Microstrip Antennas Part 2 pptx

In the case of a CP microstrip antenna an innovative radiation efficiency analysis using the Wheeler cap method was presented in Nascimento & Lacava, 2009.. 1989, Microstrip patch antenn

Design of Low-Cost Probe-Fed Microstrip Antennas 19 and a 75-mm square ground plane was designed using the HFSS software for operation at 1.603 GHz The optimized antenna dimensions are shown in Fig 28(a), the simulated input impedance and axial ratio results are presented in Fig 28(b) and the reflection coefficient magnitude in Fig 29 As expected, the microstrip antenna with the new geometry exhibits very good AR (0.1 dB) and reflection coefficient magnitude (-48 dB) characteristics at 1.603 GHz, without the need for any external matching network

1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 -30

-25 -20 -15 -10 -5 0

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

mobile-terminals require two radiators The first is designed for uplink frequencies (Tx - 1.61073 to 1.62549 GHz) while the other receives the downlink ones (Rx - 2.48439 to 2.49915 GHz) (Nascimento et al., 2007a) The antenna geometry and a photo of the prototype are shown in Figs 30(a) and (b), respectively

The optimized antenna dimensions (using the HFSS software) are presented on Table 2 for the

radiators designed on finite ground plane and dielectric (L = 140 mm; W = 85 mm)

x y

The axial ratio and reflection coefficient magnitude are presented in Figs 31 and 32 for the

Tx and Rx antennas, respectively

0 1 2 3 4 5 6 7 8 9

-55 -50 -45 -40 -35 -30 -25 -20 -15 -10

Fig 31 Globalstar antenna axial ratio and reflection coefficient magnitude: Tx radiator

Design of Low-Cost Probe-Fed Microstrip Antennas 21

0 1 2 3 4 5 6 7 8 9

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5

Fig 32 Globalstar antenna axial ratio and reflection coefficient magnitude: Rx radiator Results for the input impedance on the Smith chart are presented in Figs 33 and 34 for the

Tx and Rx antennas, respectively These results indicate that the antenna meets the Globalstar specifications

-10j 10j

-25j 25j

1.540 GHz

1.696 GHz 1.618 GHz

Fig 33 Globalstar antenna input impedance: Tx radiator

10 25 50 100 250 -10j

10j

-25j 25j

2.492 GHz

2.210 GHz 2.774 GHz

Fig 34 Globalstar antenna input impedance: Rx radiator

5.3 CP antenna radiation efficiency measurements

The radiation efficiency of a LP microstrip antenna can be efficiently measured using the

Wheeler cap (Choo et al., 2005; Pozar & Kaufman, 1988; Sona & Rahmat-Samii 2006)

According to Wheeler, the radiation resistance of an antenna can be separated from its loss

resistance by enclosing the antenna with a radiation shield cap placed at a distance greater

than λ/(2π) (Wheeler, 1959) Consequently, since a linearly-polarized microstrip antenna can

be modeled as a parallel RLC circuit, its efficiency is calculated by

where G cap is the conductance of the admittance measured with the cap in place and G out is

the conductance of the admittance measured with the cap removed

In the case of a CP microstrip antenna an innovative radiation efficiency analysis using the

Wheeler cap method was presented in (Nascimento & Lacava, 2009) This procedure is

discussed next, for the case of the Glonass antenna designed in Section 5.2.1

Differently from the standard design, the two orthogonal resonant modes in the new

approach are now asymmetrically positioned in relation to the frequency for optimal axial

ratio as presented in Fig 28 (b) In addition, at the lower resonant frequency (1.468 GHz), its

15.45-dB axial ratio shows the antenna tends to be linearly polarized around this frequency

This result supports the use of the Wheeler cap method for measuring the antenna radiation

efficiency at this frequency

The cap geometry is shown in Fig 35 where the radiator is positioned inside a cubic cavity

of electrically conducting walls of 270-mm internal dimension

Design of Low-Cost Probe-Fed Microstrip Antennas 23

Fig 35 Geometry of the Wheeler cap simulation through the HFSS package

HFSS simulation results for the real part of the input impedance are presented in Fig 36, both with and without the cubic cavity Making use of equation (11) for the lower resonant mode (G cap = 1.92 mS and G out = 7.43 mS), the radiation efficiency computed from the Wheeler method is 74.16% The free-space radiation efficiency, computed with the HFSS package is 74.68% at 1.468 GHz, which is only 0.7% off Consequently, the Wheeler cap method can be used for accurately determining the radiation efficiency of TCRP radiators

