Chapter 15: Radar Systems

Example 15.1, page no. 485

In [7]:
# Variable Declaration
PW  = 3.00*pow(10,-6)      # Pulse Width (s)
PRT = 6.00*pow(10,-3)      # Pulse Repetition Time (s)

# Calculation
import math   # Math Library
DS  = PW/PRT # Duty Cycle

# Result
print "Duty Cycle =",round(DS,4)

Duty Cycle = 0.0005

Example 15.2, page no. 485

In [8]:
# Variable Declaration
PW = 3.00*pow(10,-6)     # Pulse Width (s)
PP = 100.00*pow(10,3)     # Peak Power (W)
RT = 1997.00              # Rest Time (s)

# Calculation
import math   # Math Library
DS = 1/RT   # Duty Cycle
AP = PP*DS                 # Average Power (W)

# Result
print "Average Power =",round(AP),"W"

Average Power = 50.0 W

Example 15.3, page no. 490

In [6]:
# Variable Declaration
NF    = 9.00               # Noise Figure (dB)
k     = 1.38*pow(10,-23)   # Boltzmann's Constant (J/K)
del_f = 1.50*pow(10,6)   # Receiver Band Width (Hz)
To    = 290                # Standard Ambient temperature (K)

# Calculation
import math   # Math Library
F     = pow(10,NF/10)   # Noise Figure
P_min = k*To*del_f*(F-1)   # Minimum receivable signal in a Radar Receiver (W)

# Result
print "Minimum receivable signal in the Radar Receiver, P_min =",round(P_min/pow(10,-14),2),"* 10^(-14) W"

Minimum receivable signal in the Radar Receiver, P_min = 4.17 * 10^(-14) W

Example 15.4, page no. 490

In [10]:
# Variable Declaration
Pt     = 5.00*pow(10,5)           # Peak Pulse Power (W)
Lambda = 3.00*pow(10,-2)          # Wavelength (m)
P_min  = 1.00*pow(10,-13)         # Minimum receivable Power (W)
Ao     = 5# Capture Area of Antenna (m^2)
S      = 20                      # Radar Cross-sectional Area (m^2)

# Calculation
import math     # Math Library
r_max  = pow(Pt*pow(Ao,2)*S/(4*math.pi*pow(Lambda,2)*P_min),0.25)
       # Maximum range of the Radar System (m)
# Result
print "Maximum range of the Radar System, r_max =",round(r_max/1000),"km"

Maximum range of the Radar System, r_max = 686.0 km

Example 15.5, page no. 490

In [14]:
# Variable Declaration
F_dB  = 4.77                       # Noise Figure (dB)
f     = 8.00*pow(10,9)             # Operating Frequency (Hz)
c     = 3.00*pow(10,8)             # Speed of light in vacuum (m/s)
del_f = 5.00*pow(10,5)             # IF Bandwidth (Hz)
rmax  = 12.00                     # Maximum distance (km)
D     = 1.00                      # Antenna Diameter (m)
S     = 5.00                      # Cross sectional area (m^2)

# Calculation
import math       # Math Library
Lambda = c/f      # Wavelength (m)
F      = pow(10,F_dB/10)      # Noise Figure
Pt     = del_f*pow(Lambda,2)*(F-1)/(pow(48/rmax,4)*pow(D,4)*S) # Peak transmitted pulse power (W)

# Result
print "The peak transmitted pulse power, Pt =",round(Pt,1),"W"

The peak transmitted pulse power, Pt = 1.1 W

Example 15.6, page no. 500

In [17]:
# Variable Declaration
f     = 2.50*pow(10,9)     # Radar Operating Frequency (Hz)
c     = 3.00*pow(10,8)          # Velocity of light in vacuum (m/s)
Pt    = 25.00*pow(10,6)         # Peak Pulse Power (W)
D     = 64.00                   # Antenna Diameter (m)
F     = 1.1                     # Receiver Noise Figure
S     = 1.00                    # Radar Cross-sectional Area (m^2)
del_f = 5.00*pow(10,3)          # Receiver Bandwidth (Hz)

