microstrip antennas 2k9 10

2009-10 CRL-715 Radiating Systems for RF Communications

MICROSTRIP ANTENNAS

• Microstrip Antenna (MSA) received considerable attention in the 1970’s, although the first designs and theoretical models appeared in the 1950’s.

• They are suitable for aircraft, satellite and missile applications where size, weight, ease of installation, mechanical reliability and cost are important.

• The MSA are low profile, mechanically robust, inexpensive to manufacture, compatible with MMIC designs and relatively light and compact.

• With respect to radiation properties they are versatile in terms of resonant frequencies, polarization, pattern and impedance.

• They allow the use of additional tuning elements like pins or varactor diodes between the patch and the ground plane.


Disadvantages:

• relatively low efficiency (due to dielectric and conductor losses)

• low power

• spurious feed radiation (surface waves, strips, etc)

• narrow frequency bandwidth (at most a couple of percent)

• relatively high level of cross polarization radiation

MSA are applicable in the GHz range (f > 0.5 GHz) — for lower frequencies their dimensions are too large.


Construction and Geometry

Generally the MSA are thin metallic patches of various shapes etched on dielectric substrates of thickness h, which usually is from 0.003 λo to 0.05 λo. The substrate is usually grounded at the opposite side.

Side view


• The dimensions of the patch are usually in the range from λo/3 to λo/2.

• The dielectric constant of the substrate εr is usually in the range from 2.2 to 12.

• The most common designs use relatively thick substrates with lower εr because they provide better efficiency and larger bandwidth. On the other hand, this implies larger dimensions of the antennas.

• The choice of the substrate is very much limited by the microwave circuit coupled to the antenna, which has to be built on the same board.

• The microwave circuit together with the antenna is usually manufactured by photo-etching technology.


Types of microstrip radiators

1. Single radiating patches:


2. Single slot radiator:

The feeding microstrip line (dashed-line) is beneath (etched on the other side of the substrate)


3. Microstrip traveling wave antennas

Comb MTWA

Meander Line Type MTWA

Rectangular Loop Type MTWA

Franklin – Type MTWA

The open end of the long TEM line is terminated in a matched resistive load


4. Microstrip antenna arrays


Feeding Methods

Microstrip feed – easy to fabricate, simple to match by controlling the inset position and relatively simple to model. However, as the substrate thickness increases, surface waves and spurious feed radiation increase.

Coaxial probe feed – easy to fabricate, low spurious radiation; difficult to model accurately; narrow bandwidth of impedance matching.


Aperture coupling (no contact), micro strip feed line and radiating patch are on both sides of the ground plane, the coupling aperture is in the ground plane – low spurious radiation, easy to model; difficult to match, narrow bandwidth.(two dielectric material used in this , bottom substrate has high value of dielectric and on the other hand top sub has low value of dielectric)

Proximity coupling (no contact), micro strip feed line and radiatingpatch are on the same side of the ground plane – largest bandwidth (up to 13%), relatively simple to model, has low spurious radiation.


More examples of microstrip and coaxial probe feeds


Criteria for Substrate Selection

• Possibility for surface-wave excitation

• Effects of dispersion on the dielectric constant and low tangent of the substrate

• Magnitude of copper loss and dielectric loss

• Anisotropy in the substrate

• Effects of temperature, humidity, and aging

• Mechanical requirements: conformability, machinability, solderability, weight, elasticity, etc.

• Cost


Transmission line model – the rectangular patch

• The TL model is the simplest of all, representing the rectangular patch as a parallel-plate transmission line connecting two radiating slots (apertures), each of width W and height h:

z is the direction of propagation of the transmission line. illustrated radiating slots along the length


• The TL model is not accurate and lacks versatility.

• However, it gives a relatively good physical insight into the nature of the patch antenna, and the field distribution for all TM00n modes.

• The slots represent very high-impedance terminations from both sides of the transmission line (almost an open circuit). Thus, we expect this structure to have highly resonant characteristics depending crucially on its length along z, L.

• The resonant length of the patch, however, is not exactly equal to the physical length due to the fringing effect. The fringing effect makes the effective electrical length of the patch longer than its physical length, Leff >L.