0 60 120 180 240 300 360 420 480

methodologies are based on properties of the antenna equivalent circuit, they can be applied

to the design of microstrip radiators of arbitrary patch shapes Moreover, it is not restricted

to low-cost substrate thus applying equally well to the design of LP or CP microstrip

patches printed on any moderately thick commercial microwave laminates Experimental

results for LP and CP radiators validate the design strategies for both the LP and CP cases

Moreover, the Wheeler cap method is shown to be an effective means for simulating the

radiation efficiency of CP microstrip antennas

The excellent practical results obtained when matching microstrip patch radiators to a 50-Ω

SMA connector can be readily extended to the synthesis of inductive or capacitive input

impedances, as for example in the case of optimization of the noise figure and stability of

low-noise power amplifiers connected directly to the antenna Another possible application

is the design of low-cross-polarization probe-fed microstrip arrays (Marzall, et al., 2009;

Marzall et al., 2010)

7 References

Alexander, M J (1989) Capacitive matching of microstrip antennas IEE Proceedings of

Microwaves, Antennas and Propagation, Vol 137, No 2, (Apr 1989) (172-174), ISSN:

0950-107X

Chang, F S & Wong, K L (2001), A broadband probe-fed patch antenna with a thickened

probe pin, Proceedings of Asia-Pacific Microwave Conference, (1247-1250), ISBN:

0-7803-7138-0, Taipei, China, Dec 2001

Chen, H M.; Lin, Y F.; Cheng, P S.; Lin, H H.; Song, C T P & Hall, P S (2005), Parametric

study on the characteristics of planar inverted-F antenna IEE Proceedings of

Microwaves, Antennas and Propagation, (Dec 2005) (534-538), ISSN: 1350-2417

Choo, H.; Rogers, R & Ling, H (2005), Comparison of three methods for the measurement

of printed antennas efficiency, IEEE Transactions on Antennas and Propagation, Vol

53, No 7, (Jul 2005) (2328-2332), ISSN: 0018-926X

Dahele, J S.; Hall, P S & Haskins, P M (1989), Microstrip patch antennas on thick

substrates, Proceedings of Antennas and Propagation Society International Symposium,

pp 458-462, San Jose, CA, USA, Jun 1989

Engest, B & Lo, Y T (1985), A study of circularly polarized rectangular microstrip

antennas, Technical Report, Electromagnetics Laboratory, University of Illinois

Gardelli, R.; La Cono, G & Albani, M (2004), A low-cost suspended patch antenna for

WLAN access points and point-to-point links, IEEE Antennas and Wireless

Propagation Letters, Vol 3, (2004) (90-93), ISSN: 1536-1225

Garg, R.; Bhartia, P.; Bahl, I & Ittipiboon, A (2001) Microstrip Antenna Design Handbook,

Artech House, ISBN: 0-89006-513-6, Boston

Hall, P S (1987) Probe compensation in thick microstrip patches. Electronics Letters, Vol 23,

No 11, (May 1987) (606-607), ISSN: 0013-5194

Haskins, P M & Dahele, J S (1998), Capacitive coupling to patch antenna by means of

modified coaxial connectors, Electronics Letters, Vol 34, No 23, (Nov 1998)

(2187-2188), ISSN: 0013-5194

HFSS (2010), Product overview, Available: http://www.ansoft.com/products/hf/hfss/, (Sept 2010)

Design of Low-Cost Probe-Fed Microstrip Antennas 25 IEEE Std 145 (1993) IEEE Standard Definitions of Terms for Antennas, ISBN: 1-55937-317-2,

New York, USA

James, J R & Hall, P S (1989) Handbook of Microstrip Antennas, Peter Peregrinus, ISBN:

0-86341-150-9, London

Lee , K F & Chen, W (1997) Advances in Microstrip and Printed Antennas, John Wiley, ISBN:

0-471-04421-0, New York

Lumini, F.; Cividanes, L & Lacava, J C S (1999), Computer aided design algorithm for

singly fed circularly polarized rectangular microstrip patch antennas, International Journal of RF and Microwave Computer-Aided Engineering, Vol 9, No 1, (Jan 1999)

(32-41), ISBN: 1096-4290

Marzall, L F., Schildberg, R & Lacava, J C S (2009), High-performance,

low-cross-polarization suspended patch array for WLAN applications, Proceedings of Antennas and Propagation Society International Symposium, pp 1-4, ISBN: 978-1-4244-3647-7,

