Scilab Code for
Engineering Electromagnetics,
by William Hayt & John Buck1
Created by
Prof. R. Senthilkumar
Institute of Road and Transport Technology
rsenthil signalprocess@in.com
Cross-Checked by
——————————–
17 January 2011
1 Funded
by a grant from the National Mission on Education through ICT,
http://spoken-tutorial.org/NMEICT-Intro.This Textbook Companion and scilab
codes written in it canbe downloaded from website www.scilab.in
Book Details
Authors: William Hayt and John Buck
Title: Engineering Electromagnetics
Publisher: Tata McGraw Hill
Edition: 7th
Year: —Place: New Delhi
ISBN: 0070612234
1
Scilab numbering policy used in this document and the relation to the
above book.
Fig Figure
Exa Example (Solved example)
Eqn Equation (Particular equation of the above book)
ARC Additionally Required Codes
For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3
means a scilab code whose theory is explained in Section 2.3 of the book.
2
Contents
List of Scilab Codes
4
1 Vector Analysis
2
2 Columb’s Law and Electric Field Intensity
6
3 Electric Flux Density, Gauss’s Law and Divergence
10
4 Energy and Potential
16
5 Current and Conductors
21
6 Dielectrics and Capacitance
24
7 Poisson’s and Laplace’s Equation
27
8 The Steady Magnetic Field
32
9 Magnetic Forces, Materials and Inductance
35
11 Transmission Lines
47
12 The Uniform Plane Wave
58
13 Plane Wave Reflection and Dispersion
65
14 Guided Wave and Radiation
76
3
List of Scilab Codes
Exa 1.1
Exa 1.2
Exa 1.3
Exa 1.4
Exa 2.1
Exa 2.2
Exa 2.3
Exa 3.1
Exa 3.2
Exa 3.3
Exa 3.4
Exa 3.5
Exa 4.1
Exa 4.2
Exa 4.3
Exa 5.1
Program to find the unit vector . . . . . . . . . . . . .
Program to find the phase angle between two vectors .
Transform the vector of Rectangular coordinates into
cylindrical coordinates . . . . . . . . . . . . . . . . . .
Transform the vector of Rectangular coordinates into
spherical coordinates . . . . . . . . . . . . . . . . . . .
Program to Calculate force exerted on Q2 by Q1 . . .
Program to Calculate Electric Field E at P due to 4
identical charges . . . . . . . . . . . . . . . . . . . . .
Program to find the total charge enclosed in a volume
Program to find Electric Flux density ’D’ of a uniform
line charge . . . . . . . . . . . . . . . . . . . . . . . .
Program to calculate surface charge density, Flux density, Field Intensity of coaxial cable . . . . . . . . . . .
Program to calculate the total charge enclosed in a volume at the origin . . . . . . . . . . . . . . . . . . . . .
Program to Find the Divergence of ’D’ at the origin .
Program to verify the Divergence theorem for the field
’D’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find the work involved ’W’ in moving a
charge ’Q’ along shorter arc of a circle . . . . . . . . .
Program to find the work involved ’W’ in moving a
charge ’Q’ along straight line . . . . . . . . . . . . . .
Program to calculate E, D and volume charge density
using divergence of D . . . . . . . . . . . . . . . . . .
Program to find the resistance, current and current density . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2
2
3
4
6
7
8
10
11
12
13
14
16
17
18
21
Exa 5.2
Exa 5.3
Exa 6.1
Exa 6.2
Exa 6.3
Exa 7.1
Exa 7.2
Exa 7.3
Exa 7.4
Exa 7.5
Exa 8.1
Exa 8.2
Exa 8.3
Exa 9.1
Exa 9.2
Exa 9.3
Exa 9.4
Exa 9.5
Exa 9.6
Exa 9.7
Exa 9.8
Exa 9.9
Program to find potential at point P, Electric Field Intensity E, Flux density D . . . . . . . . . . . . . . . .
Program to determine the equation of the streamline
passing through any point . . . . . . . . . . . . . . .
Program to calculate D, E and Polarization P for Teflon
slab . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Program to calculate E and Polarization P for Teflon
slab . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Program to calculate the capacitance of a parallel plate
capacitor . . . . . . . . . . . . . . . . . . . . . . . . .
Derivation of capacitance of a parallel plate capacitor .
Capacitance of a Cylindrical Capacitor . . . . . . . . .
Program to determine the electric field of a two infinite
radial planes with an interior angle alpha . . . . . . .
Derivation of capacitance of a spherical capacitor . . .
