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Micro-strip Patch Antenna Primer J P Silver

E-mail: john@rfic.co.uk

1 ABSTRACT This paper discusses the theory and design of micro-strip patch antennas. The pertinent design parameters are given together with their relevant equations to al-low basic ‘hand’ calculations before simulation is at-tempted. Finally a worked example is given to high-light the design steps required and CAD simulations are also described.

2 INTRODUCTION Proposed by Deschamps in 1953, and the first patch an-tenna was fabricated in the early 1970’s. A microstrip patch consists of a radiating patch of any planar geometry (eg Circle, square, Ellipse, ring and rec-tangle) on one side of a dielectric material substrate backed by a ground plane on the other side. A typical patch antenna is shown in Figure 1. Radiating Patch

Conducting Ground Plane

Dielectric Substrate

Figure 1 Basic features of a patch antenna

Generally, a substrate with a low dielectric constant (εr) is used (typically ~ 2.5) to reduce the fringing fields, but in loss critical applications, Alumina (εr =10) must be used. Table 1 highlights the advantages and disadvantages of patch antennas – the main disadvantage being the narrow bandwidth. Advantages Disadvantages Lightweight, low volume Narrow bandwidth Easy to mount Loss Low fabrication cost Poor end-fire radiation

characteristics Aerodynamic (good for fitting on missiles and ships

Very limited maximum gain

Linear and circular polariza-tion easy to implement by

Poor isolation between feed and antenna

position of feed Dual frequency use possible Low power handling Solid-state devices easily in-tegrated

Feed lines and matching fab-ricated with antenna

Table 1 Advantages and disadvantages of patch anten-nas.

3 FEED ARRANGEMENTS Figure 2 shows various ways to feed patch antennas, ca-pacitive-coupling of the various design is popular.

4 RADIATION MECHANISM The important characteristic of microstrip antennas is their inherent ability to radiate efficiently despite their low pro-file. The primary source of this radiation is the electric fringing fields between the edges of the conductor ele-ment and the ground-plane behind it. Lewis[1] first analysed this in the form of a transmission line discontinuity and he discovered that the Q (quality factor) of the dielectric cavity formed by two short circuit walls and four open circuit walls depended on several parameters. The parameters are dielectric constant (εr), height (h) of the substrate, the patch dimensions and the frequency. The results showed that at high frequency, radiation loss as opposed to conductive or dielectric loss is the main source of energy dissipation. The electric field patterns of a square patch antenna are shown in Figure 3.

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Gap Coupled Feed

Quarter-wave Match Feed

λ/4

Non-radiating edge feed

Inset Feed

Probe Coupling Feed

Patch

Coaxial Connector

Substrates

Feedline

Aperture

Patch

Aperture Coupling

EM Coupling

Ground Plane

Feedline

Radiating Patch

Substrates

Figure 2 Patch antenna feed arrangements

~λ/2

hεr

Radiating Patch

Conducting Ground Plane

Dielectric Substrate (εr)

h

Feed L

W ~λ/2

Figure 3 Rectangular microstrip patch antenna electric field patterns.

The E field is considered to be constant along W and var-ies sinusoidally with L. The fringing fields at the two edges add in phase in the far field on ‘boresight’ (the vector normal to the plane of patch) and cancel along the broadside. The radiation patterns for the TM mode are shown in Figure 4. For a/b = 1.5, εr = 2.32 and 9.8. These patterns are of par-ticular interest since they provide maximum radiation on bore sight.

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EΦ

0 -10 0-10

Er = 9.8 Er = 2.32

dB

Eθ

0 -10 0-10

Er = 9.8 Er = 2.32

dB

Φ θ

Figure 4 Radiation Patterns

Looking at the radiation patterns it is clear that the effi-ciency of the patch antenna (ie the directivity) is poor. When designing these antennas, emphasis is placed on trying to maximize efficiency at the expense of gain or radiation pattern.