# Calculation
import math# Math Library
Lambda = c/f# Wavelength (m)
r_max  = 48*pow(Pt*pow(D,4)*S/(del_f*pow(Lambda,2)*(F-1)),0.25)
# Maximum range of the Radar System (km)
# Result
print "Maximum range of the Radar System, r_max =",round(r_max),"km"

Maximum range of the Radar System, r_max = 132609.0 km

Example 15.7, page no. 504

In [18]:
# Variable Declaration
v_c    = 3.00*pow(10,8)       # Velocity of light in vacuum (m/s)
f      = 5.00*pow(10,9)      # MTI radar Transmit Frequency (Hz)
PRF    = 800                    # Pulse Repetition Frequency (pps)

# Calculation
import math                    # Math Library
Lambda = v_c/f                              # Wavelength(m)
vb1    = PRF*Lambda*60*60*pow(10,-3)        # Blind Speed in for n=1 (km/h)
vb2    = 2*PRF*Lambda*60*60*pow(10,-3)      # Blind Speed in for n=2 (km/h)
vb3    = 3*PRF*Lambda*60*60*pow(10,-3)      # Blind Speed in for n=3 (km/h)

# Result
print "Lowest three blind speeds will be",round(vb1,1),",",round(vb2,1),"and",round(vb3,1),"km/h"

Lowest three blind speeds will be 172.8 , 345.6 and 518.4 km/h

Example 15.8, page no. 506

In [20]:
 
# Variable Declaration
F_dB   = 13                   # Noise Figure of beacon (dB)
Ft     = 1.1                   # Noise Figure of system
f      = 2.50*pow(10,9)        # Operating Frequency (Hz)
D      = 64                            # Antenna Diameter (m)
Db     = 1                     # Antenna Diameter of beacon (m)
del_f  = 5.00*pow(10,3)        # Bandwidth (Hz)
Ptt    = 0.50*pow(10,6)        # Peak Pulse power (W)
Ptb    = 50                    # Peak Pulse power of beacon (W)
k      = 1.38*pow(10,-23)      # Boltzman's Constant (J/K)
c      = 3.00*pow(10,8)     # Speed of light in vaccum (m/s)
To     = 290                   # Temperature (K)

# Calculation
import math# Math Library
Aot    = 0.65*math.pi*pow(D,2)/4# Capture Area (m^2)
Aob    = 0.65*math.pi*pow(Db,2)/4# Capture Area (m^2)
Lambda = c/f# Wavelength (m)
Fb     = pow(10,F_dB/10)# Noise Figure
rmax_I = pow(Aot*Ptt*Aob/(pow(Lambda,2)*k*To*del_f*(Fb-1)),0.5)
# Maximum range for the interrogation link (m)
rmax_R = pow(Aob*Ptb*Aot/(pow(Lambda,2)*k*To*del_f*(Ft-1)),0.5)
# Maximum range for the reply link (m)

# Result
print "The Maximum Tracking Range, Rmax =",round(min(rmax_I/pow(10,10),rmax_R/pow(10,10))),"million km"

The Maximum Tracking Range, Rmax = 136.0 million km

Example 15.9, page no. 507

In [26]:
# Variable Declaration
c      = 3.00*pow(10,8)          # Velocity of light in vacuum (m/s)
f      = 5.00*pow(10,9)          # CW Transmit Frequency (Hz)
v      = 100.00                  # Target Speed (km/h)

# Calculation
import math                    # Math Library
Lambda = c/f                   # Wavelength (m)
vr     = v*1000/(60*60)      # Target Speed (m/s)
f_d    = 2*vr/Lambda    # Doppler frequency (Hz)

# Result
print "Doppler frequency, f_d =",round(f_d),"Hz"

Doppler frequency, f_d = 926.0 Hz