Chapter 14 : Microstrip Antenna

1

Chapter 14 : Microstrip Antenna

• Introduction

– Advantages & Disadvantages

– Feeding Methods

– Analysis Methods

• Rectangular patch

– Transmission line model

Shapes of microstrip patch

elements

Advantages & Disadvantages

• Advantages:

– Low profile

– Conformable to planar & non-planar surfaces

– Manufactured using printed circuit technology

– Compatible with MMIC designs

• Disadvantages:

– Low power (also power due to surface waves)

– High Q

– Narrow bandwidth

Feeding Methods

Analysis Methods

• Transmission-line model

• Cavity model

• Numerical techniques:

– Method of moments (integral equation)

– Finite element (FEM)

– Finite difference time domain (FDTD)

Radiation Mechanism

6

Equivalent currents

7

2/2/;2/2/

2ˆ

ˆˆ2ˆ2

0

0

LyLLLLyL

Ez

Eyxn aSi

−≤≤∆−−∆+≤≤

−=

×−=×−= EM Top View

Radiated Field

8

Two-element array separated by a distance of L+ΔL

''sin2ˆ4

cos'sinsin''ˆ

sin2ˆ

ˆ)sinˆcosˆ(2ˆ2ˆˆ

''ˆ4

;

)cos'sinsin'(

0

0

00

'ˆ

21

dzdyeEr

ejk

zyrr

E

rrErEzr

dzdyerr

ejk

i

i

ii

S

zyjkjkr

i

S

rrjk

SS

jkr

i

∫∫

∫∫

+−

⋅−

=

+=⋅

−=

×−−=×−=×

×−=+=

θφθθφπ

θφθ

θφ

θθθπ

E

M

MEEEE

2/

2/

sinsin'

21

21

2/

2/

sinsin'2/

2/

cos'2/

2/

2/

2/

)cos'sinsin'(

sinsin;cos

2sinc

''''

L

LL

jky

L

LL

jkyW

W

jkzW

W

L

LL

zyjk

jk

eI

kWWI

IIdyedzedzdye

−

∆−−

−

∆−−−−

−

∆−−

+

=

=

== ∫∫∫ ∫

φθθ

φθ

φθθθφθ

For i=1

Radiated Field (2)

9

The total field becomes

LL

L

jky

LL

L

jkyW

W

jkzW

W

LL

L

zyjk

jk

eI

kWWI

IIdyedzedzdye

∆+

∆+

−−

∆+ +

=

=

== ∫∫∫ ∫2/

2/

sinsin'

21

21

2/

2/

sinsin'2/

2/

cos'2/

2/

2/

2/

)cos'sinsin'(

sinsin;cos

2sinc

''''

φθθ

φθ

φθθθφθ

For i=2

∆∆

∆+

×

=−

φθφθ

θθπ

φ

sinsin2

sincsinsin2

cos2

cos2

sincsin2

ˆ0

LkL

LLk

kWW

r

ejkE

jkr

E

Design Equation

10

Approximate relation for ΔL

1/for 1212

1

2

12/1

>

+−

++

=−

hWW

hrrreff

εεε

+−

++=

∆

8.0)258.0(

264.0)3.0(

412.0

h

W

h

W

h

L

reff

reff

ε

ε

where

LLLeff ∆+= 2Effective Length:

2

eff

effLλ

=At resonance:

Effective Dielectric Constant

• Effective dielectric constant = the dielectric

constant of an equivalent homogeneous medium

Design Procedure• Given εεεεr, fr and h where fr is the operation

frequency

• Design procedure

1. Calculate W

2. Determine the effective dielectric constant

3. Determine the effective length

4. Calculate ΔL

5. Determine L

12

1

2

2 +=

rrf

cW

ε

reffr

eff

efff

cL

ε

λ

22==

Design Example• Given a substrate (RT/duroid 5880) with εεεεr=2.2,

h=0.1588 cm and fr=10 GHz.

13

cm 906.0)081.0(2068.1

cm 068.1972.110102

103

cm 081.0

8.01588.0

186.1

264.01588.0

186.1

258.0972.1

3.0972.1412.01588.0

972.1186.1

1588.0121

2

12.2

2

12.2

cm 186.112.2

2

)1010(2

103

9

8

2/1

9

8

=−=

=××

×=

=+

+

−+

×=∆

=

+−

++

=

=+×

×=

−

L

L

L

W

eff

reffε

Radiation Pattern

14

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

E−plane

H−plane

Radiation Pattern (2)

Transmission line model

16

Each radiating edge can be

modeled by an equivalent

admittance Y = G + jB

1/;;

;;

2121

222111

>==

+=+=

hWBBGG

jBGYjBGY

reff

c

ccin

LjYY

LjYYYYY ε

λπ

βββ 2

;)tan(

)tan(

2

21 =

++

+=

+++==

444.1ln667.0393.1

1201

h

W

h

WYZ

reffc

c

ε

πwhere

Transmission line model (2)

17

Asymptotic values:

[ ]10

1)ln(636.01

120

)sin()()cos(2;

120

0

0

0

1

0

00012

11

<−=

+++−==

λλ

π

hhk

WB

Wk

WkWkkWSWkI

IG i

>>

<<

≈

0

0

0

2

0

1

120

1

90

1

λλ

λλ

WW

WW

G

inin RG

Z ==12

1At resonance ( f=fr), Yin=Y1+Y*

1=2G1 and

To change the value of G1, the location of the feed point has to

be moved.

Input resistance

1

02

0

2

1)0( where

;cos)0()(

GR

L

yRyyR

in

inin

=

≈=π