Potential in spherical coordinates as a function of teta
V(teta) . . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find the magnetic field intensity of a current
carrying filament . . . . . . . . . . . . . . . . . . . . .
Program to find the curlH of a square path of side ’d’
Program to verify Stokes theorem . . . . . . . . . . .
Program to find magnetic field and force produced in a
square loop . . . . . . . . . . . . . . . . . . . . . . . .
Program to determine the differential force between two
differential current elements . . . . . . . . . . . . . . .
Program to calculate the total torque acting on a planar
rectangular current loop . . . . . . . . . . . . . . . . .
Program to find the torque and force acting on each side
of planar loop . . . . . . . . . . . . . . . . . . . . . . .
Program to find Magnetic Susceptibility, H , Magnetization M . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find the boundary conditions on magnetic
field . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find magnetomotive force ’Vm’ and reluctance ’R’ . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find total Magnetic Flux Density in Weber
Program to calculate self inductances and Mutual Inductances between two coaxial solenoids . . . . . . . .
5
22
23
24
25
25
27
28
29
30
31
32
33
33
35
36
37
38
40
41
42
43
44
Exa 11.1
Program to determine the total voltage as a function of
time and position in a loss less transmission line . . .
Exa 11.2 Program to find the characteristic impedance, the phase
constant an the phase velocity . . . . . . . . . . . . .
Exa 11.3 Program to find the magnitude and phase of characteristic impedance Zo . . . . . . . . . . . . . . . . . . . .
Exa 11.4 Program to find the output power and attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 11.5 Program to find the power dissipated in the lossless
transmission line . . . . . . . . . . . . . . . . . . . . .
Exa 11.6 Program to find the total loss in lossy lines . . . . . .
Exa 11.7 Program to find the load impedance of a slotted line .
Exa 11.8 Program to find the input impedance and power delivered to the load . . . . . . . . . . . . . . . . . . . . .
Exa 11.9 Program to find the input impedance for a line terminated with pure capacitive impedance . . . . . . . . .
Exa 11.10 Program to find the input impedance for a line terminated with impedance (with inductive reactance) . . .
Exa 11.11 Program to find the voltage at the load resistor and the
current in the battery . . . . . . . . . . . . . . . . . .
Exa 11.12 Program to plot the voltage and current through a resistor . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 12.1 Program to determine the phasor of forward propagating field . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 12.2 Program to determine the instantaneous field of a plane
wave . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 12.3 Program to find the Phase constant, Phase velocity,
Electric Field Intensity and Intrinsic ratio . . . . . . .
Exa 12.4 Program to find the penetration depth and intrinsic
impedance . . . . . . . . . . . . . . . . . . . . . . . .
Exa 12.5 Program to find the attenuation constant, propagation
constant and intrinsic impedance . . . . . . . . . . . .
Exa 12.6 Program to find skin depth, loss tangent and phase velocity . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 12.7 Program to find the electric field of linearly polarized
wave . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 13.1 Program to find the electric field of incident, reflected
and transmitted waves . . . . . . . . . . . . . . . . . .
6
47
47
48
49
49
50
51
51
53
54
54
56
58
58
59
60
61
62
63
65
Exa 13.2
Exa 13.3
Program to find the maxima and minima electric field
Program to determine the intrinsic impedance of the
unknown material . . . . . . . . . . . . . . . . . . . .
Exa 13.4 Program to determine the required range of glass thickness for Fabry-perot interferometer . . . . . . . . . . .
Exa 13.5 Program to find the required index for the coating and
its thickness . . . . . . . . . . . . . . . . . . . . . . .
Exa 13.6 Program to find the phasor expression for the electric
field . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 13.7 Program to find the fraction of incident power that is
reflected and transmitted . . . . . . . . . . . . . . . .
Exa 13.8 Program to find the refractive index of the prism material
Exa 13.9 Program to determine incident and transmitted anlges
Exa 13.10 Program to determine group velocity and phase velocity
of a wave . . . . . . . . . . . . . . . . . . . . . . . . .
Exa 13.11 Program to determine the pulse width at the optical
fiber output . . . . . . . . . . . . . . . . . . . . . . . .
Exa 14.1 Program to determine the cutoff frequency for the first
waveguide mode(m=1) . . . . . . . . . . . . . . . . . .
Exa 14.2 Program to determine the number of modes propagate
in waveguide . . . . . . . . . . . . . . . . . . . . . . .
Exa 14.3 Program to determine the group delay and difference in
propagation times . . . . . . . . . . . . . . . . . . . .