Charleston, SC, USA, June 2009

Marzall, L F., NascimentoD.C., Schildberg, R & Lacava, J C S (2010), An effective strategy

for designing probe-fed linearly-polarized thick microstrip arrays with symmetrical return loss bandwidth, PIERS Online, Vol 6, No 8, (July 2010) (700-704), ISSN:

1931-7360

Nascimento, D C.; Mores Jr., J.A.; Schildberg, R & Lacava, J C S (2006), Low-cost

truncated corner microstrip antenna for GPS application, Proceedings of Antennas and Propagation Society International Symposium, pp 1557-1560, ISBN: 1-4244-0123-2,

Albuquerque, NM, USA, July 2006

Nascimento, D C.; Bianchi, I.; Schildberg, R & Lacava, J C S (2007a), Design of probe-fed

truncated corner microstrip antennas for Globalstar system, Proceedings of Antennas and Propagation Society International Symposium, pp 3041-3044, ISBN: 978-1-4244-

0877-1, Honolulu, HI, USA, June 2007

Nascimento, D C.; Schildberg, R & Lacava, J C S (2007b), New considerations in the

design of low-cost probe-fed truncated corner microstrip antennas for GPS applications, Proceedings of Antennas and Propagation Society International Symposium,

pp 749-752, ISBN: 978-1-4244-0877-1, Honolulu, HI, USA, June 2007

Nascimento, D C.; Schildberg, R & Lacava, J C S (2008) Design of low-cost microstrip

antennas for Glonass applications PIERS Online, Vol 4, No 7, (2008) (767-770),

ISSN: 1931-7360

Nascimento, D C & Lacava, J C S (2009), Circularly-polarized microstrip antenna

radiation efficiency simulation based on the Wheeler cap method, Proceedings of Antennas and Propagation Society International Symposium, pp 1-4, ISBN: 978-1-4244-

3647-7, Charleston, SC, USA, June 2009

Niroojazi, M & Azarmanesh, M N (2004), Practical design of single feed truncated corner

microstrip antenna, Proceedings of Second Annual Conference on Communication Networks and Services Research, 2004, pp 25-29, ISBN: 0-7695-2096-0, Fredericton,

NB, Canada, May 2004

Pozar, D M & Kaufman, B (1988), Comparison of three methods for the measurement of

printed antennas efficiency, IEEE Transactions on Antennas and Propagation, Vol 36,

No 1, (Jan 1988) (136-139), ISSN: 0018-926X

Richards, W F.; Lo, Y T & Harrison, D D (1981), An improved theory for microstrip

antennas and applications, IEEE Transactions on Antennas and Propagation, Vol 29,

No 1, (Jan 1981) (38-46), ISSN: 0018-926X

Sona, K S & Rahmat-Samii, Y (2006), On the implementation of Wheeler cap method in

FDTD, Proceedings of Antennas and Propagation Society International Symposium, pp

1445-1448, ISBN: 1-4244-0123-2, Albuquerque, NM, USA, July 2006

Teng, P L.; Tang, C L & Wong, K L (2001), A broadband planar patch antenna fed by a

short probe feed, Proceedings of Asia-Pacific Microwave Conference, pp 1243-1246,

ISBN: 0-7803-7138-0, Taipei, China, Dec 2001

Tinoco S., A F.; Nascimento, D C & Lacava, J C S (2008), Rectangular microstrip antenna

design suitable for undergraduate courses, Proceedings of Antennas and Propagation

Society International Symposium, pp 1-4, ISBN: 978-1-4244-2041-4, San Diego, CA,

USA, July 2008

Tzeng, Y B.; Su, C W & Lee, C H (2005), Study of broadband CP patch antenna with its

ground plane having an elevated portion, Proceedings of Asia-Pacific Microwave

Conference, pp 1-4, ISBN: 0-7803-9433-X, Suzhou, China, Dec 2005

Vandenbosch, G A E & Van de Capelle, A R (1994), Study of the capacitively fed

microstrip antenna element, IEEE Transactions on Antennas and Propagation, Vol 42,

No 12, (Dec 1994) (1648-1652), ISSN: 0018-926X

Volakis, J L (2007) Antenna Engineering Handbook 4th ed., McGraw-Hill, ISBN:

0-07-147574-5, New York

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47, No 8, (Aug 1959) (1325-1331), ISSN: 0096-8390

et al 1991) It is found that the use of such materials may have a beneficial effect on circuit or antenna (Bhartia et al 1991; Pozar, 1987) For a rigorous solution to the problem of a rectangular microstrip antenna, which is the most widely used configuration because its shape readily allows theoretical analysis, Galerkin’s method is employed in the spectral domain with two sets of patch current expansions One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other employs Chebyshev polynomials with the proper edge condition for the patch currents (Tulintsef et al 1991)

This chapter describes spectral domain analyses of a rectangular microstrip patch antenna that contains isotropic or anisotropic substrates in which entire domain basis functions are used to model the patch current, we will present the effect of uniaxial anisotropy on the characterization of a rectangular microstrip patch antenna, also because there has been very little work on the scattering radar cross section of printed antennas in the literature, including the effect of a uniaxial anisotropic substrate, a number of results pertaining to this case will be presented in this chapter

2 Theory

An accurate design of a rectangular patch antenna can be done by using the Galerkin

procedure of the moment method (Pozar, 1987; Row & Wong, 1993; Wong et al., 1993) An

integral equation can be formulated by using the Green’s function on a thick dielectric

substrate to determine the electric field at any point

The patch is assumed to be located on a grounded dielectric slab of infinite extent, and the

ground plane is assumed to be perfect electric conductor, the rectangular patch with length a

and width b is embedded in a single substrate, which has a uniform thickness of h (see Fig

1), all the dielectric materials are assumed to be nonmagnetic with permeability μ0 To

simplify the analysis, the antenna feed will not be considered

The study of anisotropic substrates is of interest, however, the designers should, carefully

check for the anisotropic effects in the substrate material with which they will work, and

evaluate the effects of anisotropy

Fig 1 Geometry of a rectangular microstrip antenna

Anisotropy is defined as the substrate dielectric constant on the orientation of the applied

electric field Mathematically, the permittivity of an anisotropic substrate can be represented

by a tensor or dyadic of this form (Bhartia et al., 1991)

yz yy yx

xz xy xx 0

εεε

εεε

εεε.ε

ε00

0ε0

00ε.ε

0

a Plan view

y

x z

h

z

x , ε ε

Radiating conductor

0

a b

b Cross sectional view Ground plan

Analysis of a Rectangular Microstrip Antenna on a Uniaxial Substrate 29

For a uniaxially anisotropic substrate the permittivity is

ε00

0ε0

00ε.ε

ε is the relative permittivity in the direction of the optical axis

Many substrate materials used for printed circuit antenna exhibit dielectric anisotropy,

especially uniaxial anisotropy (Bhartia et al 1991; Wong et al., 1993)

In the following, the substrate material is taken to be isotropic or uniaxially anisotropic with

the optical axis normal to the patch

The boundary condition on the patch is given by (Pozar, 1987)

0

inc scat+ E =

inc

E Tangential components of incident electric field

scat

E Tangential components of scattered electric field

While it is possible to work with wave equations and the longitudinal components E~ and z

z

H~ , in the Fourier transform domain, it is desired to find the transverse fields in the (TM,

TE) representation in terms of the longitudinal components Assuming an ei ω t time

variation, thus Maxwells equations

E E

∂

∂+

∂

∂+

∂

∂+

∂

∂+

ω is the angular frequency

From the above equations and after some algebraic manipulation, the wave equations for

z

E and H z are respectively

0kεzε

εyx

2 z 2 2

z

x 2 2 2

2

=+

∂

∂+

∂

∂+

∂

∂

z z

z

E

(9)

εyx

2 z 2 2

z

x 2 2 2

2

=+

∂

∂+

∂

∂+

∂

∂

z z

z

H

(10) With

0

k propagation constant for free space, k =0 ω ε0μ0

By assuming plane wave propagation of the form e± i k x xe± i y ye± i z z

A Fourier transform pair of the electric field is given by (Pozar, 1987)

