Formula sheet: RADAR (Radio Detection & Ranging) | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


Electromagnetics: RAD AR (Radio Detection &
Ranging) F orm ula Sheet for GA TE
RAD AR Basics
• Radar Range Equation : P o w er receiv ed b y the radar from a target.
P
r
=
P
t
G
t
G
r
s?
2
(4p)
3
R
4
where P
t
is transmitted p o w er (W ), G
t
and G
r
are transmitter and receiv er an tenna
gains, s is radar cross-section (m
2
), ? is w a v elength (m ), R is range to target (m ).
• Maxim um Range (R
max
) : When receiv ed p o w er equals minim um detectable signal
(S
min
).
R
max
=
(
P
t
G
t
G
r
s?
2
(4p)
3
S
min
)
1/4
• F ree-Space P ath Loss : A ccoun ts for signal atten uation.
L
fs
=
(
4pR
?
)
2
Range and Resolution
• Range to T arget : Time dela y b et w een transmitted and receiv ed pulse.
R =
ct
2
where c is sp eed of ligh t (3×10
8
ms
-1
), t is round-trip tim e (s ).
• Range Resolution : Minim um distance to distinguish t w o targets.
?R =
ct
p
2
where t
p
is pulse width (s ). In terms of bandwidth (B ):
?R =
c
2B
where B is signal bandwidth (Hz ).
Doppler Effect
• Doppler F requency Shift : F or a target mo ving with radial v elo cit y v
r
.
f
d
=
2v
r
f
c
where f
d
is Doppler frequency shift (Hz ), f is transmitted frequency (Hz ), v
r
is radial
v elo cit y (ms
-1
).
• Relativ e V elo cit y : P ositiv e v
r
for approac h ing targets, negativ e for receding.
1
Page 2


Electromagnetics: RAD AR (Radio Detection &
Ranging) F orm ula Sheet for GA TE
RAD AR Basics
• Radar Range Equation : P o w er receiv ed b y the radar from a target.
P
r
=
P
t
G
t
G
r
s?
2
(4p)
3
R
4
where P
t
is transmitted p o w er (W ), G
t
and G
r
are transmitter and receiv er an tenna
gains, s is radar cross-section (m
2
), ? is w a v elength (m ), R is range to target (m ).
• Maxim um Range (R
max
) : When receiv ed p o w er equals minim um detectable signal
(S
min
).
R
max
=
(
P
t
G
t
G
r
s?
2
(4p)
3
S
min
)
1/4
• F ree-Space P ath Loss : A ccoun ts for signal atten uation.
L
fs
=
(
4pR
?
)
2
Range and Resolution
• Range to T arget : Time dela y b et w een transmitted and receiv ed pulse.
R =
ct
2
where c is sp eed of ligh t (3×10
8
ms
-1
), t is round-trip tim e (s ).
• Range Resolution : Minim um distance to distinguish t w o targets.
?R =
ct
p
2
where t
p
is pulse width (s ). In terms of bandwidth (B ):
?R =
c
2B
where B is signal bandwidth (Hz ).
Doppler Effect
• Doppler F requency Shift : F or a target mo ving with radial v elo cit y v
r
.
f
d
=
2v
r
f
c
where f
d
is Doppler frequency shift (Hz ), f is transmitted frequency (Hz ), v
r
is radial
v elo cit y (ms
-1
).
• Relativ e V elo cit y : P ositiv e v
r
for approac h ing targets, negativ e for receding.
1
An tenna P arameters
– An tenna Gain (G ) :
G =
4pA
e
?
2
where A
e
is effectiv e ap erture area ( m
2
).
– Beam width : Appro ximate angular width of the main lob e.
? ˜
?
D
where D is an tenna dimension (m ), ? is b eam width in radi ans.
– Radar Cross-Section (s ) : Measure of target’s reflectivit y .
s = lim
R?8
4pR
2
|E
s
|
2
|E
i
|
2
where E
s
is scattered electric fi eld, E
i
is inciden t electric field.
Signal-to-Noise Ratio (SNR)
– SNR for RAD AR :
SNR =
P
r
P
n
=
P
t
G
t
G
r
s?
2
(4p)
3
R
4
kT
s
BF
whereP
n
is noise p o w er,k is Boltzmann’s constan t (1.38×10
-23
JK
-1
),T
s
is system
noise temp erature (K ), F is noise figure.
Key Notes
– Common GA TE F o cus : Radar range equation, range resolution, Doppler shift,
and an tenna gain.
– Units : Ensure consistency (e.g., R in m , ? in m , f in Hz ).
– Losses : A ccoun t for atmospheric losses or system losses if sp ecified.
– Pulse Rep etition F requency (PRF) : Affects maxim um unam biguous range:
R
max,unam biguous
=
c
2· PRF
2