Antenna for EMC
Prof. Tzong-Lin Wu
EMC Lab.
Department of Electrical Engineering
National Taiwan University
Introduction
1. Overview 2. Steps in evaluation of radiated fields 3. Ideal Dipole (Hertzian Dipole) 4. Antenna parameters 5. Dipole and Monopole 6. Small Loop Antenna 7. Antenna Arrays 8. Examples of Antenna 9. Antennas in communication systems
How antenna radiate: a single accelerated charged particle
• The static electric field originates at charge and is directed radially away from charge. • At point A, the charge begins to be accelerated until reaching point B. • The distance between the circles is that distance light would travel in time △t, and △r=rb – ra = △t * c
• Charge moves slowly compared to the speed of the light, ∴ △r >> △z and two circles are concentric. • The electric field lines in the △r region are joined together
because of required continuity of electrical lines in the absence of charges. • This disturbance expands outward and has a transverse component Et , which is the radiated field. • If charges are accelerated back and forth (i.e., oscillate), a regular disturbance is created and radiation is continuous. • This disturbance is directly analogous to a transient wave created by a stone dropped into a calm lake.
How antenna radiate : Evolution of a dipole antenna from an open-
circuited transmission line
• Open-circuited transmission line
1. The currents are in opposite directions on the two wires and behaves as a standing wave pattern with a zero current magnitude at the ends and every half wavelength from the end.
2. The conductors guide the waves and the power resides in the region surrounding the conductors as manifested by the electric and magnetic fields.
3. Electric fields originate from or terminate on charges and perpendicular to the wires.
4. Magnetic fields encircle the wires.
• Bending outward to form a dipole
1. The currents are no longer opposite but are both upwardly directed. 2. The bounded fields are exposed to the space. 3. The currents on the dipole are approximately sinusoidal. 4. The situation on the Fig. is the peak current condition. As time
proceeds and current oscillation occur, the disturbed fields are radiated.
How antenna radiate : Time dynamics of the fields for a dipole
antenna
• At t = 0, peak charges buildup occurs (positive on the upper half and negative on the lower half). current I = 0. • At t = T/4, +/- charges are neutralized and I is maximum.
• Because there are no longer charges for the termination of electric fields, they form closed loop near the dipole. • At t = T/2, peak charges buildup again, but upper half is negative and lower half is positive. I = 0. • Notice the definition of λ/2 at t = T/2.
Closed loop
Steps in evaluation of radiation fields : Solution of Maxwell
equations for radiation problems)
H
E j H
H j E J
E
0
H A
1
( ) E j A 0
E j A
A A A j j A J( ) ( )2
Magnetic vector potential
Electric scalar potential
A jIf we set
2 2 A A J
(Lorenz condition)
Vector wave equation
A J
e
Rdv
j R
v
zzz
4
'
'
Solution is
Steps in evaluation of radiation fields (Far Fields)
1. Find A '
'
ˆ n
4
j rj r r
v
eA Je dv
r
'
'
ˆ 'ˆ4
j rj r r
z
v
eA z J e dv
r
'
'
' cos 'ˆ ( )4
j rj z
v
eA z I z e dv
r
Z-directed sources
Z-directed line sources
Far field
Steps in evaluation of radiation fields (Far Fields)
2. Find E
ˆ ˆE j A A θ φω( θ φ)
E j A ω
ˆzE j A ωsinθ θ
Far field
Transverse to the propagation direction r
Z-directed sources
3. Find H
1ˆH r E
1H E
Far field (Plane wave)
Z-directed source
Far-Field Conditions
Parallel ray approximation for far-field calculations
Far Field conditions D is the length of line source
22Dr
r D
r
'ˆR r r r
The ideal dipole (Hertzian dipole) : definition
Ideal dipole: a uniform amplitude current that is electrically small with △z <<λ
∵R~r for small dipole
/ 2
'
/ 2
ˆ4
z j R
z
eA z I dz
R
ˆ4
j reA I z z
r
The ideal dipole (Hertzian dipole): E and H field
2
2
1 1 ˆ[1 ] sin4 ( )
1 1ˆ [ ] cos
2
j r
j r
I z eE j
j r r r
I z ej r
r r r
1 ˆ(1 ) sin4
j rI z eH j
j r r
H A
1
1E H
j
Far field condition : βr >> 1
120 377E
H
ˆsin4
j rI z eH j
r
ˆsin4
j rI z eE j
r
The ideal dipole (Hertzian dipole): radiated power
Power flowing density : (Unit : w/m*m)
22
2
1 1 sinˆ( )
2 2 4
I zS E H r
r
Total radiated power (Unit : W)
2 2 2 2( ) 40 ( )12
zP S ds I z I
Antenna Parameters: radiation pattern
The field pattern with its maximum value is 1 ,max
( , )E
FE
For Hertzian dipole
F(θ)=sinθ
Antenna Parameters: power pattern
2( , ) ( , )P F
( , ) ( , )dB dBP F
It is worth noting that the field patter and power pattern are the same in decibles.