5 LOSSES The antenna is a resonant circuit therefore, energy will be stored in the system. This energy stored is inversely pro-portional to the dielectric height h. We can also describe the energy stored by the parameter Q (known as Quality Factor). Losses in the antenna will allow energy to leak away and such an antenna will have a lower Q factor. The Q factor can be calculated from the following equa-tion:

small)(very loss wavesurface Psw andLoss.Conductor Pc

Loss. Dielectric Pdradiation.gh lost throuenergy Pr

cavity. in theenergy stored h1.tW

frequency.resonant rfWhere

PswPcPdPrh1.t.Wr.f2

Q

====

=⎟⎠⎞

⎜⎝⎛

=

+++

⎟⎠⎞

⎜⎝⎛

=π

The antenna efficiency is given by:

( ) %100 x PrPcPd

Pr %++

=η

Typically η can be between 80 to 90% for a patch antenna with a dielectric constant of 2.3 at 10GHz. Losses reduce the Q factor, which results in an increased bandwidth and reduced efficiency. Typical Q factors are in the range 20-200 and the band-width is given by:

VSWR s

WheresQ1)-100(s B.W

=

=

6 MODELLING Two models commonly used for analyzing patch antennas are the Transmission Line model and the Cavity model. (1) Transmission Line Model The structure is considered as a transmission line along the line joining the radiating apertures loaded by imped-ances at it’s radiating edges. The radiating wall may be characterised by an equivalent admittance, the suscep-tance being due to the fringing field and the conductance due to the radiation loss. The transmission line model is shown in Figure 5.

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G jB

G

λ/2

jB

Figure 5 Transmission line model of a patch antenna

(2) Cavity Model The region between the patch and the ground plane may be treated as a cavity, bounded by magnetic walls on the sides and electric walls on the top and bottom. The modes in this cavity are given by:

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛=

≤≤≤≤⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

∂∂

=∂∂

=

=

=+∂∂

+∂∂

2

2

2

2

22

2

2

2

am

bn.

.

integers postive are m andn where

b y 0 and a x 0 by..mcos

ax..mcos.EoEz

..j- Hy and .

.j Hx

allsboundary wat 0 Ez ,conditionsboundary Applying

equation) (Helmholtz 0Ez...yEz

xEz

µεπω

ππ

µωµω

ωµε

xEz

yEz

7 DESIGN PROCEDURE (1) Element Width The first design step is to choose a suitable dielectric sub-strate of appropriate thickness. The three most common substrate materials used are rexolite (εr = 2.6), RT Duroid (εr = 2.32) and Alumina (εr = 9.8). Element width is given by the following equation:

Tm/Aπ.x104o

/NmC109.8o

constant dielectric RelativerεFrequencyResonant Fr

Where

1rε2

o.o2.Fr.c W

7

2212

−

−

=

=

==

+=

µ

ε

µε

x

W is usually chosen to be in the range 1 <= L <= 2. Referring to Figure 6, the length of the resonant element is then obtained from:

l∆−= 2o.o.eff2.Fr.

c Lµεε

For a dielectric substrate of thickness h, an antenna oper-ating frequency of Fr, and for an effective radiator, a prac-tical width W is:

( )

( ) ⎟⎠⎞

⎜⎝⎛ +−

⎟⎠⎞

⎜⎝⎛ ++

=8.0258.0

264.03.0412.0

h∆l

hW

hW

eff

eff

ε

ε

~ λ/2

L∆l ∆l

Figure 6 Length of resonant element

(2) Radiation Pattern For two slots spaced by a distance L apart, the E and H plane radiation patterns may be plotted using the equa-tions:

( )

( ) Plane)-(E cos2

Ko.hcoscos

2Ko.h

cos2

Ko.hsinF

2Ko Plane)-(H sincos

2Ko.h

cos2

Ko.WsinF

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

=

=⎟⎠⎞

⎜⎝⎛

=

φφ

φφ

λπθ

θ

θθ

(3) Slot Susceptance

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The slot susceptance can be represented by a capacitance C:

impedance sticcharacteri theis Zo WhereC.Zol

C effε∆=

(4) Input Admittance The input impedance or admittance should be accurately known so that a good match between the element and the feed can be designed. Referring to Figure 7. The distance of the feed entry point to the edge of the patch (z) is given by:

( ) ( ) ( )

Rr1 G ;

olk. B ;

o2

Zo1 Yo

Where

1.2sin

YoBsin

YoBG.cos2GYin(z)

effeff

22

222

=∆==

=

−⎥⎦

⎤⎢⎣

⎡−

++=

Z

zzz

ελεπβ

βββ

z

W

L Patch

Feedline

Figure 7 Feed position on patch antenna

(5) Radiation Resistance/Conductance

λoW.

