Antenna & Array Fundamentals Technical Training Courses Sampler

Course Sampler From ATI Professional Development Short Course

Antenna and Antenna Array Fundamentals

Instructor:
Dr. Steven Weiss

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What you will learn from this course

• Basic antenna concepts and definitions
• The appropriate antenna for your
application
• Factors that affect antenna array designs
and antenna systems
• Measurement techniques commonly used
in anechoic chambers

Copyright 2012 © by Steven Weiss – all rights reserved

3

Example of a “Real World” Radar Antenna Array

The MU (Middle and Upper atmosphere) radar constructed by the Radio Atmospheric Science Center of Kyoto University at Shigaraki,
Shiga prefecture, Japan

• Investigates atmospheric and plasma dynamics in the wide region from the troposphere to the ionosphere.
• The radar is a powerful monostatic pulse Doppler radar operating at 46.5MHz
• It uses active phased array antenna, which consists of 475 crossed Yagi antennas and identical number of solid-state transmit/receive modules.
• The antenna beam direction can be switched to any direction within the steering range of 30deg from zenith from pulse to pulse.
• The antenna aperture is 8,330m^2 (103m in diameter), and the peak and average output power is 1MW and 50kW, respectively.
• The antenna beam has a conical shape with the round-trip (two-way) half-power beamwidth of 2.6deg. 4

Examples of Antennas

The VLA is an array of telescopes that can be linked CSIRO Parkes radio telescope is the largest and oldest
together to synthesize the resolving power of a telescope of the eight antennas comprising the 'Australian
upto 36 km (22 miles) across, or grouped together to Telescope National Facility'. The Compact Array of six
synthesize one only a km (0.6 mile) across: the varying 22-metre dishes near Narrabri and another near
resolutions are the equivalent of an astronomical zoom Coonabarabran link up with the 64 meter Parkes to
lens. This array is located near Socorro, NM synthesize a telescope some 300 kilometers across.

5

Radio Telescope
Arecibo, Puerto Rico
305m in Diameter

6

Missile Defense
Eglin FPS-85 radar located near Ft. Walton Working inside a 10-story Pave Phased Array Warning System, or
Pave PAWS, the men and women of the 7th Space Warning
Beach, FL. This phased array radar is a dedicated Squadron continuously scan the horizon for missiles, satellites and
sensor to the U.S. satellite catalog. other man-made objects in space.

7

European Remote Sensing satellite (ERS) Inmarsat
Provides information about the Used for Global Communications
Earth’s land, oceans and polar caps

8

9

10

Types of Antennas
• Electrically small antennas
• Resonant antennas
• Broadband antennas
• Aperture antennas

11

Electrically Small Antennas
The extent of the antenna structure is much less than the wavelength
• Very low directivity
• Low input resistance
• High input reactance
• Low radiation efficiency

 

Short Dipole  

Small Loop

12

Resonant Antennas
The antenna operates well at a single or selected narrow frequency band
• Low to moderate gain
• Real input impedance
• Narrow bandwidth

 
~ ~
2 2
Half-wave Dipole 
~
2
Yagi
Microstrip Patch

13

Broadband Antennas
The pattern, gain, and impedance remain acceptable and are nearly constant
over a wide frequency range. They are characterized by an active region with
a circumference of one wavelength or an extent of a half-wavelength which
relocates on the antenna as the frequency changes

• Low to moderate gain
• Constant gain
• Real input impedance
• Wide Bandwidth

Spiral
Log-periodic dipole array 14

Aperture Antennas
Have a physical aperture through which the waves flow.

• High Gain
• Gain increases with frequency
• Moderate bandwidth

Aperture Aperture

15

Basic Concepts
• Directivity
• Gain
• Antenna Patterns
• Beamwidth
• Polarization
• Bandwidth
• Radiation Resistance/Input impedance
• Reciprocity
• Effective Aperture 16

What is the directivity of antenna?

Ratio of radiation intensity in a given direction
to the radiation intensity that would be
obtained if the total power radiated by the
antenna were to be radiated isotropically

What is the gain of antenna?
Ratio of radiation intensity in a given direction to
the radiation intensity that would be obtained if
the total power accepted by the antenna were to
be radiated isotropically
17

Simple Illustration (light bulb)
Radiating with equal intensity in all
directions (isotropic radiation) Power meter reading radiated
power (isotropic)

P (isotropic)

Radiation is focused in a particular
direction due to the reflector

Power meter reading of radiated
power (in a given direction)

P (direction)

18
Note that polarization must –be considered with RF antennas
Copyright 2012 © by Steven Weiss all rights reserved

Directivity and Gain
• The directivity can be thought of as the ratio of the maximum radiation
intensity emanating from an antenna to the total power leaving the antenna
radiated isotropically per solid angle of a sphere.
• The radiation intensity of an isotropic source is: (Prad ) / (solid angle of a
sphere).
U isotropic  Pradiated / 4 
• The gain of an antenna can be thought of as the ratio of the maximum
radiation intensity emanating from an antenna to the total power introduced
into the antenna: (Pin ) / (solid angle of a sphere).
• Losses prevent the power input into the antenna from equaling the radiated
power.

Prad   Pin
• The gain of an antenna is always less than the
directivity of a antenna. 19

Formulas for Directivity and Gain
U  ,   U   ,   max
D  ,    Do 
Prad Prad
4 4

U  ,    U  ,  
G  ,       D  ,  
Pin Prad
4 4

U   ,   max  U   ,   max
Go     Do
Pin Prad
4 4

Gain is usually expressed in log form :
G dBi  10 Log (  Do )  10 Log ( Do )  10 Log (  ) 20

A Directed Beam is Described by its
Antenna Pattern

Main lobe

Side lobes

Back lobes
21

More Details about Radiation
Patterns

Beamwidth (between 3 dB points)

22

Patterns

Omni-directional pattern Hemispherical pattern
Equal power everywhere Isotropic pattern
Equal power in one plane.
in upper half-plane. Equal power everywhere.

23

Polarization

• Electric fields must be aligned for maximum
power transfer between two antennas.
• The alignment is described by a polarization loss
factor (PLF).
• Analytically, the polarization loss factor is the
electric field of the incoming wave dotted with
the electric field that would be transmitted by
the receiving antenna.

24

An Introduction to Polarization

• When speaking of “polarization,” we are describing
the behavior of electric field of the antenna.
• The field may remain oriented in one direction as the
electric field propagates (linear polarization)
• The field may spin as the electric field propagates
(circular or elliptical polarization)
• Polarization will be considered in detail later in this
course, but you already have enough material to
understand how our math can describe such electric
fields!

25


Here is an interesting antenna that has two input ports. We will
designate these as port 1 and port 2

Port 2

Port 1

26


Port 2
Port 1

Y
Add
some
geometry
!

X

27

Exciting port 1 causes an electric field to exist between the two horizontal fins
and the field at the “aperture” of the antenna is oriented in the x-direction

E  a x Eo
ˆ

Port 1
Y

X

28

Exciting port 2 causes an electric field to exist between the two vertical fins
and the field at the “aperture” of the antenna is oriented in the y-direction

E  a y Eo
ˆ
Port 2

Y

X

29

We already know that we can represent time-varying fields as phasors.
If we excited both ports at once (with equal strength) , we expect the
phasor representation of the electric field at the aperture to be of the
form:
E  a x Eo  a y Eo
ˆ ˆ
The time-dependent behavoir at the aperture becomes:
j t
 (t )  Re[ (a x E o  a y E o ) e
ˆ ˆ ]  (a x E o  a y E o ) Cos (  t )
ˆ ˆ
It is illustrative to plot this electric field using certain "snapshots" of time.
Holding "" as a constant, there is an instant when the product  t equals
zero. Similarly, there are different instances when  t equals  /2 and 
and 3 /2 and so forth. Letting E o  1 V / m, we can make a table and
parametrically plot the time-dependent electric field at the aperture. 30


t (a x  a y ) Cos (  t )
ˆ ˆ
t  
0 (a x  a y )
ˆ ˆ
 /2 0 X
  (a x  a y )
ˆ ˆ t   /2 
3 / 2 0 t  0

Y
The y-axis is pointed downward so that the z-axis would be into the page.
We observe the behavior of the electric field at z  0 (at the aperture.)
The electric field is linearly polarized oriented at a 45 Degree angle with the
y-axis (the tilt angle " .") It is also at a 45 Degree angle with the x-axis,
but we define the tilt angle with respect to the y-axis. 31

