chapter 2 –antenna parameters - universiti malaysia...

Antenna & Propagation Antenna Parameters

1

Chapter 2 – Antenna

Parameters

1. Antenna Radiation

2. Figure of Merit

3. Efficiency

4. Radiation Pattern

5. Antenna Impedance

6. Friss formula


2

Objective

To revise various antenna parameters from a system point of view:

• what they are

• how they are calculated

• where they can be used


3

Prerequisites

• Units for an angle: radian vs degree

• Definition of solid angle W:

– steradians (sr)

– degrees2

• Power density and radiation intensity

• Radiated power from a Poynting vector

• Radiation from a Hertzian dipole

• Radiation from a magnetic current element

o180=π

2

2

deg41253180.44 =

=π

ππ


4

Solid Angle: Steradian

r

Surface area dA

Solid angle dΩRadius r

Subtended angles dθ and dφ

Sphere

2r

dAd =Ω

2

2 sin

r

ddr φθθ=

φθθ ddsin=

x

z

πφθθπ π

4sin2

0 0==Ω ∫ ∫ ddSolid angle of a sphere, steradians


5

Co-ordinate System


6

Isotropic Antenna

• A theoretical point source radiating power equally in all

directions, 100% efficiency.

• Power Density: (W/m2)

• Directivity and Gain: D = G = 1 = 0 dBi

24 r

PS T

π=


7

ANTENNA RADIATION

1. Radiation pattern

2. Radiation power density

3. Radiation intensity

4. Half-power beamwidth


8

Cutting Plane


9

Radiation Pattern

• Plot of |Eq| as a function of (q, f) at a fixed r, giving rise to a 3-

dimensional radiation pattern.

• E-plane pattern:

– plot of |Eq| vs q (f = constant, e.g. f = 0)

• H-plane pattern:

– plot of |Eq| vs f (q = constant, e.g. q = p/2)

• Distinguish between:

– polar and rectangular (Cartesian) plots

– linear (ratio) and logarithmic (dB) scales

– main lobe (main beam), side lobes (minor lobes), nulls

– HPBW (qHP, fHP) and FNBW (qFN, fFN): qHP ~ qFN/2


10

Polar Pattern


11

Rectangular Pattern

Beam Efficiency (BE):

>90% for radiometry,

astronomy, radar, etc. rx_or_tx_power_total

FNBW_within_power_rx_or_txBE =

Lobes, nulls, and beamwidths (HPBW and FNBW)


12

Radiation Properties

Main lobe

Half-power

Beamwidth

HPBW

Side Lobe

Back

lobe

Minor

lobes

First-nulls

Beamwidth

FNBW

Nulls


13

E-Plane and H-Plane

r

eIdzjE

rjβ

θθβ −

=)(sin30

θθβ

θ sinsin30

Kr

IdzE ==

where K is a constant,

usually normalize K=1.

E-plane H-plane

z

x

θ

x

y

φ

Hertzian Dipole


14

FIGURE OF MERIT

1. Directivity

2. Gain

3. Antenna reciprocity


15

Gains: D, G

• Directive Gain: D(q,f) or GD(q,f)

• Directivity:D

• Power Gain: G or GP

• Relationship between D and G:

• Relationship between D and HPBW:

DG η=

Antenna D (ratio) D (dB)

isotropic 1 0

Hertzian dipole 1.5 1.76

λ/2 dipole 1.64 2.15η = antenna efficiency

D and G are power ratios.

HPHPHP

Dφθππ.

44=

Ω=

o

HP

o

HPHP

Dφθ

ππ

.

41253

180.4

2deg

2

=Ω

=


16

EIRP and ERP

• Effective Isotropic Radiated Power (EIRP):

• Effective Radiated Power (ERP):

TT GPEIRP .=

dipoleG

EIRPERP

2/λ

=

dBdBmdBm EIRPERP 15.2−=

dBdBmdBm ERPEIRP 15.2+=

EIRP is preferred in theoretical treatment for its simplicity.

ERP is sometimes used in practice as λ/2 dipole is readily available.

64.1

..

2/

TT

dipole

TT GP

G

GPERP ==

λ


17

Effective Area

• The effective area of an antenna can be used to calculate the received

power

• Q1. A thin (diameter = 5 mm) half-wave dipole at 900 MHz (mobile phone)

has Gain = 1.64.

– How long is the antenna? l = = m = mm

– Calculate its effective area. Ae= = m2 = mm2

– Assume a rectangle with the area Ae. If one side of the rectangle equals

the antenna length, what is the dimension of the other side? Compare

this with the antenna diameter!

• Q2. What is the effective area of an isotropic antenna?

17

SAtyPowerDensiAP eeR .. == GAe πλ4

2

=where


18

Effective Length or

Effective Height• For an antenna receiving a far-field wave, the effective length

le is defined by:

– where

• Voc = open-circuit voltage at antenna terminals

• Ei = incident electric field

• le = effective length

• For an electrically short dipole, le = lphysical/2

18

e

i

OC l.EV =


19

Reciprocity Theorem

• The Lorentz Reciprocity Theorem (which states that the E

and H fields generated by two different sources at the same

frequency must satisfy certain conditions) can be applied to

antennas to show that:

the receiving and transmitting

properties of an antenna can be

interchanged.• For example, the radiation pattern, feed-point impedance,

and gain are the same when a wire dipole antenna is used for

either transmitting or receiving.


