Chapter 14: Microstrip Antennas

Example 14.1, Page no. 820

In [12]:
import math
#Given
h=0.1588
epsilon=2.2
v=3*10**8
f=10*10**9

W=(float(v)/(2*f))*(math.sqrt(2/(epsilon+1)))
W_cm=W*100
print "Width of the patch:",W_cm,"cm"

epsilon_eff=((epsilon+1)/2.0)+((epsilon-1)/2.0)*(1.0+12.0*h/W)**(-0.5)
print "Effective dielectric constant:",epsilon_eff

delta_L=(h*0.412*(epsilon_eff+0.3)*((W/h)+0.264))/((epsilon_eff-0.258)*((W/h)+0.8))
print "Extended incremental length of the patch:",delta_L,"cm"

lamda=v*100/f
L=(lamda/2)-(2*delta_L)
print "Actual length of patch:",L,"cm"

L_e=L+2*delta_L
print "Effective length of the patch:",L_e,"cm"

Width of the patch: 1.18585412256 cm
Effective dielectric constant: 1.64718499279
Extended incremental length of the patch: 0.0355084748459 cm
Actual length of patch: 0.928983050308 cm
Effective length of the patch: 1.0 cm

Example 14.2, Page No. 825

In [26]:
import scipy.integrate
import math
def S_i(a):
    temp=scipy.integrate.quad(lambda x:sin(x)/x,0,a)
    return temp[0]

def J0(s):
    temp=scipy.integrate.quad(lambda x:cos(s*sin(x)),0,pi)
    temp=(1/pi)*temp[0]
    return temp
    

#Given
v=3*10**10
f=10*10**9
L=0.906
W=1.186
h=0.1588
epsilon=2.2

lamda_0=v/f
k0=(2*pi)/lamda_0
X=k0*W
I1=-2+cos(X)+X*S_i(X)+sin(X)/X
G1=I1/(120*pi**2)

temp=scipy.integrate.quad(lambda x:(((sin(k0*W*cos(x)/2)/cos(x))**2)*J0(k0*L*sin(x))*sin(x)**3),0,pi)
G12=(1/(120*pi**2))*temp[0]

Rin=1/(2*(G1+G12))
print "Input Impedance:",Rin,"ohms"

R=50.0
y0=(L/pi)*(math.acos(sqrt(R/Rin)))
print "The position of the inset feed point where input impedance is 50 ohms:",y0,"cm"

1.86272719218
Input Impedance: 228.350793292 ohms
The position of the inset feed point where input impedance is 50 ohms: 0.312568937286 cm

Example 14.3, Page no. 843

In [27]:
#All these values are taken or calculated from the previous examples
lamda=50.0
v=3*10**10
f=10*10**9
L=0.906
W=1.186
h=0.1588
epsilon=2.2
lamda_0=v/f
G1=0.00157
G12=0.00061683
I1=1.863

g_12=G12/G1
D_AF=2/(1+g_12)
D0=((2*pi*W)/lamda_0)**2*(1/I1)
D2=D0*D_AF
print "Directivity:",10*log10(D2),"dB"

I2=3.59801
D_2=((2*pi*W)/lamda_0)**2*(pi/I2)
print "Directivity:",10*log10(D_2),"dB"

Directivity: 6.77188375387 dB
Directivity: 7.31374111976 dB

Example 14.4, Page no. 847

In [32]:
#given
epsilon=2.2
h=0.1588
fr=10*10**9

F=(8.791*10**9)/(fr*sqrt(epsilon))

a=F/(1+((2*h)/(pi*epsilon*F))*((log(pi*F/(2*h))+1.7726)))**0.5
print "Actual radius of the microstrip patch antenna: %f cm"% a

Actual radius of the microstrip patch antenna: 0.524986 cm

Example 14.5, Page no. 864

In [34]:
#given
fc=10*10**9
h=0.1588
frac_bw=0.05
VSWR=2

Qt=(VSWR-1)/(frac_bw*VSWR**0.5)
print "The total Quality Factor: %f" % Qt

f1=fc/(sqrt(1+(1/Qt)))
f2=fc*(sqrt(1+(1/Qt)))

print "The resonant frequencies are : %f GHz, %f GHz" %(f1/10**9,f2/10**9)

rel_ratio=1+1/Qt

print "The relative ratio is %f. Thus the patch is nearly square," % rel_ratio

The total Quality Factor: 14.142136
The resonant frequencies are : 9.664156 GHz, 10.347515 GHz
The relative ratio is 1.070711. Thus the patch is nearly square,