Now we make one "small" change to our phasor representation of
ˆ
the electric field at the aperture placing a "j" in front of the a y term:
So,
E  a x Eo  j a y Eo
ˆ ˆ
This term has a significant impact on the time-dependent behavoir of
the elctric field:
j t
 (t )  Re[ (a x E o  j a y E o ) e
ˆ ˆ ]
 Re[ (a x E o  j a y E o ) (Cos (  t )  j Sin (  t )) ]
ˆ ˆ
 a x E o Cos (  t )  a y E o Sin (  t )
ˆ ˆ
Again, we hold "" as a constant and parametrically plot the time-
dependent electric field at the aperture. Again, let E o  1 V / m.
32


t a x Cos (  t )  a y Sin (  t )
ˆ ˆ
0 ˆ
ax
 /2 ay
ˆ t   /2

  ax
ˆ
3 / 2 ˆ
ay
X

t   t  0

 t  3 / 2
Y

The electric field is spinning in a counter-clockwise direction!
33

Is it right-hand or left-hand polarization?
1) Place your thumb towards the direction of propagation. This would be
into the page.
2) If your fingers align with the "spin" you have answered the question!
Try it with each hand and you will find that this example is left-hand
circularly polarized (LHCP.) t   /2

X

t   t  0

 t  3 / 2 34
Y

So, is left-hand polarization counterclockwise and right-hand clockwise?
Answer: Not enough information!
You must state whether the field is "leaving" or "arriving."
A thumb pointed away from you indicates a leaving wave.
A thumb pointed toward you indicates an arriving wave.

le ft-h a n d is le ft-h a n d is r ig h t-h a n d is r ig h t-h a n d is
c o u n te rc lo c k w is e c lo c k w is e c lo c k w is e c o u n te r c lo c k w is e
le a v in g a rr iv in g le a v in g a r r iv in g 35

Port 2
Port 1
Y

X

This antenna is capable of exciting orthogonal electric fields (i.e., in the x- and y-directions.)
If the fields are excited in phase, the field leaving the antenna will be linearly polarized
leaving the antenna at a 45 Degree angle – if the signal strength is the same at both feeds.

For example: Port 1 = V o Cos (  t ) and Port 2 = V o Cos (  t )
36

Port 2
Port 1
Y

X

Again, the antenna is capable of exciting orthogonal electric fields (i.e., in the x- and y-
directions.) If the fields are excited in phase quadrature, the field leaving the antenna will
be circularly polarized – if the signal strength is the same at both feeds.

For example: Port 1 = V o Cos (  t ) and Port 2 =  V o Sin (  t )
37


We could achieve circular polarization with and RF source, a power splitter, and a 90 Degree
phase shifter.

Power Splitter

90 

RF Source

38

Polarization (elliptical)
 y , x Assume any value

Ex , E y Not necessarily equal

OA
AR  Axial Ratio  
OB
1  AR  

+ for RH polarization
- for LH polarization
Tilt angle
 
 1 1  2 E x E y 
   tan  cos  
 Ex 2  E y 
2
2 2
       39
x y

CP Measurements
Axial Ratio


Polarization Loss Factor
2
EInc  ETrans
PLF  2 2
EInc ETrans

EInc ETrans
w 
ˆ a 
ˆ
EInc Etrans

2
PLF   w   a
ˆ ˆ

The electric fields are in phasor form and
may be complex quantities
41

Polarization
Polarization is a critical issue when considering antennas

Proper alignment – Maximum power transferred from antenna A to antenna B.

A B

Antenna “A” transmits a Antenna “B” is oriented
vertically polarized signal to receive a vertically
polarized signal
Improper alignment – Minimum power transferred from antenna A to antenna B.

A B

Antenna “A” transmits a Antenna “B” is oriented
vertically polarized signal to receive a horizontally
polarized signal

Circular to linear – 1 / 2 the power transferred from antenna A to antenna B.

A B

Antenna “A” transmits a Antenna “B” is oriented to receive
circularly polarized signal linear polarization in any direction 42

Bandwidth
• There are 3 equivalent ways do describe the
bandwidth of an antenna

– Return loss (-10 dB convention)

– VSWR (2:1 convention)

– Polar Plot (Smith chart)   0.316228

43

Definition of the Reflection Coefficient
Characteristic impedance of the transmission line

Transmitted Voltage
V

Zo
V
Reflected Voltage

 Reflection Coefficient – a complex ratio of the
V reflected voltage divided by the transmitted voltage
 
V measured at a defined reference place (e.g., the input
port of the antenna.
44

Reflected Power
      r  j i   r  j i    
2 * 2 2
r i


2
 1  
2

2
  Percentage of power reflected from the antenna
1  
2
  Percentage of power entering the antenna
Note that the power entering the antenna is not equal to the power radiated
by the antenna. Some power is consumed in conductor and other losses
45

Bandwidth – A Logarithmic Plot
A return loss of -10 dB is conventionally defines as the bandwidth of the antenna

Bandwidth  f H  f L
0 fH
fL -5
- 10
dB

- 15
- 20
- 25

2 4 6 8 10
Frequency

fo 46

Bandwidth – VSWR Plot
1  
2
1.75 
1.5
1.25 The impedance mismatch between the
1 Antenna’s input impedance and the
0.75 characteristic impedance of the
0.5 transmission line causes a standing
wave to exist along the length of the
0.25
transmission line.
0.2 0.4 0.6 0.8 1
Distance back from the reference plane
Frequency

1    6

5

Bandwidth  f H  f L 4
V SWR

3

VSWR 
1    2
fH
1   
fL 1

fo 2 4 6 8
47
10
Frequency

Bandwidth – Polar Plot
I
Bandwidth  f H  f L   1

Discrete Data points
measured on a
fL
Network Analyzer

R
fH fo

  0.316228 48

Bandwidth – Polar Plot/Smith Chart
From transmission line theory I
ZL  Zo
  R  j I 
ZL  Zo
When the real and
fL
imaginary parts of the load
impedance are
determined as a function
of the real and imaginary R
parts of the reflection
coefficient, the resulting fH
fH
circles and arcs define the
Smith Chart.

  0.316228 49

Realized (or actual) Gain

Grealized  ( 1   ) Go  ( 1   )  Do
2 2

50

Bandwidth – Equivalent Quantities

 Return Loss VSWR 1 
2

0.316228 -10 dB 1.9245 0.9

0.100000 -20 dB 1.2222 0.99

0.031622 -30 dB 1.0653 0.999

51

Antenna Impedance
(Transmit)
The input impedance is the
impedance presented by an
antenna at its terminals

generator a radiated waves
Zg
b

Z A  RA  jX A

radiation resistance

RA  RR  RL
52

Input Impedance of Antennas (Transmit)
Vg Vg From circuit theory
Ig  
ZA  Zg ( RR  RL  Rg )  j ( X A  X g )

2
1 2 Vg  Rr 
Pr  I g RR    Power delivered to the
2 2  ( RR  RL  Rg ) 2  ( X A  X g ) 2 
  antenna for radiation

Power dissipated as
2
1 2 Vg  RL 
PL  I g RL    heat on the antenna
2 2  ( RR  RL  Rg ) 2  ( X A  X g ) 2 
 
2 Power dissipated as heat
1 2 Vg  Rg  on the internal resistance
Pg  I g Rg   
2 2  ( RR  RL  Rg ) 2  ( X A  X g ) 2  of the generator
 
ZA  Zg
*
Conjugate matched conditions deliver
the the maximum power to the antenna. RR  RL  Rg
X A  X g
53

Input Impedance of Antennas (transmit)
2
Vg Rr Radiated power assuming conjugate matching
Pr 
8 ( RR  RL ) 2
2
Vg RL Dissipated power in the antenna assuming conjugate matching
PL 
8 ( RR  RL ) 2
2 2
Vg Rg Vg Dissipated power in the generator’s internal impedance
Pg  
8 ( RR  RL ) 2
8 Rg

The total power is: Pg  PR  PL
2
Power supplied by the 1 Vg 1
generator : Pg  Vg I g 
*

2 4 RR  RL

Therefore, under conjugate match conditions, half the power that is
supplied by the generator is dissipated as heat in its internal resistance
and the other half is delivered to the antenna.
54

Antenna Impedance
(receive)

Again, the input impedance is
the impedance presented by
an antenna at its terminals

55

Input Impedance of Antennas (receive)
Assuming conjugate matched conditions delivering the maximum power to the antenna.

