This document discusses phased array antennas and antenna synthesis. It describes how a phased array antenna uses multiple antennas with adjustable phase delays to steer beams in different directions. It also covers techniques for antenna synthesis, including Dolph-Chebyshev and Taylor methods, to design arrays with low sidelobes and optimize parameters like element spacing and excitation amplitudes. Finally, it compares conventional antennas to smart antenna arrays, noting that adaptive arrays can actively direct beams towards desired signals while rejecting interference.

1. Antenna Synthesis
ALBERTO DI MARIA
AJAL.A.J – AP ECE DEPT
UNIVERSAL ENGG COLLEGE
MAIL: EC2REACH@GMAIL.COM

2. APP. A: PHASED ARRAY ANTENNA :
SINGLE ANTENNA

3. APP. A: PHASED ARRAY ANTENNA:
MULTIPLE ANTENNAS

4. APP. A: PHASED ARRAY ANTENNA:
BEAM STEERING

5. MWP » MWP IN PAAS » SMART » CONCLUSIONS » QUESTIONS »
APP. A: PHASED ARRAY RECEIVE
ANTENNA: DELAYS
T
2T

6. MWP » MWP IN PAAS » SMART » CONCLUSIONS » QUESTIONS »
antenna 1
antenna 2
antenna 3
+
+
T
2T

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8. ANSYS Conference & 27. CADFEM Users’ Meeting 2009 – Nov. 19th
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HFSS complete antenna model
The model is electrically large and
complex

12. ANSYS Conference & 27. CADFEM Users’ Meeting 2009 – Nov. 19th
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HFSS complete antenna model
Field Animation: Antenna, feed and enclosure
Vertical Polarization

13. ANSYS Conference & 27. CADFEM Users’ Meeting 2009 – Nov. 19th
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HFSS complete antenna model
Field Animation: Antenna, feed and enclosure
Horizontal Polarization

14. ANSYS Conference & 27. CADFEM Users’ Meeting 2009 – Nov. 19th
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HFSS complete antenna model

15. Simulations to computeSimulations to compute TTAA
15

16. 16
Observable Sky

17. Antenna Synthesis
1. Basic principle for antenna synthesis
2. Line source synthesis (Fourier transform,
woodward-lanson sampling)
3. Linear array synthesis (Fourier series, woodward-
lanson sampling)
4. Low sidelobe synthesis (Dolph-Chebyshev,
Taylor)

18. Synthesis Problems
Given affordable SLL, No. of elements,
how to synthesize?
Ideal case: narrow beam, constant side-lobe envelope
Approaches: Dolph-Chebyshev, Taylor Line Source….
Secret behind: to synthesize a polynomial like pattern….

19. Examples of Chebyshev polynomials.

20. Dolph-Chebyshev Linear Array
The Chebyshev polynomials:





 −
=
−
−
−
)coshcosh(
)coscos(
)coshcosh()1(
)(
1
1
1
xn
xn
xn
xT
n
n
1−<x
11 <<− x
1>x

188)(
34)(
12)(
)(
1)(
24
4
3
3
2
2
1
0
+−=
−=
−=
=
=
xxxT
xxxT
xxT
xxT
xT )()(2)( 11 xTxxTxT nnn −+ −=
Property used:
)][cos()cos( ψψ nTn =

21. Chebyshev Polyminals

22. Symmetrically Excited Array







−
+
=
∑
∑
=
−
=
2/
1
2/)1(
1
0
]
2
)12cos[(2
)cos(2
)( P
m
m
P
m
m
mi
mii
f
ψ
ψ
ψ,mm ii =−
, P odd
, P even
)][cos()cos( ψψ nTn =
Property:
)(ψf is P-1 th polynomial of )
2
cos(
ψ
)
2
cos(0
ψ
xx =Let
Choose appropriate to match the coefficients to those in
Chebyshev polynomial, we obtain,
mi
)]
2
cos([)( 01
ψ
ψ xTf P−=

23. Chebyshev Polynomial Example

24. Synthesis Standards
SLL=-20log R (dB)
so ]cosh)1cosh[()( 0
1
01 xPxTR P
−
− −==
]cosh
1
1
cosh( 1
0 R
P
x −
−
=












−=
−
π
γ
λ
1
cos
1
1
optd












−=
−
π
γλ
1
cos
1
2
1
optd
Optimum spacing,
Broadside: Endfire:
)]1ln(
1
1
cosh[ 2
−+
−
= RR
P
γ, where

25. Beamwidth and Directivity
In general, d
HP h
β
ψ
π 1
cos2 −
−= (broadside)
)1(cos 1
d
HP h
β
ψ
−= − (endfire)
, where












−
−
=
−
−
−
]cosh
1
1
cosh[
]
2
cosh
1
1
cosh[
cos2
1
1
1
R
P
R
P
nψ
An approximation for the broadside:
L
RHP
λ
π
)2ln(
1
=
Beambroadening factor: )2ln(637.0
866.0
)2ln(
1
R
R
bHP == π
HPR
R
D 2
2
1
2
+
=Directivity:

26. Synthesized Array Factor

27. Example No.2
Optimum Spaced 10-Element, -30dB Side Lobe,
Dolph-Chebyshev Endfire Array

28. Transformed Chebyshev Polynomial

29. Bionomial array

31. 4×4 Two Dimensional Beam Steering
Array
Antenna
Nonlinear
Delay LineBias Board
Power Divider

32. Tapering of Arrays

33. Tapering may not reduce sidelobes.
• The dish antenna theory: Tapering of the current distribution at the apperture
leads to the side lobes decrease.
• This statement may not be true at the case of the arrays. Tapering is
multiplication of the UV coverage with the tapering function. So at the
image plane, it leads to the convolution of the untapered beam pattern with
the Fourier transform of the tapering function. The convolution leads to the
broadening of the main beam as well of the sidelobes. But the level of
sidelobes may not be reduced, if the distance between the sidelobes is bigger
than the width of the Fourier transform of the tapering function

34. Super directive arrays

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beamformerAntenna
array
RF
front-end to
receiver(s)
40x40
gain
beam
width
scan
angle
optical
with
amplitude
tapering
8x8 8x1

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OBFN
electrical » optical optical » electrical
RF front-end
LNA
TIA
DM laser
chirp!
E/O and O/E conversions?
• low optical bandwidth;
• high linearity;
• low noise
photo-
diode

37. 37 / 42MWP » MWP in PAAs » SMART » Conclusions » Questions »
mod.
OBFN
RF front-end
LNA
spectrum
frequency
TIA
electrical » optical optical » electrical
CW laser
10.7 GHz
12.75 GHz2 x 12.75 = 25.5 GHz
photo-
diode

38. Conventional Antennas & Arrays
Antenna
Top View
Antenna
Array
Top View
Omnidirectional Sectorized

39. WHY SMART ANTENNA ARRAYS ARE
SUPERIOR TO CONVENTIONAL ANTENNAS
Switched Beam System Adaptive Array
Antenna
Array
Desired
User
Interfering
User
Antenna
Array
Active
Beam

40. Interference Rejection Comparison
Desired Signals
Co-channel Interfering Signals

41. TYPES (summary)

42. ANSYS Conference & 27. CADFEM Users’ Meeting 2009 – Nov. 19th
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Thank you