# Chapter 17: Antenna Temperature, Remote Sensing and Radar Cross Section

### Example 17-1.1, Page number: 623

In [1]:
from math import pi

#Variable declaration
Ta = 0.24   #Antenna temperature (K)
ang = 0.005     #Subtended angle (degrees)
hpbw = 0.116    #Antenna half power beamwidth (degrees)

#Calculations
Ts = Ta*(hpbw**2)/(pi*(ang**2/4))

#Result
print "The averate temperature of the surface is", round(Ts), "K"

The averate temperature of the surface is 164.0 K


### Example 17-1.2, Page number: 625

In [2]:
from math import pi, sqrt

#Variable declaration
eff_aper = 500      #Antenna effective aperture (m^2)
wave_lt = 20e-2        #Wavelength (m)
Tsky = 10.0           #sky temperature (K)
Tgnd = 300.0          #Ground temperature (K)
beam_eff = 0.7      #Beam efficiency (unitless)
aper_eff = 0.5      #Aperture efficiency (unitless)

#Calculations
phy_aper = aper_eff/eff_aper    #Physical aperture (m^2)
diam = 2*sqrt(phy_aper/pi)  #Antenna diameter (m)
diam_l = diam/wave_lt       #Antenna diameter (lambda)

ta_sky = Tsky*beam_eff      #Sky contribution to antenna temp. (K)
ta_side = 0.5*Tsky*(1-beam_eff) #Side-lobe contribution to antenna temp. (K)
ta_back = 0.5*Tgnd*(1-beam_eff) #Back-lobe contribution to antenna temp. (K)

Ta = ta_sky + ta_side + ta_back

#Result
print "The total antenna temperature is", Ta, "K"

The total antenna temperature is 53.5 K


### Example 17-2.1, Page number: 629

In [3]:
#Variable declaration
Tn = 50.0     #Noise temperature (K)
Tphy = 300.0      #Physical temperature (K)
Eff = 0.99       #Efficiency (unitless)
Tn_stg = 80.0       #Noise temperature of first 3 stages (K)
gain_db = 13.0       #Gain (dB)
Tphy_tr = 300   #Transmission line physical temperature (K)
Eff_tr = 0.9    #Transmission line efficiency (unitless)

#Calculations
gain = 10**(gain_db/10)
T_r = Tn_stg + Tn_stg/(gain) + Tn_stg/(gain**2)
Tsys = Tn + Tphy*(1/Eff - 1) + Tphy_tr*(1/Eff_tr - 1) + (1/Eff_tr)*T_r
#System temperature (K)

#Result
print "The system temperature is", round(Tsys), "K"

The system temperature is 180.0 K


### Example 17-2.2, Page number: 630

In [7]:
from math import sqrt

#Variable declaration
phy_aper = 2208     #Physical aperture (m^2)
f = 1415e6          #Frequency (Hz)
aper_eff = 0.54     #Aperture efficiency (unitless)
Tsys = 50           #System temperature (K)
bw = 100e6          #RF Bandwidth (Hz)
t_const = 10         #Output time constant (s)
sys_const = 2.2     #System constant (unitless)
k = 1.38e-23        #Boltzmann's constant (J/K)

#Calculations
Tmin = sys_const*Tsys/(sqrt(bw*t_const))    #Minimum detectable temperature(K)
eff_aper = aper_eff*phy_aper        #Effective aperture (m^2)
Smin = 2*k*Tmin/eff_aper        #Minimum detectable flux density (W/m^2/Hz)

#Result
print "The minimum detectable flux density is %.1e W/m^2/Hz" % Smin

The minimum detectable flux density is 8.1e-29 W/m^2/Hz


### Example 17-3.1, Page number: 631

In [8]:
from math import pi, log10

#Variable declaration
k = 1.38e-23    #Boltzmann's constant (J/K)
trans_pow = 5   #Transponder power (W)
r = 36000e3     #Distance (m)
wave_lt = 7.5e-2    #Wavelength (m)
ant_gain = 30   #Antenna gain (dB)
earth_ant = 38  #Earth station antenna gain (dB)
Tsys = 100      #Earth station receiver system temperature (K)
bw = 30e6       #Bandwidth (Hz)

#Calculations
s_n = wave_lt**2/(16*(pi**2)*(r**2)*k*Tsys*bw)
s_n = 10*log10(s_n)     #Signal to Noise ratio (dB)

trans_pow_db = 10*log10(trans_pow)  #Transponder power (dB)
erp = ant_gain + trans_pow_db       #Effective radiated power (dB)

s_n_downlink = erp + earth_ant + s_n    #Signal to Noise ratio downlink(dB)

#Result
print "The earth station S/N ratio is", round(s_n_downlink,1), "dB"

The earth station S/N ratio is 13.2 dB


### Example 17-4.1, Page number: 634

In [9]:
from math import exp

#Variable declaration
tf = 0.693      #Absorption co-efficient (unitless)
Te = 305        #Earth temperature (K)
Ta = 300        #Satellite antenna temperature (K)

#Calculations
Tf = (Ta - Te*exp(-tf))/(1-exp(-tf))

#Result
print "The forest temperature is", round(Tf), "K"

The forest temperature is 295.0 K


### Example 17-5.1, Page number: 639

In [14]:
#Variable declaration
f = 10e9        #Frequency (Hz)
wind_speed = 350    #Wind speed (km/h)
c = 3e8         #Speed of light (m/s)
vr = 1e3          #Differential velocity (m/h)

#Calculations
wave_lt = c/f   #Wavelength (m)
freq_shift = 2*(wind_speed*1000/3600)/wave_lt
#Doppler Frequency shift (Hz)
T = 1/(2*freq_shift)    #Pulse repetition interval (s)
prf = 1/T           #Pulse repetition frequency (Hz)

fmin = 2*(vr/3600)/wave_lt  #Frequency resolution (Hz)
N = 1/(round(fmin,1)*T)      #Number of pulses

#Result
print "The minimum pulse repetition frequency is", round(prf,-3), "Hz"
print "The number of pulses to be sampled is", round(N)

The minimum pulse repetition frequency is 13000.0 Hz
The number of pulses to be sampled is 699.0