• Thus, the resonance condition depends on Leff and L:

( ) 1,2,...2

neffL n n

• The E-field distribution for the first (dominant) resonant mode, n=1:


• Effective patch length:

1 21 1

0.3 0.264

1 12 12

0.4120.258 0.8

2

2

reff

reff

ef

ef

f

r rr f

WL h

Whh

L L L

hW h

W


• Resonant frequency of the dominant TM001 mode:

001 0

2 2 2r

reff

cf

L L

The field of the TM001 mode does not depend on the x and y coordinates but itstrongly depends on the z coordinate, along which a standing wave is formed.

Field distribution along z when the patch is in resonance.


• The patch width W:

2

2 1r r

cW

f

• The width W equal to half-wavelength resonant mode leads to good radiation efficiencies and acceptable dimensions.

• Thus, the patch can be viewed as a continuous planar source consisting of infinite number of infinitesimally thin half-wavelength dipoles.


Equivalent circuit of the patch:

• The dominant TM001 mode has a uniform field distribution along the y-axis at the slots formed at the front and end edges of the patch.

• The equivalent conductance and susceptance can be obtained from the theory of uniform apertures

2

0 0 0

0 0 0

1 2 11

120 24 10

2 11 0.636ln

120 10

W hG h

W hB h


• The limitation (h/λ0)<0.1 is necessary since a uniform field distribution along the x-axis is assumed.

• The equivalent circuit of a slot is constructed as a parallel R-C circuit:

G=1/R represents the radiation losses, while B=jωC is the equivalentsusceptance, which represents the capacitive nature of the slot.


• More accurate values for the conductance G can be obtained through the cavity model:

2

2

0

0 0 0 00

3

0

0

2 sin

120

sin cos2

sincos

sin2 cos

x

i

i

yX k W k S

IG

k W

I d

XX XS X

y

X

x dy

Asymptotic values of G2

00

00

1

90

1

120

WG W

WG W


• The equivalent circuit representing the whole patch in the TM001 mode includes the two radiating slots as parallel R-C circuits and the patch connecting them as a transmission line whose characteristics are computed in the same way as those of a microstrip transmission line.

Zc is the characteristic impedance of the line, and βg is its phase constant.


• Ideally, the resonant input impedance of the patch for the dominant TM001 mode is entirely resistive and equal to half the transformed resistance of each slot:

• There is always some mutual influence between the two slots, described by a mutual conductance and it should be included for more accurate calculations:

• ‘+’ sign is used for modes with anti-symmetric resonant voltage distribution beneath the patch and between the slots; ‘-’ is used for symmetric resonant voltage distribution

1

1 1

2in inin

Z RY G

1 12

1

2inR G G


• For most patch antennas fed at the edge, Rin is greater than the characteristic impedance Zc of the microstrip feed line (typically Zc = 50Ω).

• Hence, inset-feed technique is widely used to achieve impedance match.


20 0( ) ( 0)cosin inR y y R y y

L


• Design a rectangular microstrip antenna using a substrate with dielectric constant 2.2, h = 0.1588cm so as to resonate at 10 GHz. Calculate the input impedance and position of the inset feed-point where the input impedance is 50Ω.


Cavity Model for the Rectangular Patch

• The TL model is very limited in its description of the real processes taking place when a patch is excited. It takes into account only the TMx

00n modes where the energy propagates only in the longitudinal z direction.

• The field distribution along the x and y axes is assumed uniform. Although the dominant TMx

001 is prevalent but the performance of the patch is very much affected by higher-order modes, too.

• The cavity model is a more general model of the patch which imposes open-end conditions at the side edges of the patch. It represents the patch as a dielectric-loaded cavity with: electrical walls (above and below), magnetic walls (around the perimeter of the patch).


• The magnetic wall is a wall at which:

ˆ 0

ˆ 0

n H

n E

H is purely normal

E is purely tangential

• If we treat the microstrip antenna only as a cavity, we can’t represent radiation because an ideal loss-free cavity does not radiate and its input impedance is purely reactive. To account for the radiation, a loss mechanism has to be introduced. This is done by introducing an effective loss tangent, δeff.

• The thickness of the substrate is very small. The waves generated and propagating beneath the patch undergo considerable reflection at the edges of the patch. Only a very small fraction of them is being radiated. Thus, the antenna is quite inefficient.