,k,k

~ i k x i y

z y x

y x

2 ~ k ,k ,k e e dk dkπ

4

1zy,

,k,k

z y x

y x

2 ~ k ,k ,k e e dk dkπ

4

1zy,

It is worth noting that ~ is used to indicate the quantities in spectral domain

In the spectral domain ikx

After some straightforward algebraic manipulation the transverse field can be written in

terms of the longitudinal components E~ , z H~ z

z 2 s

z 2 s

k

E k

z

~εkεi

x x

z 2 s

k

E k

z

~ε

kεi

~kεεω

~ z 0 y x

∂

∂+

−

2 s z 2 s x

H k E k

z

~ki

~kεεω

~ z 0 x y

∂

∂+

−

2 s z 2 s y

H k

E k

s

k is the transverse wave vector, k s=kxxˆ+kyyˆ, ks= k s

kx and ky are the spectral variables corresponding to x and y respectively

From the wave equations (9) and (10), the general form of E~ and z H~ is z

Analysis of a Rectangular Microstrip Antenna on a Uniaxial Substrate 31

z i z

i z e ze

~

1 1

z C D

z i z

i z e ze

~

2 2

z C D

C 1 , D 1 , C 2 and D 2 are the unknowns to be determined

By substitution of (19) and (20) in (15)-(18) and after some algebraic manipulation the

transverse field in the (TM, TE) representation can be written by

s h s s e s s

k E k E k

s z

ez,

~ ,z

~z,

h s s e s s

k H k H k

z,

~ ,z

~z,

The superscripts e and h denote the TM and the TE waves, respectively

A and B are two unknowns vectors to be determined, note that are expressed in terms of C 1,

e z x 0

μω

k0

0kεεω

ε

εkε

k =⎜⎜⎛ − ⎟⎟⎞ and ( )2

1 2 s 2 0 x h

By eliminating the unknowns A and B, in the equations (21) and (22) we obtain the

following matrix which combines the tangential field components on both sides z1 and z2 of

the considered layer as input and output quantities

−

−

−

s e(h) s

s s

s

k J k

H k E I

g

g I

,

~ ,z

~hkcoshksini

hksinihkcosz

,

~ ,z

~

1 h 1 h e(h)

z e(h)

z

e(h) z 1 e(h)

z 2

h

2 h

(24)

I is the unit matrix

( )s

e(h) k

J~ is the current on the patch

In the spectral domain the relationship between the patch current and the electric field on

the patch is given by

hksinkkiω

1

z1 z x z1 e

z1 z e z 0

e

+

−

=ε

(k h) kcos(k h)sin

ik

hksinkiω

1

z1 h z z1 z

z1 2

In the case of the isotroipc substrate

( ) ( )

z1 0

0 e

khkcotkεi1

hkcosε

khkcotki1hkcos

1ε

k = − ( )k s

J~ is the current on the patch which related to the vector Fourier transform of J(rs), as

(Chew & Liu, 1988)

ekkkkk

1, , r s=x +xˆ yyˆ (28)

xˆ unit vector in x direction

yˆ unit vector in y direction

The surface current on the patch can be expanded into a series of known basis functions Jxn

1 n

xn

0b0

Ja

s

s

r r

k k J k

k

1 m m x

y xn

N

1 n y

k

k1

~ak

k1

Analysis of a Rectangular Microstrip Antenna on a Uniaxial Substrate 33

( )k s

Jxn

~ and ~Jym( )k s are the Fourier transforms of Jxn( )r s and Jym( )r s respectively

One of the main problems with the computational procedure is to overcome the complicated

time-consuming task of calculating the Green’s functions in the procedure of resolution by

the moment method The choice of the basis function is very important for a rapid

convergence to the true values (Boufrioua & Benghalia, 2008; Boufrioua, 2009)

Many subsequent analyses involve entire-domain basis functions that are limited to

canonical shapes such as rectangles, circles and ellipses Recently, much work has been

published regarding the scattering properties of microstrip antennas on various types of

substrate geometries Virtually all this work has been done with entire domain basis

functions for the current on the patch

For the resonant patch, entire domain expansion currents lead to fast convergence and can

be related to a cavity model type of interpretation (Boufrioua, 2009; Pozar & Voda, 1987)

The currents can be defined using a sinusoid basis functions defined on the whole domain,

without the edge condition (Newman & Forrai, 1987; Row & Wong, 1993), these currents

associated with the complete orthogonal modes of the magnetic cavity Both x and y

directed currents were used, with the following forms (Chew & Liu, 1988; Row & Wong,

axaπn

axaπm

a/2

1 x ik xn

2

bybπncosedy2

axaπnsinedx

a/2

1 x ik ym

2

bybπmsinedy2

axaπmcosedx

s

k

Since the chosen basis functions approximate the current on the patch very well for

conventional microstrips, only one or two basis functions are used for each current

component

Using the equations (32.a) and (32.b), the integral equation describing the field E in the patch

can be discretized into the following matrix

Z

Z Z

(33) Where the impedance matrix terms are

k

1

d 2 e 2 h xk xn2

s kn