Power pattern parameters
Antenna Parameters: Directivity
Directivity: The ratio of the radiation intensity in a certain direction to the average radiation intensity.
2
2 2
1ˆRe( )
( , ) ( , ) / 2( , )( , ) ( , ) / / 4ave ave
E H rU U r
DU U r P r
Radiation intensity: the power radiated in a given direction per unit solid angle
21ˆ( , ) Re( )
2U E H r r
Average radiation intensity:
1( , ) ( , ) / 4
4aveU U d P
Antenna Parameters: Directivity
When directivity is quoted as a single number without reference to a direction, maximum directivity is usually intended.
2
4
( , )
m
ave
UD
U F d
Directivity of Hertzian dipole
2 21( , ) ( ) sin
2 4
I zU
21( , ) / 4 ( )
3 4ave
I zU P
21( )
2 4m
I zU
310log1.5 1.75
2D dB
Antenna Parameters: Gain
Gain : 4π times the ratio of radiation intensity in a given direction to The net power accepted by the antenna from the connected transmitter
4 ( , )( , )
in
UG
P
• If all input power appeared as radiated power (Pin=P), Directivity = Gain. • In reality, some of the power is lost in the antenna absorbed by the antenna and nearby structures). • Radiation efficiency:
, (0 1)r r
in
Pe e
P
rG e D
Antenna Parameters: antenna impedance, radiation efficiency
A A AZ R jX
RA: Dissipation = Radiation + Ohmic loss XA: Power stored near the antenna
• Input impedance
2 21 1
2 2in ohmic r A ohmic AP P P R I R I
• Efficiency
rr
in ohmic A
P P Re
P P P R
• For Ideal dipole
Rr is very small since △z << λ
2 2 2
2 2
2( ) 80 ( )
12r
A
P zR I z
II
Antenna Parameters: ideal dipole is an ineffective radiator
Example
For radiator △z = 1cm, f0 = 300MHz (λ= 1m) → Rr = 79mΩ
∴ It needs 3.6A for 1W of radiated power.
For radiator △z = 1cm, f0 = 1GHz (λ= 30cm) → Rr = 0.87Ω
∴ It needs 1.5A for 1W of radiated power.
Antenna Parameters: How to increase the radiation resistance
(efficiency) of the short dipole
Practical short dipole with triangular-like current distribution
1. Capacitor-plate antenna: the top-plate supply the charge such that the current on the wire is constant
2 280 ( )r
zR
2 220 ( )r
zR
Antenna Parameters: How to increase the radiation resistance
(efficiency) of the short dipole
2. Transmission line loaded antenna
3. Inverted-L antenna or Inverted-F antenna
Looks like uniform distribution if △z<<L
Image theory
Antenna Parameters: effective aperture
e
R av
he effective aperture of an antenna, A ,is the ratio of power received in its load
impedance, P , to the power density of the incident wave, S ,when the
polarization of the incident wave an
a. T
2
d the polarization of receiving antenna
ard matched:
in m
The maximum effective aperture A is the A when the maximum powerem e
transferring to the load
b.
R
eav
PA
S
takes place, which means load impedance is the conjugate
to the antenna impedance.
c. Example: compute the Aem (maximum effective aperture) of
a Hertzian dipole antenna.
Ans: To solve Aem, two conditions should be kept in mind:
(1)matched polarization for the incident
wave and the antenna.