20

EFFICIENCY

1. Antenna efficiency

2. Radiation efficiency


21

Radiation Resistance: Rr

• Rr is a fictitious resistance to account for the power radiated

by an antenna.

• Power radiated, (E,H = rms value)

• (1)

•

• But, according to (I = rms value) (2)

• Therefore, equating (1) & (2)

21

∫∫= dSExHPr .

∫∫=ππ

φθθπ

0

222

0

sin 120

ddrE

Pr

∫∫=ππ

φθθπ

0

222

0

2 sin

120

1ddr

E

IRr

rr RIP 2=


22

Radiation Resistance of an

Electrically Short Dipole

• Electrically short means dl < l/10

• Hertzian dipole is an electrically short dipole

• For example:

– If dl/l = 0.01, then Rr = 0.08 W

– If dl/l = 0.1, then Rr = 7.90 W

22

22

2 79080

=

=λλ

πdldl

Rr(Ω)


23

Feed-Point Impedance: Za

• Za = antenna impedance at its feed-point.

• Za is complex generally.

• Za can be determined by numerical methods, such as

Moments Method, FDTD, etc.

• For a dipole with total l<l/2 (or monopole with h<l/4), Xa is

negative (i.e. capacitive).

23

aaa jXRZ +=Za


24

Antenna Efficiency: η

• Definition:

• In a lossless antenna,

• In an antenna with loss,

• Losses are due to:

– conduction (ohmic) loss

– dielectric loss

– reflection (mismatch)

• Total efficiency:

24

lossr

r

RR

R

losspowerradiatedpower

radiatedpower

+=

+=

η

ra RR =

lossra RRR +=

)1(2

Γ−== dcrdc ηηηηηη


25

ANTENNA IMPEDANCE

1. Input Impedance

2. Bandwidth


26

Feed-Point Impedance: Za

• Za = antenna impedance at its feed-point.

• Za is complex generally.

• Za can be determined by numerical methods, such as

Moments Method, FDTD, etc.

• For a dipole with total l<l/2 (or monopole with h<l/4), Xa is

negative (i.e. capacitive).

26

aaa jXRZ +=Za


27

Dipole Antenna


28

Feed-Point Impedance of a

Dipole Antenna• Dipole Za represented by a 4-element equivalent circuit.

• L, C, and R elements are determined from the physical dimensions of dipole, independent of frequency.

• <10% error in Ra and Xa for dipole length (2h) up to 0.6λ.

• Equivalent circuit can be used in electronic circuit simulation software such as PSPICE.

h = dipole half-length

a = dipole radius


29

Equivalent Circuit

[Tang, Tieng & Gunn, IEEE Trans.AP, Jan. 1993, pp.100-103]

pFah

hc

7245.0)/2log(

0674.1231 −

=

[ ]pF

ahhc

−−

= 02541.0861.0)/2log(

89075.02

8006.032

[ ] 02389.02

31 )/2(40754.7)/2log(41288.0 −+= ahahR

[ ] HahhL µ6188.0)/2log(4813.12.0012.1

31 −=

Ω− k27408.7


30

ANTENNA BANDWIDTH

1. Operating Frequency


31

Antenna Bandwidth:

Frequency Range

• (There are various definitions of antenna bandwidth.)

• The bandwidth of an antenna is the band of frequencies, over which it is considered to perform acceptably.

• The wider the range of frequencies a band encompasses, the wider the bandwidth of the antenna.

• Antennas are ordered pre-tuned by the manufacturer, for use in a specified band segment.

• The trade-off in designing an antenna for a wider bandwidth is that it would generally not have as good of performance in comparison to a similar antenna that is optimized for a narrower bandwidth.


32Rick Graziani [email protected] 32

Antenna Bandwidth:

Frequency Range


33

FRIIS FORMULA

1. Definition


34

Definition

The Friis Transmission Equation is used to calculate the power

received from one antenna (with gain G1), when transmitted

from another antenna (with gain G2), separated by a distance R,

and operating at frequency f or wavelength lambda.


35

Frii’s Transmission Equation

• Example:

– For a transmitter-receiver distance of 20 m at 10.2 GHz,

with PT = 100 W, PR = 3 mW, and GR = 15 dB, (a) what is

the required GT? (b) what is the maximum power density

at a point 20 m from the transmitter?

– Ans. (a) 18.4 dB, (b) 1.44 W/m2 or 0.144 mW/cm2

35

24 r

GPS TT

π=

πλ

π 4.

4.

2

2

RTTeR

G

r

GPASP == RT

T

R GGrP

P2

4

=πλ

S = power density

Ae = effective area


36

Simple Questions• What is the difference between POWER GAIN, DIRECTIVE

GAIN, and DIRECTIVITY of an antenna?

• What is the difference between EIRP and ERP?

• What is the significance of the effective area of a receiving

antenna?

• What is the significance of the radiation resistance of a

transmitting antenna?

• How would the feed-point impedance (sometimes called the

antenna impedance) affect the performance of an antenna?

• Derive the Frii’s Transmission Equation and/or the Radar

Equation.

• What is the significance of the G/T ratio of a satellite

receiving station?36

chapter 2 –antenna parameters - universiti malaysia...

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