## Example 1,Page No:449¶

In :
import math

#Variable Declaration
PRF     = 1000;         #Pulse repetitive frequency in Hz
t       = 0.15*10**-3; #Round propagation time in s
c       = 3*10**8;     #velocity of EM waves in m/s
#calculations
R       = (c*t)/float(2);      #Range
Runamb  = c/float((2*PRF));     #Max unambiguous range

#Result
print'Target Range = %3.1f Km' %(R/float(1000));
print'Maximum Unambiguous range = %d Km'%(Runamb/float(1000));

Target Range = 22.5 Km
Maximum Unambiguous range = 150 Km


## Example 2,Page No:450¶

In :
import math

#Variable Declaration
f       = 10*10**9;      # radar Tx frequency
c       = 3*10**8;       # velocity of EM waves in m/s
V       = 108;          # vel of car in kmph

# Calculations
lamda   = c/float(f);          # wavelength in m
Vr      = V*(5/float(18));     # vel of car in m/s
fd      = (2*Vr)/float(lamda);  # Doppler shift in Hz
fr      = f + fd        # received freq
fr_away = f-fd          # Rx frequency if the car is moving away from radar

# Result
print'Doppler Shift = %d Khz'%(fd/float(1000));
print'Frequency of Received signal = %3.6f Ghz'%(fr/float(10**9));
print'Received Frequency if car is moving away from radar = %3.6f Ghz'%(fr_away/float(10**9));

Doppler Shift = 2 Khz
Frequency of Received signal = 10.000002 Ghz
Received Frequency if car is moving away from radar = 9.999998 Ghz


## Example 3,Page No:450¶

In :
import math

#Variable Declaration
f       = 10*10**9;      # radar Tx frequency
PRF     = 2000;          # Pulse repetitive frequency in Hz
Vr      = 0.5;           # radial vel in Mach
c       = 3*10**8;        # velocity of EM waves in m/s
vs      = 330;           # velocity of sound in m/s

# Calculations
lamda           = c/float(f);          # wavelength in m
max_unamb_fd    = PRF/2;        # maximum unambiguous doppler shift
Vrunamb         = (lamda*max_unamb_fd)/2; # doppler shift
Vaircraft       = 0.5*vs;       # Converting from Mach to m/s
fd_desired      = (2*Vaircraft)/lamda;
PRF_desired     = 2*fd_desired; # desired PRF

# Output
if  Vrunamb < Vaircraft:
print'The radar is not capable of determining unambiguously the velocity of the approaching aircraft\n';

print'Desired Pulse Repetition Rate = %d Khz'%(PRF_desired/1000);

The radar is not capable of determining unambiguously the velocity of the approaching aircraft

Desired Pulse Repetition Rate = 22 Khz


## Example 4,Page No:450¶

In :
import math
# Given Data
PW_tx   = 10**-6;            # Transmitted pulse width
Rx_PW   = 10**-6;            # Received pulse width
c       = 3*10**8;           # velocity of EM waves in m/s

# Calculations
RR      = (c*Rx_PW)/float(2);      # Range Resolution in m

# output
print'This Radar can resolve upto an inter target separation in range of %d m\nTherefore,given radar will be able to resolve the targets'%RR;

This Radar can resolve upto an inter target separation in range of 150 m
Therefore,given radar will be able to resolve the targets


## Example 5,Page No:451¶

In :
import math

#Variable Declaration
CRR     = 100;      # Cross range resolution in m
R       = 3000;     # radial range

# Calculations
# CRR  = (R*theta3)*(math.pi/180);
theta3  = (180*CRR)/(math.pi*R)         # 3 dB beamwidth

# Result
print'3 dB beamwidth = %3.2f°'%theta3;

3 dB beamwidth = 1.91°


## Example 6,Page No:451¶

In :
import math

#Variable Declaration
Vs      = 330;          # velocity of sound in m/s
NM      = 1.85*(5/float(18))   # 1NM equivalent in m/s
V1      = 0.5;          # velocity of first aircraft in mach
V2      = 400;          # velocity of second aircraft in NM/hr
theta   = 30;           # angle with radial axis in degrees
lamda   = 3*10**-2;      # wavelength in m

# Calculations
v1      = V1*Vs         # velocity of first aircraft in m/s
fd1     = (2*v1)/float(lamda); # doppler freq.
v2      = V2*NM*(math.cos(30*(math.pi/180)));  # velocity of second aircraft in m/s
fd2     = (2*v2)/float(lamda);  # doppler freq
dd      = fd2 - fd1;    # doppler difference
Tl      = 1/float(dd);         # look time in s

# Result
print'Required minimum look time = %3.2f ms'%(Tl/float(10**-3));
print'\nNote: Cos(30) value is taken as 0.5 in textbook';

Required minimum look time = 1.15 ms

Note: Cos(30) value is taken as 0.5 in textbook


## Example 7,Page No:451¶

In :
import math
# Given Data
# Rmax     = [1000000/(12.4*PRF)]NM
#          = [1000000*t/12.4]NM
print'The Numerator represents round trip propagation time in us\n';
print'Therefore, number 12.4 represents the units microseconds per nautical miles\n';
print'In other words, this means that the round propagation time for one nautical mile is 12.4 us which is equivalent to 6.66us for 1km range'

The Numerator represents round trip propagation time in us

Therefore, number 12.4 represents the units microseconds per nautical miles

In other words, this means that the round propagation time for one nautical mile is 12.4 us which is equivalent to 6.66us for 1km range


## Example 8,Page No:464¶

In :
import math

# variable Declaration
PW      = 10*10**-6;         # pulse width in sec
f       = 10*10**9;          # frequency in Hz
fm      = 1000;              # modulating frequency

# calculations
BW_M    = 1/float(PW);              # matched bandwidth
cf1     = f+fm;             # closest freq.
cf2     = f-fm;             # closest freq.
fo      = f;                # centre freq.

# Output
print'Centre of frequency spectrum = %d Khz'%(fo/float(10**3));
print'The two closet frequencies to the center of the spectrum are %d Khz'%(cf1/float(10**3)),' and %d Khz'%(cf2/float(10**3));

Centre of frequency spectrum = 10000000 Khz
The two closet frequencies to the center of the spectrum are 10000001 Khz  and 9999999 Khz


## Example 9,Page No:464¶

In :
import math

# Variable Declaration
fc1     = 495;      # freq in Mhz
fc2     = 505;      # freq in Mhz

# Calculations
fo      = (fc1 + fc2)/float(2);        # Center of spectrum in Mhz
BW      = fc2 - fc1;            # Bandwidth in Mhz
PW      = 1/float(BW);                 # compressed pulse width in us

# Result
print'Center of spectrum = %d Mhz\n'%fo,'Matched Bandwidth = %d Mhz\n'%BW,'Compressed Pulse width = %3.1fus'%PW;

Center of spectrum = 500 Mhz
Matched Bandwidth = 10 Mhz
Compressed Pulse width = 0.1us


## Example 10,Page No:464¶

In :
import math

# variable Declaration
f       = 10**9;         # CW radar waveform freq.
fm      = 100;           # modulation freq. in Hz
MaxfD   = 500;           # max freq deviation in Hz
c       = 3*10**8;       # vel. of EM waves in m/s

# Calculations
Mf      = MaxfD/float(fm);      # Modulation index
BW      = 2*(Mf + 1)*fm # Bandwidth
RR      = c/float((2*BW));     # Range Resolution in m

# Result
print'Bandwidth = %d Hz\n'%BW,'Range Resolution = %d Km'%(RR/float(1000));

Bandwidth = 1200 Hz
Range Resolution = 125 Km


## Example 11,Page No:465¶

In :
import math

# Variable Declaration
f       = 10**9;         # Centre freq. of spectrum
t       = 13             # pulse width in us
N       = 13;            # N-bit Barker code

# Calculations
Sub_PW  = t/float(N);          # sub pulsewidth
match_BW= 1/float(Sub_PW);     # Matched bandwidth in Mhz

# Output
print'Matched Bandwidth = %d Mhz\n'%match_BW,'Center Frequency of the spectrum = %d Ghz'%(f/float(10**9));

Matched Bandwidth = 1 Mhz
Center Frequency of the spectrum = 1 Ghz


## Example 12,Page No:479¶

In :
import math

# Variable Declaration
PW      = 10**-6;            # Pulse width in sec
Pp      = 100*10**3;          # Peak power in watts
PRF     = 1000;              # pulse rep.rate
N_target= 20;                # no of target hits in 1 dwell period