(2)matched load. (ie. )
E
θ
LZ
radR jX
inZ
radR jX
*
L antZ Z
Suppose the incident wave is arriving at an
angle
(1)the open-circuit voltage produced at the
terminals of the antenna is
ˆ = E sin ocV dl
ocV LZ
radR jX
inZ
radR jX
2
0
2 2 2 2
2
2
rad
(2)power density in the incident wave
1
2
(3) the load is matched
sin the received power
8 8
1 1 ( I R= R )
2 2 2
(4)radiation resistance for H
av
oc
Rrad rad
oc
rad
ES
V E dlP
R R
V
R
2
2
0
2 220
2
ertzian dipole
80
sin640
222 00(5) , 1.5 sin ,
44
rad
R
dlR
EP
PR
A Dem Sav
2
0
2
0
d. For general antennas, the above relation hold.
4 , , for lossless antenna.
4 , , for lossy antenna.
The maximum effective aperture of an antenna used
em
em
D A
G A
for reception is
related to the directive gain in the direction of the incoming wave of
that antenna when it is used for transmission.
Antenna Factor
a. Antenna factor is a common way to
characterize the reception properties of
EMC antenna.
b. Antenna factor is defined as the ratio of
the incident electric field at the surface of the measurement antenna to the received voltage at the antenna terminals:
recZocV
radR jX
Antenna Spectrum
analyzer
recV
recZ
recV
incEReceived
dBExpressed as dB AF
inc
rec
EAF
V
VdB dB V
m
(incident field) (received voltage)
d. Ex: please find the antenna factor at 100MHz for following measurement data.
(1)the field intensity of antenna surface
is 60dBuV/m
(2)The specturm Analyzer measures
40dBuV
(3)coaxial loss=4.5dB/100ft
sol:
.The antenna factor is usually furnished by the manufacture of the antenna.c
Specturm
Analyzer 30ft antV
recV
dB
3AF 60 (40 4.5 )
10
=18.65
VdB dB V dB
m
dB
2
0
2 2
0
22 2
0 0
2
0
.
4
4 . .
4
f av
out av e
rav r
L
rr
L r L r
ES
P S A
VS G
Z
E EVG A F
Z V Z G
rV
outP
ZL =50Ω
E
The Friss transmission equation
a. The coupling of two antennas.
T Tθ ,
PR
d
R Rθ ,
T T T
eT T T
G θ ,
A θ ,
R R R
eR R R
G θ ,
A θ ,
2
R
(1) The power density at the receiving antenna of distance d.
( , )4
(2) and by the definition of effective asperture, the received power P
b. Friss transmission equation:
Tav T T T
PS G
d
2
2
20
,
( , ) ,
4
(3) and we know
4 , ,
( , ) , ( )4
(4) In terms of dB
10 log
R av eR R R
T T T eR R RR
T
R R R eR R R
RT T T R R R
T
R
T
P S A
G AP
P d
G A
PG G
P d
P
P
, , 20log 20log 147.6T dB R dBG G f d
c. :
Friss transmission equation is valid under two assumptions:
(1) the receiving antenna must be matched to its load
impedance and the polarization of the inco
Note
2
ming wave.
(2) two antenna should be in the far field
. . d > 2D / ( for surface antennas )
d > 3 ( for wire antennas )
o
o
i e
Half-wave Dipole Antenna:
( ) sin[ ( )]4
mI z I z
'' cos '
2
sin ( )4
2 cos[( / 2)cos ] sin
sin
j rj z
j r
m
eE j I z e dz
r
I ej
r
Input impedance = 73+ j42.5Ω
If the length is slightly reduced to achieve resonance, the input impedance is about 73 + 0Ω
cos[( / 2)cos ]( )
sinF
Dipole Antenna: length v.s. directivity
Type Short dipole A λ/2 dipole A λ dipole longer
Directivity 1.5 1.64 2.41 ↓
HP width 78° 47° 32°
Out-of-phase and Cancellation in the far field
In-phase and enhancement in the far-field
Directivity is dropped
Dipole Antenna: length v.s. radiation resistance
Input resistance is near infinity because the input current is zero at the feeding point.
Monopole
,,
,
, ,
112
2
A dipoleA mono
A A dipole
A mono A dipole
VVZ Z
I I
1. Radiation resistance is half 2. Directivity is double
2mono dipoleD D
EMI due to Common-mode current can be explained by The theory of monopole antenna.
Small loop antenna:
2
2
ˆsin4
ˆsin4
1 ˆˆ sin4
j r
j r
j r
IeA j
r
IeE S
r
IeH r E S
r
The fields depend only on the magnetic moment (IS) and not the loop shape.
