# Chapter 2: Fundamental Parameters of Antennas¶

## Example 2.1, Page 37¶

In [31]:
from scipy.integrate import quad,dblquad

#formula for beam solid angle theta_a=double_integration of d_omega

#formula for approx angle=delta1*delta2
delta1=pi/3
delta2=pi/3
theta_a1=delta1*delta2
theta_a1=delta1**2

Exact Beam Solid Angle: 0.841787214477 steradians
Approximate Beam Solid Angle: 1.09662271123 steradians


## Example 2.7, Page 52¶

In [9]:
import scipy

#The half power point of the pattern occurs at 60 degrees. Therefore theta_1r=2*pi/3
theta_1r=(2*pi)/3
theta_2r=(2*pi)/3

#Given U=B0*cos(theta)
exact_theta_a=dblquad(lambda x,y:cos(x)*sin(x), 0, (2*pi), lambda x:0, lambda x:(pi/2))

#Formula for approx theta = theta_1r*theta_2r
approx_theta_a=theta_1r*theta_2r

#formula for exact directivity=4*pi/exact_beam_angle
exact_direct=((4*pi)/(exact_theta_a[0]))

#formula for approx directivity=4*pi/approx_beam_angle
approx_direct=((4*pi)/(approx_theta_a))

#exact directivity in dB
exact_direct_db=10*log10(exact_direct)

#approx directivity in dB
approx_direct_db=10*log10(approx_direct)

print 'Exact directivity:',exact_direct_db,'dB'
print 'Approx. directivity:',approx_direct_db,'dB'

Exact Beam Solid Angle: 3.14159265359 steradians
Approximate Beam Solid Angle: 4.38649084493 steradians
Exact directivity: 6.02059991328 dB
Approx. directivity: 4.57092636745 dB


## Example 2.8, Page 58¶

In [34]:
import scipy

#Maximum intensity
u_max=1

#Calulation of maximum directivity

#Directivity in dB
D0_db=10*log10(D0)
print 'Directivity:',D0_db,'dB'

deg=90

#Calculation od directivity
D0_1=101/(deg-0.0027*deg**2)
D0_1_db=10*log10(D0_1)
print 'Directivity:',D0_1_db,'dB'

#Calculation of directivity
D0_2=(-172.4)+(191*sqrt((0.818+(1/deg))))
D0_2_db=10*log10(D0_2)
print 'Directivity:',D0_2,'dB'

Radiated Power: 8.37758040957 W
Directivity: 1.76091259056 dB
Directivity: 1.70982984843 dB
Directivity: 0.346803154212 dB


## Example 2.9(a), Page 61¶

In [33]:
import scipy

B0=1
#Maximum intensity
u_max=1

a=sin(array([10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180])*pi/180)**2

#Calculation of directivity

print 'Directivity using numerical techniques:',D0

#Directivity

print 'Directivity:',D01

Power Radiated: 2.46740110027 W
Directivity using numerical techniques: 5.09295817894
Directivity: 5.09295817894


## Example 2.9(b), Page 63¶

In [16]:
import scipy

B0=1

#Maximum intensity
u_max=1

a=sin(array([5,15,25,35,45,55,65,75,85])*pi/180)**2
b=sin(array([5,15,25,35,45,55,65,75,85])*pi/180)**2

#Calculation of directivity

print 'Directivity using 18 divisions:',D0

Directivity using 18 divisions: 5.09295817894


## Example 2.10, Page 68¶

In [17]:
import scipy

#maximum intensuty
u_max=1
B0=1

#Input impedance in Ohms
inp_imp=73
#Characteristic impedance in Ohms
char_imp=50

#Calulation of directivity

#conduction & dielectric efficiency ecd=1 since antenna is loseless
ecd=1

#Maximum Gain
G0=ecd*D0
G0_db=10*log10(G0)

#Reflection Coefficient Tau
tau=float(inp_imp-char_imp)/float(inp_imp+char_imp)

#Reflection efficiency=1-tau**2
er=1-tau**2
er_db=10*log10(er)

#Total efficiency
e0=er*ecd
e0_db=10*log10(e0)

#Absolute Gain
G0_abs=e0*D0
G0abs_db=10*log10(G0_abs)

print 'Maximum Gain:',G0_db

print 'Reflection efficiency:',er_db

print 'Total efficiency:',e0_db

print 'Absolute Gain:',G0abs_db

Maximum Gain: 2.29848855242
Reflection efficiency: -0.154573670944
Total efficiency: -0.154573670944
Absolute Gain: 2.14391488148


## Example 2.11, Page 77¶

In [56]:
import scipy

#unit vector of the wave
rho_w=array([1,0])

#unit vector of the electric field
rho_a=array([1/sqrt(2),1/sqrt(2)])

#Polarization factor
PLF=abs(dot(rho_w,rho_a))**2
print 'Polarization Factor:',PLF

0.5


## Example 2.12, Page 78¶

In [57]:
import scipy

#unit vector of the wave
rho_w=array([1/sqrt(2),1/sqrt(2)])

#unit vector of the electric field
rho_a=array([1/sqrt(2),-1/sqrt(2)])

#Polarization Factor
PLF=abs(dot(rho_w,rho_a))**2

print 'Polarization Factor:',PLF

0.0


## Example 2.13, Page 86¶

In [18]:
import scipy

#Frequency of antenna
f=10**8

#Velocity
v=3*10**8

#Wavelength
lamda=v/f

#Length of antenna
l=lamda/2

#Perimeter of the antenna
b=(3*10**-4)*lamda
C=2*pi*b

#value of omega
w=2*pi*f

#Constant
mu0=4*pi*10**-7

#Conductivity
sigma=5.7*10**7

#High frequency resistance
Rhf=(l/C)*(sqrt((w*mu0)/(2*sigma)))

Rl=Rhf/2

#calculation of conduction & dielectric efficiency
ecd_db=10*log10(ecd)

print 'Conduction-dielectric efficiency:',ecd_db

Conduction-dielectric efficiency: -0.0138216614754


## Example 2.16, Page 98¶

In [30]:
import scipy

lamda=1

#Maximum directivity of transmitter
D0_t_db=16
D0_t=10**(float(D0_t_db)/10)

D0_r_db=20
D0_r=10**(D0_r_db/10)

#Reflection coeficients of transmitter and receiver
tau_r=0.1
tau_t=0.2

#Power at transmitter
P_t=2

#Calculation of Power to the receiver
P_r=(1-tau_r**2)*(1-tau_t**2)*((lamda/(4*pi*100*lamda))**2)*D0_t*D0_r*P_t

Power delivered to the load of receiver: 0.00479199874075 W


## Example 2.18, Page 108¶

In [23]:
import scipy

Ta=150

#physical temp of transmission line
T0=300

#thermal efficiency of the antennna
eA=0.99

#antenna physical temperature
Tp=300
l=1

#antenna temp at antenna terminals due to physical temperature
T_ap=Tp*(1/eA-1)

#Loss of waveguide in dB/m
alpha_db=0.13

#Loss of waveguide in Np/m
alpha_np=alpha_db/0.868

#Calulation of effective temperature
T_A=Ta*exp(-l*alpha_np*2)+T_ap*exp(-l*alpha_np*2)+T0*(1-exp(-l*alpha_np*2))
print 'Effective temperature:',T_A,'K'

Effective temperature: 191.071984919 K

In [ ]: