Chapter 9: Broadband Dipoles and Matching Techniques

Example 9.1, Page no. 526

#Given
N=2
RL=100
Z0=50

#Function to calculate factorial
def fact(n):
    if n==0:
        return 1
    return n*fact(n-1)

#Function to calculate the value of rho
def rho(n,N,RL,Z0):
    temp=(2**(-N))*(float((RL-Z0))/(RL+Z0))*(fact(N)/(fact(N-n)*fact(n)))
    return temp


def char_imp(rho,Z0):
    temp=Z0*(1+rho)/(1-rho)
    return temp


rho_0=rho(0,N,RL,Z0)
rho_1=rho(1,N,RL,Z0)

Z1=char_imp(rho_0,Z0)
Z2=char_imp(rho_1,Z0)

frac_bw=0.375
rho_m=(float(RL-Z0)/(RL+Z0))*(cos((-pi/4)*(frac_bw-2)))**2

print "Maximum tolerable co-efficient:",rho_m

VSWR=(1+rho_m)/(1-rho_m)

print "VSWR:",VSWR

Maximum tolerable co-efficient: 0.0280883979496
VSWR: 1.05780031412

Example 9.2, Page no. 536

#given
f=15*10**6
v=3*10**8
lamda=v/float(f)

a=0.95*10**-3*lamda
a1=3.175*10**-4*lamda
s=3.81*10**-3*lamda
u=ceil((a/2)/(a1/2))
v=ceil(s/(a1/2))
print "u: %f, v: %f" %(u,v)

alpha=log(v)/(log(v)-log(u))
print "Alpha: %f" %alpha

step_up=(1+alpha)**2
print "Step-up ratio: %f" %step_up

Za=30.44*(1-1j)
Z2=step_up*Za/2
print "Z2:",Z2,"ohms"

Z0=276*log10((2*s)/sqrt(a*a1))
print "Z0:",Z0,"ohms"

z2=Z2/Z0
print "z2:",z2,"ohms"

y2=1/z2
print "y2:",y2,"ohms"

#zg is calculated using smith's chart
zg=0+0.23j

yg=1/zg
print "Generator admittance:",yg,"siemens"

yin=y2+yg
print "Input admittance:",yin,"siemens"

zin=1/yin
print "Input impedance:",zin,"ohms"

Zin=Z0*zin
print "Unnormalized impedance:",Zin,"ohms"

C=1/(2*pi*f*Zin.imag)
print "Capacitance: %f pF" %(C*10**12)

u: 3.000000, v: 24.000000
Alpha: 1.528321
Step-up ratio: 6.392406
Z2: (97.2924229345-97.2924229345j) ohms
Z0: 315.253079871 ohms
z2: (0.308616883217-0.308616883217j) ohms
y2: (1.62013171408+1.62013171408j) ohms
Generator admittance: -4.34782608696j siemens
Input admittance: (1.62013171408-2.72769437288j) siemens
Input impedance: (0.160964593914+0.27100402593j) ohms
Unnormalized impedance: (50.7445839816+85.4348538319j) ohms
Capacitance: 124.192049 pF