2 2 2 2
22 / 20( ) 31200( )r
SR P I S
The radiation resistance can be increased by using multiple turns (N)
2
231200( )r
NSR
S is the area of the loop
Small loop antenna:
• The small loop antenna is very popular in receiving antenna.
• Single turn small loop antennas are used in pagers.
• Multi-turn small loops are popular in AM broadcast receiver.
• Small loop antennas are also used in direction-finding receivers and for EMI field strength probes.
Yagi-Uda Antenna
Array Antenna can be used to increase directivity.
Array feed networks are considerably simplified if only a few elements are fed directly. Such array is referred to as a parasitic array.
A parasitic linear array of parallel dipole is called a Yagi-Uda antenna.
Uda antennas are very popular because of their simplicity and relatively high gain.
Yagi-Uda Antenna: Principles of operation
incident driverE E
If a parasitic element is positioned very close to the driver element, it is excited with roughly equal amplitude. Because the tangential E field on a good conductor should be zero. From array theory, we know that the closely spaced, equal amplitude, opposite phase elements will have end-fire patterns.
parasitic incident driverE E E
Why null here?
Yagi-Uda Antenna: Principles of operation
The simplistic beauty of Yagi is revealed by lengthening the parasite The dual end-fire beam is changed to a more desirable single end-fire beam. The H-plane pattern is obtained by the numerical method. Such a parasite is called a reflector because it appears to reflect radiation from the driver.
0.49λ 0.4781λ
Yagi-Uda Antenna: Principles of operation
0.45λ 0.4781λ
Spacing = 0.04λ
If the parasite is shorter than the driver, but now placed on the other side of the driver, the patter effect is similar to that when using a reflector in the sense that main beam enhancement is in the same direction. This parasite is then referred to as a director since it appears to direct radiation in the direction from the driver toward the director.
Yagi-Uda Antenna: Principles of operation
The single endfire beam can be further enhanced with a reflector and a director on opposite Sides of a driver. The maximum directivity obtained from three-element Yagi is about 9dBi or 7dBd.
Yagi-Uda Antenna: Principles of operation
Optimum reflector spacing SR (for maximum directivity) is between 0.15 and 0.25 wavelengths. Director-to-director spacings are typically 0.2 to 0.35 wavelengths, with the larger spacings being more common for long arrays and closer spacings for shorter arrays. The director length is typically 10 to 20% shorter than their resonant length. The addition of directors up to 5 or 6 provides a significant increase in gain.
saturation
Yagi-Uda Antenna: Principles of operation
The main effect of the reflector is on the driving point impedance at the feeding point and on the back lobe of The array. Pattern shape, and therefore gain, are mostly controlled by The director elements.
Broadband Measurement Antennas
a.FCC prefers to use tuned half-wave dipoles. For measurement of radiated
emission from 30MHz~1GH, it is time consuming because its length must be
physically adjusted to provide /2 at each f requency.
b. Broadband measurement antennas for EMC.
1.Input / output impedence is fairly constant over the frequency band.
2.The pattern is fairly constant over the frequency band.
two commonly used antenna
1.biconical antenna -- 30MHz~200MHz
2.log-periodic antenna -- 200MHz~1GHz
The Biconical Antenna
^
E^
H
z
h
+
-
h
^ ^ ^
^ ^ ^
a. Infinite biconical antenna
1. half angle .
2.feed point with small gap.
b. In the free space , the symmetry
suggests:
H H a
E E a
, 0
(1/ sin ) / (sin ) 0 .....(1)
(-1/ ) / ( ) .....(2)
r
H j E J for J
r H j E
r r rH j E
▽
c. by the Faraday’s and Ampere’s law
0
0
^
0
^
0 0 0
^ ^
0
( /sin ) /
from (1) => sin / 0
and ( / sin ) /
from (2) and TEM mode type
=>
so , we may uniquely define voltage between two point
j r
j r
H H e r
H
E H e r
E H
s on the
cores as was the case in tx lines.
