Adding Decibels
The Passive Sonar Equation
Will the sensor detect the red submarine?
Signal to Noise Ratio
Signal Signal Intensity

Noise Noise Intensity
Signal
The higher the SNR, the more likely
you are to hear (detect) the signal.
Noise (quiet)
Noise (Loud
Source Level and Transmission Loss
 IS 
SL  10log  
 I0 
SL
TL
 IS 
TL  10log  
 IR 
LR  SL  TL
 Noise Intensity 
 Noise Intensity 
 Signal 
LS/ N  10log 

L

10log

SL

TL

10log




R

I
I
 Noise 
0
0




Sources of Noise
•
•
•
•
Shipping Noise
Omni directional Noise
Wind and Weather
Marine Life – Biologic Activity I
I
I
Self Noise
N
N
N
– Flow of Water
– Machinery
Receiver
IN
IN
Detector
Isotropic Noise
IN
IN
Directivity Factor
• Some detectors are only able to provide a voltage proportional to all
incident sound from all directions. (non-directional = ND)
• Other detectors use more sophisticated signal processing and form
beams thereby providing a voltage proportional to sound incident
from a particular direction. (directional = D)
IN
N ND
d
ND
IN
IN
IS
Receiver
IN
IN
Detector
ND  Electrical power generated by actual directional receiver
IN
N ND  Electrical power generated by equivalent non-directional receiver
IN
The Passive Sonar Equation
 Noise Intensity 
 Noise Intensity 
 Signal 
LS/ N  10log 

L

10log

SL

TL

10log




R

Noise
I
I


0
0




 Signal 
LS/ N  10 log 
  L R  L N Received  SL  TL   NL  DI 
 Noise 
LS/ N  SL  TL   NL  DI 
 IS 
SL  10log  
 I0 
 IN 
NL  10log  
 I0 
I 
TL  10log  S 
 IR 
DI  10log  d 
Figure of Merit
• Often a detection threshold is established such that a
trained operator should be able to detect targets with
that LS/N half of the time he hears them. Called
“Recognition Differential.” (RD)
• Passive sonar equation is then solved for TL allowable at
that threshold. Called “Figure of Merit.” (FOM)
TLallowable = Figure of Merit = SL- LS/N Threshold - (NL-DI)
• Since TL logically depends on range, this could provide
an estimate of range at which a target is likely to be
detected. Called “Range of the Day.” (ROD)
• Any LS/N above the Recognition Differential is termed
“Signal Excess.” (SE) Signal Excess allows detection
of targets beyond the Range of the Day.
Example
• A hostile submarine with a
Source Level, SL = 130 dB re
1 mPa is near a friendly
submarine in a part of the
ocean where the Noise Level
from all sources, NL = 70 dB re
1 mPa. The directivity factor is
3000 for the friendly
submarine’s sonar. If the
Recognition Differential for the
friendly submarine is 20 dB,
what is the Figure of Merit?
• If the actual Transmission Loss
is 50 dB, what is the Signal
Excess.
Signal to Noise Level
 Signal Intensity 
 Noise Intensity 
 Signal Intensity 
LS/ N  10log 

10log

10log





Noise
Intensity
I
I


0
0




But we will be measuring the signal
intensity level at the receiver/detector, IR
(in the frequency band of the detector)
This is different from the signal intensity
level leaving the target, IS
(in the frequency band of the detector)
IS
I R IS I R I 0


I 0 I 0 IS IS
IR
OR
 IR
10log 
 I0
Fraction of emitted intensity reaching receiver

 IS 
 IS 
  10log    10log  
 IR 

 I0 
LR  SL  TL
Noise Level and Directivity Index
I N Received I N 1

I0
I0 d
OR
L N Received
 I N Received
 10log 
I0

 IN 
NL  10log  
 I0 
L N Received  NL  DI
IN
DI  10log  d 
IN
IN
d
IS

 IN 
  10log    10log  d 

 I0 
N ND
ND
Receiver
IN
IN
Detector
ND  Electrical power generated by actual directional receiver
IN
N ND  Electrical power generated by equivalent non-directional receiver
IN