• The cavity model assumes that the E field is purely tangential to

the slots formed between the ground plane and the patch edges (magnetic walls). Moreover, it considers only TMx modes, i.e., modes with no Hx component.


• The TMx modes are fully described by a single scalar function Ax – the x-component of the magnetic vector potential:

ˆxA A x

• In a homogeneous source-free medium, Ax satisfies the wave equation:

Can be solved using separation of variables.

2 2 0x xA k A

L

W


The general solution can be written as:

2

1 1 2 2

3 3

2 2 2

cos( ) sin( ) cos( ) sin( )

cos( ) sin( )

x x x y y

z z

x y z

A A k x B k

k

x A k y B k y

A k z

k

z

k

k

k

B

Kx, ky, kz are wavenumbers along x, y and z dimensions and are determined by boundary conditions.

• The fields in the cavity are related to the vector potential by:2

22

2

2

10

1 1

1 1

x x x

x xy y

x xz z

E j k A Hx

A AE j H

x y z

A AE j H

x z y

Characteristic equation


• The boundary conditions are:

' 0,0 ' ,0 ' ' ,0 ' ,0 ' 0

0 ' ,0 ' , ' 0 0 ' ,0 ' , ' 0

0 ' , ' 0,0 ' 0 ' , ' ,0 ' 0

y y

y y

z y

E x y L z W E x h y L z W

H x h y L z H x h y L z W

H x h y z W H x h y L z W

• Applying these boundary conditions, we would get the vector potential as:

0,1,2,..

c

.

os

0,1,2,...

0,1,

( ')cos

2,

( '

.

)cos( ')

..

x

y

z

x mnp x y z

mk m

h

nk

A

nL

pk p

W

A k x k y k z

m=n=p0


The wavenumbers should satisfy the characteristic (constraint) equation:

2 2 22 2 2 2

2 2 2

2

1

2r mnp

x y z r r

m

m n pf

h L W

n pk k k k

h L W

• The mode with the lowest resonant frequency is the dominant mode.

• Since usually L > W, the lowest-frequency mode is the TMx

010 mode, for which:

010

1

2 2r

r

cf

L L


The field distribution of some low-order modes:

TMx010 TMx

001

TMx020 TMx

002


Cavity model for the radiated field of a rectangular patch

• The microstrip patch is represented by the cavity model reasonably well assuming that the material of the substrate is truncated and does not extend beyond the edges of the patch.

• The four side walls (the magnetic walls) represent four narrow apertures (slots) through which radiation takes place. To calculate the radiation fields, the equivalence principle is used.

• The field inside the cavity is assumed equal to zero, and its influence on the field in the infinite region outside is represented by the equivalent surface currents on the surface of the cavity.


• As the substrate height (h) is very small, the field is concentrated beneath the patch.

• There is some actual electrical current at the top metallic plate, however, its contribution to radiation is negligible. as it is backed by a conductor, and is very weak compared to the equivalent currents at the slots.

• The actual electrical current density of the top patch is maximum at the edges of the patch, but still its values are negligible in comparison with the radiation effect from the slots.

• In the cavity model, the side walls employ magnetic-wall boundary condition, which sets the tangential H components at the slots equal to zero. Therefore:

ˆ 0s aJ n H


• Only the equivalent magnetic current density has substantial contribution to the radiated field:

ˆs aM n E

• The influence of the infinite ground plane is accounted for by the image theory:

ˆ2s aM n E


Assuming the dominant mode within the cavity is TMx010,

the electric and magnetic fields can be written as:

0

0

cos '

sin '

0

x

z

y z x y

E E yL

H H yL

E E H H


The equivalent magnetic current densities along two slots (Wh) are of same magnitude and same phase

Two-element array with sources of same magnitude and phase separated by L. They will add up in a direction normal to the patch and ground plane: Broadside Pattern.

Radiating Slots:


Non-Radiating Slots:

• The current densities on each wall are of the same magnitude but of opposite direction, the fields radiated by the two slots cancel each other in H-plane (x-z plane).

• Corresponding slots on opposite walls are 180 out of phase, the corresponding radiations cancel in E-plane (x-y plane).

microstrip antennas 2k9 10

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