0
0 0
0
^
0 0
0 0 0 0
2^ ^-
0
0
d. ( ) - - ( / sin )*
- / sin 2 ln (cot( / 2))
by Ampere's law => ( ) sin 2
e
h h
h h
h
h
j r
j r j r
h
j r
V r E dl H e r rd
H e d H e
I r H r d H e
^ ^ ^
00
^ ^
. Input impedence : ( at 0)
( ) / ( ) ( / ) ln(cot( / 2)) 120ln(cot( / 2))
Usually , the half angle is choosen such that
in h hr
in C
r
Z V r I r
Z Z
^
rad
2-2 ^2
00
-22
0 0 0 0
f. for infinite biconnical antenna
R = Z
proof => / 2 sin
* / sin 2 *ln(cot( / 2))
h
h
h
h
in
avrad S
h
P S ds E r d d
H d H
20 0
^ ^ ^2 2
(1/ 2)(2 ) ( / *ln(cot( / 2)))
(1/ 2)( ) (1/ 2)( )
h
inrad
H
I R I Z
^
^'
in
f. note : (1) Z is independent of frequency ( flat response) for infinite core
(2) but , practice antenna is finite length , so
Z = R + jX some
in
storage energy will apear
g. EMC biconical antenna
- +
With wire element
- +
Log-Periodic Dipole Array (LPDA) Antenna
1 1n
n
R
R
Scale factor
Spacing factor
2
n
n
d
L
Why is the LPDA constructed as below?
Log-Periodic Dipole Array (LPDA) Antenna
It is convenient to view the LPDA operation as being similar to that of a Yagi-Uda antenna. The longer dipole behind the most active dipole behaves as a reflector and the adjacent shorter dipole in front acts as a director. The radiation is then off of the apex.
Antenna Arrays:
• Hertzian dipole, small loop, half dipole, and monopole are all omnidirectional because of symmetry of the structure. • Two or more omni-directional antennas can change the pattern (create null or maximum). Better both for communication and EMI considerations. • This can be achieved by phasing the currents to the antennas and separated them sufficiently such that the fields will add constructively and destructively to result in the null/maximum patterns.
Antenna arrays
a. By using two or more omni-directional antennas to produce maxima and/or nulls in the resulting pattern.
b. The far fields at point P due to each antenna are of the form:
ψ x
y
z
d
θ1 θ2 θ
r r1 r2
-d/2 d/2
P
0 2
0 2
1
1
2
2
ˆˆ
ˆ 0ˆ
j r
j r
MIE e
r
MIE e
r
1 2
note:
1. 0 and , we assume that the currents of the two
antennas are equal in magnitude but with phase difference .
ˆ 2. depends on the type of antennas used.
I I I I
M
0 0
0
1 2
ˆ for Hertzian dipole: sin4
ˆ for long dipole : .
c. The total field at point P
0 1 0 22 2 2ˆ ˆ ˆ ˆ
1 2
using for field
dlM j
M j F
j j jj r j re e
E E E MIe e er r
1 2
1
2
approximation.
(1) for distance term.
(2) cos sin sin2 2
cos sin sin ,where cos sin sin2 2
r y
r r r
d dr r r
d dr r r a a
sin sin sin sinˆ 0 02 2 2 202ˆ
02 ˆ 2 cos sin sin
20
pattern of individual F
d dj j jj rMIE e e e e
r
j j rIe d
e Mr
array
array ,
elements
d. The principle of Pattern Multiplication:
The resultant field is the product of the individual antenna element and
the array factor F , .
e. Some example
s of the patternsof two-element array
d=λ/2,α=0 (1)
I∠α I∠0
ψ X
Y
0
array
sinF ( =90 , )=cos
2
(2) d=λ/2,α=π
I∠α
I∠0
d
d
x
y 0
array
sinF ( =90 , )=cos
2 2
Antenna Arrays:
• Two arbitrary omni-directional antennas • Separate a distance d • currents on two antennas are equal in amplitude and phase delay α
0
/ 2
0
2 [ ] cos( sin sin )2
j rj Ie d
E e Mr
Pattern of individual antenna
Array pattern
2 21
2r
m nf
a b
port1(5cm,4cm)
port2(4cm,8cm)
port3(1cm,9cm)
port4(6cm,6cm)
10cm
10cm
1.6mmX
Y
(0,0)
Microstrip Antenna and Resonance frequency
Antenna Examples: Microstrip Antenna with edge coupled (at 2.1GHz)
3cm x 4cm
ε=2.2
Current distribution
2D
3D
Antenna Examples: Microstrip Antenna with inserted feed and edge coupled (at 2.1GHz)
Current distribution
2D
3D
Antenna Examples: Microstrip Antenna with inserted feed and edge coupled (at 2.1GHz)
Gain: 6.4dB Efficiency: 49.1%
Top Related