microstrip patch width and

found them to be independent [9]. Therefore, this study illus-

trates the importance of examining both radiation and mismatch

efficiency when determining the best width for patch antenna ef-

ficiency, especially in substrates with higher loss.

IV. EFFECT OF PROBE PLACEMENT ON EFFICIENCY

The effect of probe placement on radiation, mismatch, and

total efficiencies was studied, and simulation results are pre-sented inFig. 3. The patch had a width of 84.52 mm and a length

of 62.56 mm. The dielectric used was Rogers Duroid 6010 sub-

strate, and the probes were placed at 10, 12, 16, 20, and 24 mm

along the length of the patch referenced to the edge. The probe

locations presented in the figure were normalized by the patch

length .

Fig. 3 indicates that mismatch, radiation, and total efficiencies

are all affected by probe placement. In addition, mismatch and

radiation efficiency both peak at different probe locations. The

changes in radiation efficiency may be explained using the trans-

mission line model. Unlike radiation resistance or conductance,

which is modeled as loads at the ends of the transmission line,

dielectric and conductor losses are distributed along the trans-mission line. Therefore, changing the placement of the probe

Fig. 4. Simulated and measured total efficiency for patches built on Duroid6010 substrate. All widths are normalized by .

causes changes of different magnitudes to the input values of

loss and radiation resistance, resulting in changes in radiation ef-

ficiency. Therefore, when determining the probe placement for

highest efficiency, the antenna engineer should not only be con-

cerned with mismatch efficiency, but also radiation efficiency.

V. SIMULATED AND MEASURED TOTAL EFFICIENCY

In order to validate our simulation data, patches were built

on Duroid 6010 substrate and the total efficiencies were mea-

sured and compared to simulation data. In measurement, radia-

tion efficiency at each width was determined using the Wheeler

cap method [19], [20]. Mismatch and total efficiencies were ob-

tained by (4) and (2), respectively. Good agreement between

simulated and measured data as indicated in Fig. 4 suggests that

the methodology used to extract patch antenna efficiency in sim-

ulation may be used to predict measured efficiency well.

In the cases considered here, it does not appear that substrate

anisotropy is significant in changing the effective patch widthor the efficiency, given that the simulations using isotropic ma-

terials agree well with measurements. However, in cases where

the substrate does possess anisotropy, the resonant conditions

and effective patch width could be affected [21], [22], leading

to changes in total efficiency. Also, the antennas radiation pat-

terns do not change appreciably with changes in patch width or

probe placement since the antennas are all operated in their fun-

damental mode.

VI. PROPOSED PATCH DESIGN METHOD

The results of this study indicate that mismatch and radiation

efficiencies often do not peak at the same width or probe loca-tion. However, in order to design the most efficient patch, patch

parameters must be found such that total efficiency, which is

the product of mismatch and radiation efficiencies, is highest.

We propose that total efficiency is highest when the resonant

frequency and the frequency of best match intersect for a par-

ticular patch width. A plot of the simulated resonant frequency

and frequency of highest impedance match for multiple widths

for patches built on Duroid 5880 substrate is presented in Fig. 5.

Similar to Figs. 1 and 2, all widths are normalized by . The

nominal width of 73.1 mm was normalized to 0.582.

Fig. 5 indicates that the two frequencies are closest for a nor-

malized width of 0.9, thus suggesting that this would be the best

width for efficiency, and not the width predicted by (1). This isconfirmed by a plot of total efficiency against width as indicated

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1174 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009

Fig. 5. Simulated frequencies of resonance and best match for patches built onDuroid 5880 substrate.

Fig. 6. Simulated total efficiency at resonance and best match frequencies forpatches built on Duroid 5880 substrate.

in Fig. 6. Again, these observations agree with measured data.

An identical study was done with patches built on Duroid 6010

substrate with similar results.

The agreement of simulation and measurement data indicates

that simulations can be used to predict the best width for effi-ciency. However, instead of simply varying the width and probe

location to minimize return loss as is frequently done in mi-

crostrip patch antenna design, it is also necessary to ascertain if

the antenna is resonant. The results of our study suggest that the

efficiency of a microstrip patch is highest only when both these

conditions are satisfied. Therefore, antennas designed using em-

pirical formulas such as those derived by Kara with considera-

tion only to return loss may achieve good mismatch efficiency

without good radiation efficiency [4], [5]. Consequently, the

total efficiency of the antenna may still be poor.

VII. CONCLUSION

This study indicates that there are widths where radiation,

mismatch, and overall efficiency peak and (1) does not do a good

job of determining the optimal width for efficiency. In addition,

it was determined that mismatch and radiation efficiencies peak

at different widths, and it is important to consider both to maxi-

mize total efficiency. Furthermore, the results of the study indi-

cate that probe placement affects not only mismatch efficiency,

but radiation efficiency as well, and this variation may be ex-

plained using the transmission line model. These results were

validated through measurement. Finally, our data indicates that

in order to determine the best microstrip patch width for effi-

ciency, the antenna engineer should pick the width at which the

resonant and best match frequencies are coincident. This can be

done through simulation before fabrication of the antenna itself.

ACKNOWLEDGMENT

The authors thank Rogers Corporation for providing the sub-

strate materials used in this work.

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