Graphics Programs Reference
In-Depth Information
P r
P D
m 2
-------
σ
=
(1.45)
where is the power reflected from the target. Thus, the total power deliv-
ered to the radar signal processor by the antenna is
P r
P t G σ
R 2
P Dr
=
--------------------
A e
(1.46)
) 2
(
Substituting the value of
A e
from Eq. (1.40) into Eq. (1.46) yields
P t G 2 λ 2 σ
4( 3 R 4
P Dr
=
----------------------
(1.47)
Let denote the minimum detectable signal power. It follows that the
maximum radar range
S min
is
R max
P t G 2 λ 2 σ
4( 3 S min
14
R max
=
-------------------------
(1.48)
Eq. (1.48) suggests that in order to double the radar maximum range one must
increase the peak transmitted power sixteen times; or equivalently, one
must increase the effective aperture four times.
P t
In practical situations the returned signals received by the radar will be cor-
rupted with noise, which introduces unwanted voltages at all radar frequencies.
Noise is random in nature and can be described by its Power Spectral Density
(PSD) function. The noise power
is a function of the radar operating band-
N
width,
. More precisely
B
N
=
ise
SDB
×
(1.49)
The input noise power to a lossless antenna is
N i
=
kT e B
(1.50)
–
23
where is BoltzmanÓs constant, and
is the effective noise temperature in degrees Kelvin. It is always desirable that
the minimum detectable signal ( ) be greater than the noise power. The
fidelity of a radar receiver is normally described by a figure of merit called the
noise figure
k
=
1.38
×
10
joule
degree
Kelvin
T e
S min
(see Appendix 1B for details). The noise figure is defined as
F
(
SNR
) i
S i
N i
F
=
------------------
=
----------------
(1.51)
(
SNR
) o
S o
N o
and are, respectively, the Signal to Noise Ratios (SNR) at the
input and output of the receiver.
(
SNR
) i
(
SNR
) o
S i
is the input signal power;
N i
is the input
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