# Calculations
PE      = Pp*PW;            # Pulse energy in Joule
LE      = N_target *PE;     # look energy
DC      = PW*PRF            # Duty cycle
Pav     = Pp*DC;            # Average power
Pavg    = 10*math.log10(Pav);    # Avg power in dB

# result
print'Average power = %d dB\n'%Pavg,'Look Energy = %3.0f Joules'%LE;

Average power = 20 dB
Look Energy =   2 Joules


## Example 13,Page No:479¶

In :
import math

# Variable Declaration
PW      = 10**-6;            # Pulse width in sec
Pp      = 100*10**3;         # Peak power in watts
PRF     = 1000;              # pulse rep.rate
N_target= 20;                # no of target hits in 1 dwell period

# Calculations
PE      = Pp*PW;            # Pulse energy in Joule
LE      = N_target *PE;     # look energy
DC      = PW*PRF            # Duty cycle
Pav     = Pp*DC;            # Average power
Pavg    = 10*math.log10(Pav);    # Avg power in dB
Pp_dB   = 10*math.log10(Pp);     # Peak power in dB
DCCF    = Pp_dB - Pavg      # Duty cycle correction factor

# result
print'Duty cycle correction factor = %d dB'%DCCF;

Duty cycle correction factor = 30 dB


## Example 14,Page No:479¶

In :
import math

# Variable Declaration
G_rx        = 97;       # Rx gain in dB
Bn          = 5*10**6;   # Bandwidth in Hz
To          = 300;      # temperature in kelvin
K           = 1.38*10**-23;  # Boltzmann constant in J/k
n           = -3             # o/p noise power in dBm

# calculations
Pn_dB      = n-G_rx       # input noise power
Pn         = 10**(Pn_dB/float(10))*10**-3       # converting from dBm to watts
# Pn      = KToBnF;
F          = Pn/float((K*To*Bn))  # Noise Factor
T          = To*(F - 1);    # Equivalent Noise Temperature

# Result
print'Equivalent Noise Temperature = %3.2d °K'%T;

Equivalent Noise Temperature = 1149 °K


## Example 15,Page No:480¶

In :
import math

# Variable Declaration
Gx      = 60;       # gain of Rx 'X' in dB
Gy      = 70;       # gain of Rx 'Y' in dB
Fx      = 3;        # Noise factor of 'X'
Fy      = 2;        # Noise factor of 'Y'

# calculations
Gx_W    = 10**(Gx/float(10));    # gain in watts
Gy_W    = 10**(Gy/float(10));    # gain in watts
# k    = Pnx/float(Pny);      # Ratio of noise power levels produced at the o/p's of Rx 'X' and 'Y'
k       = (Fx*Gx_W)/float((Fy*Gy_W));    # Ratio of noise power levels produced at the o/p's of Rx 'X' and 'Y'

# result
print'Ratio of noise power levels produced at the outputs of Rx X and Y = %3.2f'%k;

Ratio of noise power levels produced at the outputs of Rx X and Y = 0.15


## Example 16,Page No:480¶

In :
import math

# Variable Declaration
Pn      = -70;          # Noise power in dBm
fl      = 10**6;         # lower cut-off freq in Hz
fh      = 11*(10**6);      # upper cut-off freq in Hz
BP_fl   = 13*(10**6);      # Bandpass filter lower cutoff freq
BP_fh   = 14*(10**6);      # Bandpass filter lower cutoff freq

# Calculations
Pn_W    = (10**(Pn/10))*10**-3;     # coversion from dBm to Watts
BW      = fh - fl
PSD     = Pn_W/BW              # Noise power spectral density
# Since white noise has the same spectral power density through the frequency spectrum,
# therefore Noise power in second case
B       = BP_fh - BP_fl
Pn_2    = PSD*B;                # Noise power in second case

# Output
print'Noise power for BandPass filter having Cutoff frequencies 13Mhz and 14Mhz = %3.0e W'%Pn_2;

Noise power for BandPass filter having Cutoff frequencies 13Mhz and 14Mhz = 1e-11 W


## Example 17,Page No:483¶

In :
import math
# Given Data from Figure triagle OAB
OA      = 100       # in Km
OB      = OA*math.cos(60*math.pi/180);       # Range of Target 2

# Result
print'Range of Target-2 = %d Km\n Azimuth angle of target-1 = 60°\n Azimuth angle of Target-2 = 120°'%OB;

Range of Target-2 = 50 Km
Azimuth angle of target-1 = 60°
Azimuth angle of Target-2 = 120°