1201 Gr λo W

2

λoW.

901 Gr λo W

Wλo120. Rr λo W

Wλo90. Rr λo W

For

2

2

=≥

⎟⎠⎞

⎜⎝⎛=≤

=≥

=≤

(6) Probe position[1] The equations given for calculating the feed position are very complicated but can be simplified to give a starting point for computer simulation.

( ) 5section from that isGr WhereGGr2

1R12

IN ±=

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However G12 is complicated and is given by:

( )

zero.order of kindfirst theoffunction Bessel theis Where

sinsin.cos

cos2

sin

1201G 3

0212

Jo

dLKoJo

KoW

θθθθ

θ

ππ

∫⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡⎟⎠⎞

⎜⎝⎛

=

Luckily G12 << Gr and so in most cases can be ignored. We find that Rin is given by:

( ) ( )

( )

( )

radiansin Calculate eConductanc RadiatingGr

patch ofLength Ledgepatch from feed ofposition yo

Where

.L

2sin1Gr.21

)(2sin1)(cos

.L

cosGr.21

G Gr as

.L

cosGGr2

1

2

2

12

2

12

Note

yoyoyRin

xx

yoyoyRin

yoyoyRin

===

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−==

∴−=

⎟⎠⎞

⎜⎝⎛==

>>

⎟⎠⎞

⎜⎝⎛

±==

π

π

π

(7) Q Factor and Losses The quality factor (Qr) associated with the radiation resis-tance is:

( )( )4.Fr.hC.

Qr effε=

The equivalent resistances for the conductor loss Rc and dielectric loss Rd are then:

RcRdRr Rt Where

RrQr.Rt Qt

isQt factor quality total theand

Qr.L.Wλoh..

Er30.tan Rd

GHz)in (Fr .QrWL.Fr0.00027Rc

2

2

++=

=

∂=

=

(8) Antenna Efficiency The efficiency (which increases as h increases) may be expressed in terms of the equivalent resistances.

100 * RtRr%η =

(9) Bandwidth The bandwidth may be increased by increasing the induc-tance of the radiators by cutting holes or slots in them or by adding reactive components to improve the match of the radiator to the feedline. (10) Directivity and Gain The directivity (D) of the antenna is defined as the ratio of the maximum power density in the main beam to the aver-age radiated power density. The gain G is given by:

η.DG= The gain increases with resonant frequency and h and decreases with increase in εr. The directivity is independ-ent of the resonant frequency. (11) Beamwidth The half power beamwidth is equal to the angular width between directions where the gain decreases by 3dB, or the radiated field reduces to ½ of the maximum value. The half power beamwidths in the H and E planes are given by:

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( )⎟⎟⎠⎞

⎜⎜⎝

⎛

+=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛ +

=

−

−

22o

22o

1BE

o

1BH

hkL3.k03.7cosθ

2.Wk12

1cos.2θ

Thus beamwidth can be increased by choosing a smaller element, thus reducing W and L. For a given resonant frequency these dimensions may be changed, by selecting a substrate having a higher relative permittivity. As beamwidth increases, element gain and directivity de-crease, however, efficiency is unaffected.

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8 EXAMPLE For this example we shall design a patch antenna for re-ception of Meteosat WEEFAX at 1691MHz Channel 1 and 1694.5MHz for channel 2 . The patch will be used as a feed for a ‘TV’ offset feed dish and therefore, we re-quire a patch that will have a wide beamwidth to provide optimum illumination of the dish. The frequencies of 1691MHz and 1694.5MHz which equates to a very narrow bandwidth of 0.002%, and there-fore, we can optimize the design to produce as much gain as possible. Before we analyse the design using Agilent Momentum (part of ADS) we need to perform some hand calcula-tions. Design considerations: We want a cheap design so we could design a patch using an air dielectric or use inexpensive PTFE RT Duroid. To achieve high gain we need to use a low dielectric con-stant (εr (air) =1 or εr=2.3 (RT Duroid 5880) and large h (RT Duroid 5880 is available with a maximum thickness of 3.185mm). The completed antenna will feed an LNA designed to work with a 50-ohm input impedance, so the feed design could be a quarter-wave transformer, insert feed or a probe coupling. For this design RT Duroid 5880 was used and we select the channel 1 frequency of 1691MHz. Eeff ~ 1.898 (1) Patch Width (W)

