Antenna : Fundamentals and Practice

Antenna :

Fundamentals and Practice

Sangwook Nam

2008. 5. 8

Antenna Concept

• Mode conversion point of view:

A transition device between a guided wave and a space wave.

• Energy conversion point of view:

A converter between photons and currents.

• Circuit point of view:

One-port black box with input impedance .

• Signal transmission point of view:

A spatial filter.

Zin

Conceptual antenna

Sources of Radiation

• Maxwell’s equations in time-domain

• accelerated Ù time varying charges currents

Å

Electromagnetic Field Radiation

equation continuity

) : , ) (

, (

law Gauss'

: 0 )

, (

law Gauss'

: ) , ( )

, (

law s

Ampere' ) :

, ) (

, ( )

, (

law s

Faraday' ) :

, ) (

, (

t t t

t

t t

t t t

t

t t t

∂

− ∂

=

⋅

∇

=

⋅

∇

=

⋅

∇

∂ + ∂

=

×

∇

∂

− ∂

=

×

∇

r r J

r B

r r

D

r r D

J r

H

r r B

E

ρ ρ

Charge accelerating structures

Radiation from a short current filament

zˆ IdA

*(E, H) A

x

y z

( )

r r e

r jk

4 ⁰ ˆ

0

μ

π

= −

A

π φ

θ 1 _ˆ

4

sin ₀

2

0 jk r

r e r

jk

Id ₋

⎟⎠

⎜ ⎞

⎝

⎛ +

= A

H

E

r r e

r jk k

Id

jZ _{jk r}

1 ˆ 2 cos

0

3 2

0 0

0 −

⎟⎠

⎜ ⎞

⎝

⎛ +

= θ

π E A

θ

π θ ^ˆ

sin 1 4

0

3 2

0 2

0 0

0 jk r

r e r

jk r

k k

Id

jZ ₋

⎟⎟⎠

⎞

⎜⎜⎝

⎛− + +

− A

Characteristics of short dipole(I)

• In far-field region

1. proportional to I, dl(linear superposition)

2. propagate in the r-direction with E_θ, H_φ only(TEM wave)

3. (E_θ, H_φ in time phase)

4. sin θ space-variation(signaling)

5. distance dependence(power conservation)

6. phase dependence(propagation delay) 2 ) ,

, (

2

0 λ

λ r dl r ^dl

r 〉〉 〉〉 〉

π θ

θ ^ˆ

sin 4

0

0

0 r

k e Id jZ

r

−jk

= A

E

π φ

θ ^ˆ

sin 4

0

0 r

k e jId

r

− jk

= A

H

r 1

r

e

Ω

= 377

φ θ

H E

Characteristics of short dipole(II)

• In near-field region(quasi-stationary)

1. Electric fields(E_r, E_θ) in time phase quadrature with H_φ: energy storage in resonator

2. sin θ variation of E_θ, H_φ and cos θ variation of E_r components

3. or dependence: confinement of field in vicinity of dipole(radian

distance )

field magnetic

static ˆ

4 sin

2 →

= φ

π θ r H IdA

fields dipole

sin ˆ cos ˆ

2

4 ^{3 3} ⎟→

⎠

⎜ ⎞

⎝

⎛ +

= θ θθ

π r r

r QdA

E

3

1

2 r 1 r

π λ

≤ 2 r

Power flux with distance

Radiation patterns

• Representation of radiation as a function of direction in space

• 2-D/ 3-D pattern 1. E-plane pattern :

plane including maximum radiation direction and electric field direction

2. H-plane pattern :

plane including maximum radiation direction and magnetic field direction

dipole short

Pattern Examples

Directivity, Gain

• Directivity : D (dimensionless)

1. Ratio of the maximum radiation intensity to the average radiation intensity

2.

• Gain : G

1. Depends on both directivity and efficiency

2. G=ηD

where η =efficiency factor of antenna(0< η <1) 3. Due to Ohmic losses in the antenna

π φ θ φ

θ

4 /

) , ( )

,

( _{max max}

r

av P

U U

D = U =

Antenna Input Impedance

• Input impedance

Γ Γ Γ

−

= +

+

= −

1 Z 1 Z

Z Z

Z Z

c a

c a

c a

a a

a I

Z = V

( )

2

2 0

1 2

I

W W

j P

P_r + _d + _m − _e

= ω

Where P_r : radiated power

P_d : ohmic loss of antenna

W_m : storage of magnetic energy W_e : storage of electric energy

Near field contribution only

Radiation resistance Loss resistance

⇓

BOX

(antenna)

CKT

CKT

a loss r

in

R I

P P

P

2

2 = 1

+

=

R_a = R_r+ R_loss P_in

I

• Antenna input resistance :

radiation loss and Ohmic loses

• Input reactance :

near-field energy storage

( )

2

2 0

1 2

I

W W

jX j ^m − ^e

= ω

Antenna efficiency

• Antenna efficiency : η

Ex) for small dipole

2

0 2

2 r r

80 d I

P

R 2 ⎟⎟⎠

⎜⎜ ⎞

⎝

= ⎛

= π λ^A

) 300 (

1 ,

1m f MH m

dA = = _Z λ =

Ω 0084 0

R_r= .

⇒ high reactance

equivalently

small resistance R_r

X >> R_r : low efficiency very low gain

An Efficient antenna must be comparable to a wave length in size!

matching element loss

loss r

r in

r

R R

R P

P

= + η =

Polarization

• The orientation of the electric field E.

(1) linear polarization - horizontal

- vertical

(2) elliptical polarization - axial ratio:

(3) circular polarization - right-hand

- left-hand

) 1

(

1

2 ≤ ≤ ∞

= AR

E AR E

Half-wave dipole antenna

θ θ π

π sin ^ˆ

2 cos cos

) 2

( ^{0 0 0}

⎟⎠

⎜ ⎞

⎝

⎛

= e^{−jk r} r

Z r jI

E

θ φ π

π sin ^ˆ

cos 2 ) 2

ˆ ( ) 1

( ^{0 0}

0

⎟⎠

⎜ ⎞

⎝

⎛

=

×

= e^{−jk r}

r r jI

Z E r r

H

Characteristics of half-wave dipole

2

sin 2 cos cos

64 . 1 ) , (

⎥⎥

⎥⎥

⎦

⎤

⎢⎢

⎢⎢

⎣

⎡ ⎟

⎠

⎜ ⎞

⎝

⎛

= θ

π θ φ

θ D

D=1.64 (2.15 dB) HPBW : 78°

2. Radiation Resistance :

3. Input impedance :

losses Ohmic

73Ω >>

≅ Ra

Uav

U 1. Directivity :

(1) resonance near : half wave dipole 2

λ0

( 0.48 )λ₀

(2) thicker antenna wide band characteristic

(3) 2

1

0

<<

A λ • Ra is very small

• large capacitive reactance

• inductor tuning additional Ohmic loss lower efficiency

• small bandwidth

(4) The junction capacitance and surrounding structures influence in

resonance near : parallel resonance ( is large)

λ0 Ra

Za

Principal use of small

antennas

Dual-frequency PIFA

Two separate patches with a dual feed

Dual-frequency PIFA

Patch with an L-shaped or folded slit

Dual-frequency PIFA

Patch with a U-shaped slot

) (

4 ),

(

4 _{1 1} ² _{2 2}

1 L W

f c W

L f c

≈ +

≈ +

Dual-frequency PIFA

Patch with a branch line slit

λ λ/0.5 25 . 0