# Chapter 14 : Transmission lines and waves¶

## Example 14.1 Page No : 471¶

In [1]:
# Variables
f = 1.*10**6;  #Hz

# Calculations and Results
lembda = 3.*10**8/f;   #m
print 'The free space wavelength is  =  %i m '%(lembda);
l = .1*lembda;
print ' Length , l =  %i m'%(l);
The free space wavelength is  =  300 m
Length , l =  30 m

## Example 14.2 Page No : 471¶

In [2]:
# Variables
f = 1.*10**8;  #Hz

# Calculations and Results
lembda = 3.*10**8/f;   #m
print 'The free space wavelength is  =  %i m '%(lembda);
l = .1*lembda;
print ' Length ,l =  %.1f m'%(l);
The free space wavelength is  =  3 m
Length ,l =  0.3 m

## Example 14.3 Page No : 472¶

In [3]:
# Variables
f = 1.*10**9;  #Hz

# Calculations and Results
lembda = 3.*10**8/f;   #m
print 'The free space wavelength is  =  %i cm '%(lembda*100);
l = .1*lembda;
print ' Length , l =  %i cm'%(l*100);
The free space wavelength is  =  30 cm
Length , l =  3 cm

## Example 14.4 Page No : 474¶

In [5]:
import math
# Variables
L = 320.*10**-9;   #H/m
C = 90.*10**-12;   #F/m

# Calculations
R0 = math.sqrt(L/C);

# Results
print 'The characteristc impedance, R0  =  %.2f ohm '%(R0);
The characteristc impedance, R0  =  59.63 ohm

## Example 14.5 Page No : 476¶

In [6]:
import math

# Variables
L = 320.*10**-9;   #H/m
C = 90.*10**-12;   #F/m

# Calculations
v = 1/math.sqrt(L*C);

# Results
print 'The velocity of propagation is, v  =  %.3f 10**8 m/s '%(v*10**-8);
The velocity of propagation is, v  =  1.863 10**8 m/s

## Example 14.6 Page No : 476¶

In [8]:
import math
# Variables
L = 320*10**-9;   #H/m
C = 90*10**-12;   #F/m

# Calculations
v = 1./math.sqrt(L*C);   #from Ex14.5
Er = (3*10**8/v)**2;

# Results
print 'The dielectic constant is, Er  =  %.2f  '%(Er);
The dielectic constant is, Er  =  2.59

## Example 14.6.1 Page No : 479¶

In [9]:
import math

# Variables
d = .3;  #cm
D = 1.02;  #cm
Er = 2.25;

# Calculations and Results
x = math.log(D/d);   #variable
L = 2*10**-7*x;
print 'a)The inductance per unit length is, L  =  %.1f nH/m '%(L*10**9);
C = 55.56*10**-12*Er/x;
print ' b)The capacitance per unit length is, C  =  %.2f nH/m '%(C*10**12);
R0 = 60/math.sqrt(Er)*x;
print ' c)The characteristic impedance is, R0  =  %.3f ohm '%(R0);
c = 3*10**8;
v = c/math.sqrt(Er);
print ' d)The velocity of propagation is, v  =  %i*10**8 m/s '%(v*10**-8);
a)The inductance per unit length is, L  =  244.8 nH/m
b)The capacitance per unit length is, C  =  102.15 nH/m
c)The characteristic impedance is, R0  =  48.951 ohm
d)The velocity of propagation is, v  =  2*10**8 m/s

## Example 14.7 Page No : 480¶

In [10]:
#prob no. 14.7;

# Variables
Rin = 50.   #ohm
Rout = 50.;   #ohm
Vrms = 400.;  #V

# Calculations and Results
Zin = Rin;
print 'a)The input impedance is, Zin  =  %i ohm'%(Zin);
Irms = Vrms/(Rin+Rout);  #A
print ' b)The rms current , Irms  =  %i A '%(Irms);
Pin = Irms**2*Rin;
print ' c)The input power is, Pin  =  %i W '%(Pin);
Pl = Pin;
print ' d)The load power is, Pl  =  %i W '%(Pl);
a)The input impedance is, Zin  =  50 ohm
b)The rms current , Irms  =  4 A
c)The input power is, Pin  =  800 W
d)The load power is, Pl  =  800 W

## Example 14.8 Page No : 481¶

In [11]:
# Variables
Rin = 50.   #ohm
Rout = 50.;   #ohm
Vrms = 400.;  #V
l = 50.;      #m

# Calculations and Results
Ldb = .01*l;   #dB
L = 10**(Ldb/10);
print 'The abslute loss is, L  =  %f '%(L);
Irms = Vrms/(Rin+Rout);  #A
Pin = Irms**2*Rin;

PL = Pin/L;
print ' The actual Power reaching the load is, PL  =  %.1f W '%(PL);
The abslute loss is, L  =  1.122018
The actual Power reaching the load is, PL  =  713.0 W

## Example 14.9 Page No : 484¶

In [14]:
from numpy import angle

# Variables
ZL = complex(50,100);
R0 = 50.;

def R2P(x):
return abs(x), angle(x)

# Calculations and Results
TauL = (ZL-R0)/(ZL+R0);
print 'a)The reflection coefficient at load is',
print (TauL);
R,theta = R2P(TauL)   #polar(TauL);
print 'OR , %.4f angle %i'%(R,theta*180/math.pi);

S = (1+R)/(1-R);
print ' b) The stading wave ratio is, S  =  %.3f '%(S);
a)The reflection coefficient at load is (0.5+0.5j)
OR , 0.7071 angle 45
b) The stading wave ratio is, S  =  5.828

## Example 14.10 Page No : 484¶

In [15]:
# Variables
ZL = 100.;   #ohm
RL = ZL;
R0 = 300.;    #ohm

# Calculations and Results
TauL = (RL-R0)/(RL+R0);

print 'a)The reflection coefficient at load is =   %0.2f'%(TauL);

S = R0/RL;
print ' b) The stading wave ratio is, S  =  %.0f '%(S);
a)The reflection coefficient at load is =   -0.50
b) The stading wave ratio is, S  =  3

## Example 14.11 Page No : 485¶

In [16]:
import math

# Variables
ZL = 100.;   #ohm
RL = ZL;
R0 = 300;    #ohm

# Calculations
TauL = (RL-R0)/(RL+R0);
mismatch_loss_dB = -10*math.log10(1-TauL**2);

# Results
print ' The mismatch loss dB , S  =  %.2f dB'%(mismatch_loss_dB);
The mismatch loss dB , S  =  1.25 dB

## Example 14.12 Page No : 487¶

In [17]:
import math
# Variables
Ex = 3. #V/m
n0 = 377.;

# Calculations and Results
Hy = Ex/n0;
print 'a) The vaulue of Hy is, Hy  =  %.3f * 10**-3 A/m'%(Hy*10**3);

Px = Ex**2/n0;
print ' b) The power density Px is, Px  =  %.3f * 10**-3 W/m**2'%(Px*10**3);
A = 10*30;
P = Px*A;
print ' c) The net power transmitted is, P  =  %.3f W '%(P);
a) The vaulue of Hy is, Hy  =  7.958 * 10**-3 A/m
b) The power density Px is, Px  =  23.873 * 10**-3 W/m**2
c) The net power transmitted is, P  =  7.162 W