Tm/Aπ.x104o

/NmC8.9x10o

constant dielectric RelativerεFrequencyResonant Fr

Where6.98cm W

12.22

π.x104.8.9x10.2.1.691x101 W

1rε2

o.o2.Fr.1 W

7

2212

7129

−

−

−−

=

=

==

=

+=

+=

µ

ε

µε

(2) Patch Length (L)

6.43cm 1.898.10x691.1.2

10x32.Fr.

c L9

8

eff

===ε

However L will be slightly shortened due to the end effect:

( )

( )

( )

( )

6.086cm 2(1.72) - 64.3 L modified Therefore,

1.72mm ∆l

3.175x10).312.1(412.0 ∆l )312.1(412.0h∆l

8.03.175x10

06.0258.0858.1

264.03.175x10

06.03.0858.1412.0

h∆l

8.0258.0

264.03.0412.0

h∆l

3

3

3

==

=

=∴=

⎟⎠⎞

⎜⎝⎛ +−

⎟⎠⎞

⎜⎝⎛ ++

=

⎟⎠⎞

⎜⎝⎛ +−

⎟⎠⎞

⎜⎝⎛ ++

=

−

−

−

hW

hW

eff

eff

ε

ε

(3) Approximate position of probe/feedpoint (yo) The very approximate relationship between input resis-tance (Rin) and probe position (yo) is given by the follow-ing:

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radiansin calculate Note .yoLπ2.sin1

21

G11

.yoLπcos

G11 Rin

1.719E

2

E691.13E

6.98E.901 G

2

λoW.

901 G λo WAs

λoW.

1201 G λo W

2

λoW.

901 G λo W

For

2

3-

9

8

2-

1

1

1

1

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−=

⎟⎠⎞

⎜⎝⎛≈

=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=

=⎟⎠⎞

⎜⎝⎛=≤

=≥

⎟⎠⎞

⎜⎝⎛=≤

Ω≈

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−

=

−

50Rin

.2160.8π2.sin1

E719.1.21

21mmyo Assume

3

These values were then simulated and optimized (for in-put match) using Momentum within Agilent ADS.

9 MOMENTUM ANALYSIS Now we have a basic design we can check it using an EM simulator and for this we will use ADS Momentum. The following steps are required to enter the layout of the patch antenna, the substrate details and the frequency of operation. (1) Layout Using the layout window, draw the patch antenna on the upper conductor layer. Add the lower conductor (ie the boundary of the patch PCB) and add a port to the point where the feed will be (on the upper conductor layer). (2) Substrate details Open the create/modify substrate dialogue box and under substrate layers enter the following data: For the layer between Freespace and ground enter

Substrate layer Name: RT5880 Thickness: 3.175mm, Permittivity: 2.2, Loss Tangent: 0.001, You should see FREESPACE RT5880 //////GND//////// Under Metallisation layers click on the dotted layer under freespace and select ‘strip’. You should see FreeSpace ------Strip Upper Conductor RT5880 //////GND//////// Finally, precompute (3) Port definition Open the Port Properties Editor and select the port on the layout. Select 50-ohms, Internal port and select OK. (4) Mesh Select setup mesh and enter the highest simulation fre-quency used eg 1.7GHz. Then pre-compute mesh which, should appear as shown in Figure 8.

Figure 8 Computed mesh and port. (Patch size L = 5.83cm, W = 5.89cm – optimized)

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(5) Frequencies Select simulation – S-parameters and add start and stop frequencies 1.65 and 1.7GHz. Select update, apply and finally simulate. (6) Results The position of the test port was moved from the center of the patch antenna to the edge, until a good input return loss was obtained as shown in Figure 9. The center fre-quency, was optimized for 1.691MHz, by adjusting L and W to be 5.83cm and 5.89cm respectively.

Figure 9 Input return loss prediction

Momentum can also produce the radiating fields in 2D and 3D views. The 2D view of gain and efficiency is shown in Figure 10.

Figure 10 Predicted gain (dB) and efficiency for the patch antenna.

10 REFERENCES [1] Antenna Theory, C.Balanis, Wiley, 2nd edition (1997), Chapter 14. ISBN 0-471-59268-4.