Transcript Antennas & Propagation

Lecture IV
Antennas & Propagation
-1-
Antennas
&
Propagation
Mischa Dohler
King’s College London
Centre for Telecommunications Research
Lecture IV
Antennas & Propagation
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Overview of Lecture IV
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Review of Lecture III
-
Extensions of the finite length Dipole
-
Definitions Mutual and Self Impedance
Lecture IV
Antennas & Propagation
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Review
The following definitions are applicable to all antennas:
1. Power Density w = Re{S}
2.Total Radiated Power P
3. Radiation Resistance Rr
4. Antenna Impedance ZA
Lecture IV
Antennas & Propagation
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Review
5. Equivalent Circuit
6. Load matching
7. Effective Length le
8. Effective Area Ae
9. Radiation Intensity U
12. Directivity D
10. HPBW / Bandwidth B
13. Radiation Efficiency e
11. Directive Gain g
14. (Power) Gain G
Dipole of finite length
jk
Hφ 
I 0  e  jkr  le θ 
4πr
E    H φ
Lecture IV
Antennas & Propagation
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Review
sin 
jkzcos
le   
I
(
z
)

e
 dz

I ( 0) L
I ( z )  I max
 1

 sin k   L  z  ,

 2
I max
1 
 I (0) / sin  kL
2 
L/a > 60 : Hallén's Integral  Transmission Line
Hallén's Integral Equation
Objective:
Lecture IV
Antennas & Propagation
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Review
(1)
Current distribution I along a wire
(2)
Input impedance
Proceedings: (Derivation on blackboard!)
(1)
Obtain magnetic vector potential A inside a wire due to
driven voltage V.
(2)
Obtain magnetic vector potential A outside a wire due
to current I.
(3)
Equate the tangential component of both at the surface
of the wire.
(4)
Solve the equation to obtain I and Za
Pattern Factor P

Lecture IV
Antennas & Propagation
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Review



cos 1 kL cos  cos 1 kL
2
2
P  
sin  
Radiation Power
Radiation Resistance Rr
Directivity D
Lecture IV
Antennas & Propagation
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Extensions
of the finite length Dipole
1 2
Pradiated   I max feeding   Rr geometry 
2
Lecture IV
Antennas & Propagation
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Problem with /2 Dipole
For practical applications
1. Is there an antenna with similar geometric
properties (size) but a higher radiation resistance?
2. Is there an antenna with similar radiation
properties (pattern, etc) but smaller size?
“A folded dipole has a radiation pattern the same as a
dipole but with a four-fold increase in radiation resistance.”
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Folded Dipole
double strength = double amplitude = four-fold power = four-fold resistance
L=/2 : Rr = 4*73 = 292
“A monopole antenna is a straight conductor above a
conducting plane. It behaves like a dipole twice its length
but double directivity.”
Lecture IV
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Monopole Antenna
Tool of Analysis: Image Theory.
half power = half radiation resistance
L=/4 : Rr = 36.5 D = 3.28
Lecture IV
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Reciprocity
Theorem
“If a voltage VA is applied to the terminal of antenna A and
the current IB measured at the terminal of another antenna
B, then an equal current IA will be obtained at the terminal
Lecture IV
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Reciprocity Theorem (Carson)
of antenna A if the same voltage VB is applied to the
terminal of antenna B.”
2 Antennas
VA ( z1  0) VB ( z2  0)

I B ( z2  0) I A ( z1  0)
1 Antenna
VA ( z1  0) VA ( z1  z )

I A ( z1  z ) I A ( z1  0)
Transmitting – Receiving Antenna
All the concepts introduced for the transmitting antenna hold for
the receiving and vice versa!
Lecture IV
Antennas & Propagation
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Consequences
impedance, effective length, effective area, directional pattern, etc
Friis Transmission Formula
Preceived
  
 GA  GB  

Ptransmitted
 4r 
2
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Mutual and Self
Impedance
Self Impedance
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Definitions
V (0)
Za 
I (0)
Mutual Impedance
V21
V12
Z 21 
 Z12 
I1
I2
Both antennas are driven.
I2
I1
Lecture IV
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2-Pole Theory
V2
V1
V1  I1  Z11  I 2  Z12
V2  I1  Z 21  I 2  Z 22
n-pole  numerical calculations
Z a  Z11 