# Chapter 12 Transmission Lines¶

## Example 12.1 Page no 573¶

In [2]:
#given
L=73.75*10**-9                    #inductance, H
C=29.5*10**-12                    #capacitance
x=5280

#calculation
import math
Z=math.sqrt(L/C)
z1=math.sqrt((x*L)/(x*C))

#result
print"characterstics impedence for 1-ft =",Z,"ohm"
print"characterstics impedence for 1-mi = ",z1,"ohm"

characterstics impedence for 1-ft = 50.0 ohm
characterstics impedence for 1-mi =  50.0 ohm


## Example 12.2 Page no 574¶

In [7]:
#given
a=2                           #parallel wire line
b=2.35                        #coaxial line
D=0.285
d=0.08
e=1.0                         #dielectric constant of insulating material relative to air

#calculation
import math
z=(276/e)*math.log10(2*2)
z1=(138/e)*math.log10(b)
z2=(138/math.sqrt(2.3)*math.log10(D/d))

#result
print"(a) characterstics impedence for a parallel wire = ",round(z,0),"ohm"
print"(b) characterstics impedence for a air dielectric coaxial line= ",round(z1,1),"ohm"
print"(c) characterstics impedence = ",round(z2,0),"ohm"

(a) characterstics impedence for a parallel wire =  166.0 ohm
(b) characterstics impedence for a air dielectric coaxial line=  51.2 ohm
(c) characterstics impedence =  50.0 ohm


## Example 12.3 Page no 579¶

In [11]:
#given
L=73.75*10**-9                #inductance, H
C=29.5*10**-12                #capacitance
d=1                           #distance

#calculation
import math
t=math.sqrt(L*C)
Vp=d/t

#result
print"the delay introduced is t =",round(t,10),"s"
print"The velocity of propagation is  ",round(Vp*10**-8,3),"*10**8 ft/s"

the delay introduced is t = 1.5e-09 s
The velocity of propagation is   6.78 *10**8 ft/s


## Example 12.4 Page no 580¶

In [1]:
#given
v=2.07*10**8                     #velocity
c=3.0*10**8                      #velocity of light
Er=2.3                           #relative dielectric constant

#calculation
import math
vf=(v/c)                         #velocity factor
vf1=1/math.sqrt(Er)

#result
print"The velocity = ",vf,"m/s"
print"vf = ",round(vf1,3)

The velocity =  0.69 m/s
vf =  0.659


## Example 12.5 Page no 581¶

In [1]:
#given
c=3*10**8                         #speed of light
f=100.0*10**6                     #frequency of signal
x=2.07*10**8                      #velocity of wave propagation

#Calcultion
w=c/f                             #wavelength in free-space
w1=x/f                            #wavelength while traveling through an RG-8A/U coaxial cable

#Result
print"In free space, lambda =",w,"m"
print"While traveling through RG-8A/U cable, lamda= ",w1,"m"

In free space, lambda = 3.0 m
While traveling through RG-8A/U cable, lamda=  2.07 m


## Example 12.7 Page no 592¶

In [1]:
#Given
Zo=50.0                                      #characteristic impedance
v=2.07*10**8                                 #velocity in RG-8A/U cable
f=27.0*10**6                                 #operating frequency of citizen's band transmitter
Po=4                                         #output power of transmitter
l=10                                         #length of RG-8A/U cable
Rl=300                                       #input resistance of antenna

#calculation
T=((Zl-Zo)/(Zl+Zo))                          #reflection coefficient
h=v/f                                        #length of cable in wavelength
le=l/h                                       #electrical length
x=Rl/Zo                                      #VSWR
y=((1+T)/(1-T))                              #VSWR
rp=(T)**2*Po                                 #reflected power
#part(a): The reflection coefficient

#result
print"(a) reflection cofficient = ",round(T,2)
print"(b) electrical length =",round(le,2),"lambda"
print"(c) VSWR = ",y
print"(d) the reflected voltage = ",round(Pl,2),"W"

(a) reflection cofficient =  0.71
(b) electrical length = 1.3 lambda
(c) VSWR =  6.0
(d) the reflected voltage =  1.96 W


## Example 12.8 Page no 597¶

In [10]:
#given
Zo=100.0                             #characteristic impedance
j=1j
l=4.3                                #length of transmission line

#calculation
x=200/Zo
y=150/Zo
a=0.4*Zo
b=0.57*Zo

#result
print"Zin = ",a,"Ohm","+j*",b,"Ohm"

Zin =  40.0 Ohm +j* 57.0 Ohm


## Example 12.9 Page no 599¶

In [8]:
#given
import cmath
j=1j
RL=120                                     #load resistance from smith chart
Z0=50.0                             #characteristic impedance

#calculation
import math
z1=ZL/Z0
z=2.4                                      #normalized z at a point that is purely resistive
ar=z*Z0                                    #actual resistance
x=math.sqrt(Z0*RL)

#Result
print"zl= ",z1
#VSWR,zin,R can be found out from smith chart manually
print"characteristic impedance is =",round(x,2),"ohm"

zl=  (1.5+1j)
characteristic impedance is = 77.46 ohm


## Example 12.10 Page no 601¶

In [7]:
#given
import cmath
Z0=75.0                              #characteristic impedance
j=1j

zL = (0.666666666667-1.33333333333j)