Date post: | 18-Jan-2018 |
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Superposition
Fourier Series
Constructive Interference of a pulse
Destructive Interference of a pulse
Constructive Interference of Harmonic Waves
Destructive Interference of Harmonic Waves
2 Dimensional Example
Single Hydrophone
Display1
tpMtv
“omni-directional”
hydrophoneprocessor
2output v 2
2 Mp tvPowerR R
Two Hydrophones
Beam Former
1
2 21 2output v v
hydrophones processor
Display
2 21 2output v v Why not ???
tpMtv
Incident Wave
Beam Former
1
2xd
21 2output v v
Display
1 1 max
2 2 max
221 2 max
v Mp t Mp cos k 0 t
v Mp t Mp cos k x t
output v v Mp cos t cos t
where k x kdsin
Identities
cos cos 2cos sin2 2
2 2sin cos 1
cos cos cos sin sin
2 1 1cos cos 22 2
ie cos i sin
1cos cos cos cos2
Power Output from the Processor 2
2max coscos ttR
MpP
cos1
cos2cos21
21
cos2cos212coscos
coscos2coscos
2max
2max
222
max
222
max
RMpP
tR
MpP
tttR
MpP
ttttR
MpP
R
MpP2
max20
k x kdsin
Beam Pattern Function
2max
2max
Mp1 cosP Rb
P 0 Mp1 cos 0
R1 cos kdsin
b2
sincos
or 2sincos
2
2
db
kdb
21 cos 2 cos2
Trig identity
k x kdsin
Example = .5 d
null
max
BW
Beam Pattern Function (/d = 0.5)
array elements
=0
Maximum Power Directions
dn
dn
nd
d
db
1max
max
max
max
max2max
sin
sin
.0,1,2,3,..n wheresin
1sin
cos
sincos1
null
max
BW
Beam Pattern Function (/d = 0.5)
array elements
=0
Null Angles
dndn
nd
d
db
null
null
null
nullnull
2sin
2sin
.1,3,5,7,..n where2
sin
0sin
cos
sincos0
1
null
2
null
max
BW
Beam Pattern Function (/d = 0.5)
array elements
=0
Beam Width
• The beamwidth of a beam is the angular displacement between the angles where the beam pattern function, b(), is greater than 0.5.
• 3 dB down points • The beamwidth is
important because it is proportional to the bearing accuracy of the specific beam.
null
max
BW
Beam Pattern Function (/d = 0.5)
array elements
=0
3-d Beam Pattern
Effect of Increasing Frequency Frequency = 750 Hz Frequency = 1500 Hz
Frequency = 3000 Hz Frequency = 6000 Hz