Chapter 21: Antenna Measurements

Example 21-2.1, Page number: 720

In [1]:
from math import pi

#Variable declaration
f = 900e6       #Frequency (Hz)
length = 25e-3  #Length of antenna (m)
len_cell = 110e-3   #Length of handset chassis (m)
c = 3e8         #Speed of light (m/s)
del_L = 0.5     #Peak to Peak measurement uncertainty (dB)

#Calculations
Dm = length + len_cell  #Maximum Dimension of antenna (m)
wave_lt = c/f           #Wavelength (m)
r_rnf = (wave_lt/(2*pi))    #Outer boundary of reactive near field (m)

r_ff = 2*(Dm**2)/wave_lt    #Fraunhofer region (m)

r2_ff = r_rnf/(10**(del_L/40)-1)    
            #Minimum distance where effect of near field is small (m)

r3_ff = 2*Dm/(10**(del_L/10)-1)
            #Minimum distance where effect of rotation of AUT is small (m)

#Result
print "The Outer boundary of reactive near field is at a distance", round(r_rnf,3),"m"
print "The Fraunhofer region starts at a distance", round(r_ff,3),"m"
print "The Minimum distance where effect of near field is small enough is",\
                                 round(r2_ff,1),"m"
print "The Minimum distance where effect of rotation of AUT is small enough \
is", round(r3_ff,1),"m"

The Outer boundary of reactive near field is at a distance 0.053 m
The Fraunhofer region starts at a distance 0.109 m
The Minimum distance where effect of near field is small enough is 1.8 m
The Minimum distance where effect of rotation of AUT is small enough is 2.2 m

Example 21-2.2, Page number: 720

In [3]:
from math import pi

#Variable declaration
horn_len = 350e-3   #Length of horn (m)
ap_wid = 200e-3     #Aperture width (m)
ap_hei = 150e-3     #Aperture height (m)
del_L = 0.2         #Peak to peak uncertainty (dB)
f = 10e9            #Frequency (Hz)
c = 3e8             #Speed of light (m/s)

#Calculations
wave_lt = c/f       #Wavelength (m)
r_rnf = wave_lt/(2*pi)  ##Outer boundary of reactive near field (m)

r_ff = 2*(ap_wid**2)/wave_lt    #Fraunhofer region (m)

r2_ff = r_rnf/(10**(del_L/40)-1)    
            #Minimum distance where effect of near field is small (m)

r3_ff = 2*horn_len/(10**(del_L/10)-1)
            #Minimum distance where effect of rotation of AUT is small (m)

#Result
print "The Outer boundary of reactive near field is at a distance", round(r_rnf,4),"m"
print "The Fraunhofer region starts at a distance", round(r_ff,1),"m"
print "The Minimum distance where effect of near field is small enough is",\
                                 round(r2_ff,2),"m"
print "The Minimum distance where effect of rotation of AUT is small enough \
is", round(r3_ff,1),"m"

The Outer boundary of reactive near field is at a distance 0.0048 m
The Fraunhofer region starts at a distance 2.7 m
The Minimum distance where effect of near field is small enough is 0.41 m
The Minimum distance where effect of rotation of AUT is small enough is 14.9 m

Example 21-2.3, Page number: 721

In [6]:
#Variable declaration
D = 0.5     #Antenna diameter (m)
f = 300e9   #Frequency (Hz)
c = 3e8     #Speed of light (m/s)

#Calculations
wave_lt = c/f   #Wavelength (m)
r_ff = 2*(D**2)/wave_lt    #Fraunhofer region (m)

#Result
print "The Fraunhofer region starts at a distance", r_ff,"m"
print "At 300 GHz the attenuation of the atmosphere is around 10dB/km making\
 the measurement difficult in full-size ranges"

The Fraunhofer region starts at a distance 500.0 m
At 300 GHz the attenuation of the atmosphere is around 10dB/km making the measurement difficult in full-size ranges

Example 21-4.1, Page number: 726

In [7]:
from math import pi

#Variable declaration
D = 1       #Diameter of antenna (m)
f = 10e9    #Frequency (Hz)
c = 3e8     #Speed of light (m/s)

#Calculations
wave_lt = c/f       #Wavelength (m)
hpbw = 70*wave_lt/D #Half power beamwidth (degrees)
mea_dist = 2*(D**2)/wave_lt #Measurement distance (m)
trav_dist = hpbw*pi*mea_dist/180    #Traverse distance (m)
taper = ((0.5/(trav_dist/2))**2)*(-3) #Amplitude taper (dB)

#Result
print "The amplitude taper is", round(taper,1), "dB"

The amplitude taper is -0.5 dB

Example 21-4.2, Page number: 735

In [8]:
from math import log10

#Variable declaration
pat_lev1 = -22.3    #Pattern level maximum (dB)
pat_lev2 = -23.7    #Pattern level minimum (dB)

#Calculations
S = abs(pat_lev2-pat_lev1)  #Amplitude ripple (dB)
a = (pat_lev1+pat_lev2)/2   #Pattern level (dB)

R = a + 20*log10((10**(S/20) - 1)/(10**(S/20) + 1))
                    #Reflectivity (dB)

#Result
print "The reflectivity is", round(R),"dB"

The reflectivity is -45.0 dB

Example 21-5.1, Page number: 739

In [9]:
from math import pi, sin, cos, log10

#Variable declaration
En = 1      #Field illuminating the AUT (unitless)
tilt_diff = 88   #Difference in tilt angles (degrees)

#Calculations
En_pol = En*sin(tilt_diff*pi/180)   #Co-polar component of field (unitless)
En_crosspol = En*cos(tilt_diff*pi/180)
                    #Cross-polar component of field (unitless)
meas_cross = 20*log10(En_crosspol)

#Result
print "The measure cross-polar level is", round(meas_cross), "dB\
 relative to the co-polar field"

The measure cross-polar level is -29.0 dB relative to the co-polar field

Example 21-5.2, Page number: 743

In [10]:
from math import pi, log10

#Variable declaration
f = 1.4e9       #Frequency (Hz)
Tant = 687      #Increase in antenna temperature (K)
phy_ap = 2210   #Physical aperture (m^2)
S = 1590        #Flux density of Cygnus A (Jy)
k = 1.38e-23    #Boltzmann's constant (J/k)
c = 3e8         #Speed of light (m/s)

#Calculations
wave_lt = c/f       #Wavelength (m)
gain = (8*pi*k*Tant)/(S*(10**-26)*wave_lt**2)   #Gain(unitless)
gain_db = 10*log10(gain)       #Gain (dBi)

Ae = gain*wave_lt**2/(4*pi)     #Effective area (m^2)

eff_ap = Ae/phy_ap          #Aperture efficiency (unitless)

#Result
print "The gain of the antenna is", round(gain_db), "dBi"
print "The aperture efficiency is", round(eff_ap,2),"or",round(eff_ap*100),"percent"

The gain of the antenna is 55.0 dBi
The aperture efficiency is 0.54 or 54.0 percent