2
VT Power delivered to the antenna’s terminating impedance
PT 
8 RT

VT 2
RR  Power across the radiation resistance of the antenna
Pr   
8  ( R R  R L )2 
 

VT
2
RL 
PL   2  Power dissipated as heat due to the losses in the antenna
8  (R R RL ) 
 

56

Reciprocity for Antennas

V2 ( ,  ) I2
1 2
I1 V1 ( ,  )

Transmitting pattern of antenna “1” Receiving pattern of antenna “2”
V2 ( ,  ) V2 ( ,  )
Z12 ( ,  )  Z 21 ( ,  ) 
I1 I1
Z12 ( ,  )  Z 21 ( ,  )
Important Point!!! The transmit and receive patterns of an antenna are
the same for a reciprocal antenna. 57

Aperture Size
• Antenna engineers frequently discuss antennas in
terms of Aperture Size.
• A common term is the “effective aperture” size.
• Another term is the “physical aperture” size.
• Aperture size is related to the beamwidth and
accordingly the directivity and gain.

ZL

58

Effective Aperture Size
• The effective aperture size is a relationship between the
incident electromagnetic field and the power delivered to the
terminating impedance on the antenna’s input port.
PT
Aeffective  (m 2 )
Wincident
PT  The power developed across the terminating impedance (w)
Wincident  The strength of the incident electromagnetic field
at the aperture of the antenna (w/m 2 )

PT
Wincident ZL

59

Effective Aperture Size
• The effective aperture size is related to the directivity of the antenna
• Anything that diminishes the power across the terminating impedance
decreases the effective aperture size
• If no power develops across the terminating impedance, the effective
aperture size is zero - even if there is an incident electromagnetic field.
2
Ae m  DO (m 2 )
4
PT 2 2
Ae    cd 
(1   ) DO w  a
2
ˆ ˆ (m 2 )
W inc 4

PT
Wincident ZL

60

Physical Aperture Size and
Aperture Efficiency

Area  Length x Width Area   r 2

Ae m Maximium Effective Aperture
 ap  
Ap Physical Area 61

Friis Transmission Formula

62

Friis Transmission Formula
Time average power density transmitted by satellite Satellite
Antenna
Pr  W Aer effective aperture of Pt , Gt
receiving antenna R

total transmitted power Gr
dish
antenna
Pt
W Gt gain of transmitting antenna
4 R 2

4 2
Gr  2 Aer so Aer  Gr
 4
 2
Friis transmission formula Pr  Pt Gt Gr
(4 R) 2
63

Communication Link

Gt ( t , t ) Gr ( r , r )

R
ZL

Pr  2
 (1  t ) (1   r ) ( ) Gt ( t ,  t ) Gr ( r ,  r )  w  a
2 2 2
ˆ ˆ
Pt 4 R

64

Communication Links in dBm
 Power Milliwatts 
Pr (dBm)  10 Log10  
 1 Milliwatt 

2
Friis transmission formula Pr  Pt Gt Gr
(4 R) 2
G (dB)  10 log G
Divide each side by 1 mw and take the log

Pr (dBm)  Pt (dBm)  Gt (dB)  Gr (dB )
 20 log R (km)  20 log f ( MHz )  32.44
c C = Speed of light
Note:  
f F = frequency
65

The Friis Transmission Formula

Our work with the Friis transmission
formula presumed a rather pristine
environment where one did not have
to worry about the attenuation through
the atmosphere. Of course, these
effects cannot be ignored. Shown to
the left is a plot of attenuation effects
due to oxygen and water vapor.

Accordingly, any link budget would need
to be adjusted to take these (and other)
propagation effects into account. At this
point we begin to leave the study of
antenna theory and enter the realm of
propagation theory.

R. E. Collin, Antennas and Radiowave Propagation, New York, McGraw Hill, 1985, pp 409.
66

Much more!!!

67

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Hyperspectral and Multispectral Imaging

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