Exa 14.4 Program to determine the operating range of frequency
for TE10 mode of air filled rectangular waveguide . . .
Exa 14.5 Program to determine the maximum allowable refractive index of the slab material . . . . . . . . . . . . . .
Exa 14.6 Program to find the V number of a step index fiber . .
ARC 1
Program to calculate the attenuation constant of good
dielectric . . . . . . . . . . . . . . . . . . . . . . . . .
ARC 2
Program used to convert cartesian coordinates into cylindrical coordinates . . . . . . . . . . . . . . . . . . . .
ARC 3
Program used to convert cartesian coordinates into spherical coordinates . . . . . . . . . . . . . . . . . . . . . .
ARC 4
Program used to find the cross product of two vectors
ARC 5
Program used to convert the cylindrical coordinates into
ARC 6
Program to find the dot product of two vectors . . . .
ARC 7
Program to find the electrical length . . . . . . . . . .
7
66
68
68
69
70
71
72
73
74
74
76
76
77
78
79
79
79
80
80
80
81
81
81
ARC 8
ARC
ARC
ARC
ARC
9
10
11
12
ARC 13
ARC 14
ARC
ARC
ARC
ARC
ARC
ARC
ARC
ARC
ARC
ARC
ARC
15
16
17
18
19
21
22
23
24
25
26
ARC 27
ARC 28
Program used to calculate the electric field intensity of
a line charge . . . . . . . . . . . . . . . . . . . . . . .
Program to finid the group delay difference . . . . . .
Program to find the group delay . . . . . . . . . . . .
Program to find the intrinsic impedance of dielectric .
Program to find the intrinsic imedance of a good dielectric . . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find the free space permittivity and free
space permeability . . . . . . . . . . . . . . . . . . . .
rogram used to find the capacitance of a parallel plate
Capacitor . . . . . . . . . . . . . . . . . . . . . . . . .
Program to find the impedance of a parallel connection
Program used to calculate the phase angle . . . . . . .
Program to find the phase constant of dielectric . . . .
Program to find the phase constant of a good dielectric
Program to find the phase velocity . . . . . . . . . . .
Program to find the propagation constant . . . . . . .
Program to find the reflection coefficient . . . . . . . .
Program to find the reflection coefficient . . . . . . . .
Program to calculate the skin depth of a good conductor
Program to find the refracted angle using snell’s law .
Program used to convert spherical coordinates into cartesian coordinates . . . . . . . . . . . . . . . . . . . . .
Program used to find the Unit vector . . . . . . . . . .
Program to find the Voltage Standing Wave Ratio VSWR
8
81
82
82
82
82
83
83
83
84
84
84
85
85
85
85
86
86
86
87
87
List of Figures
11.1 To be provided . . . . . . . . . . . . . . . . . . . . . . . . .
1
57
Chapter 1
Vector Analysis
Scilab code Exa 1.1 Program to find the unit vector
1 // C a p t i o n : Program t o f i n d t h e u n i t v e c t o r
2 // Example1 . 1
3 // p a g e 8
4 G = [2 , -2 , -1]; // p o s i t i o n o f p o i n t G i n c a r t e s i a n
c o o r d i n a t e system
5 aG = UnitVector ( G ) ;
6 disp ( aG , ’ U n i t V e c t o r aG = ’ )
7 // R e s u l t
8 // U n i t V e c t o r aG =
9 //
0.6666667 − 0.6666667
− 0.3333333
Refer to the following Scilab code for UnitVector ARC 27
Scilab code Exa 1.2 Program to find the phase angle between two vectors
1
2
3
4
5
6
// C a p t i o n : Program t o f i n d t h e p h a s e a n g l e b e t w e e n
two v e c t o r s
// Example1 . 2
// p a g e 11
clc ;
Q = [4 ,5 ,2]; // p o i n t Q
x = Q (1) ;
2
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
y = Q (2) ;
z = Q (3) ;
G = [y , -2.5* x ,3]; // v e c t o r f i e l d
disp (G , ’G( rQ ) = ’ )
aN = [2/3 ,1/3 , -2/3]; // u n i t v e c t o r − d i r e c t i o n o f Q
G_dot_aN = dot (G , aN ) ; // d o t p r o d u c t o f G and aN
disp ( G_dot_aN , ’G. aN = ’ )
G_dot_aN_aN = G_dot_aN * aN ;
disp ( G_dot_aN_aN , ’ (G. aN ) aN= ’ )
teta_Ga = Phase_Angle (G , aN ) // p h a s e a n g l e b e t w e e n G
and u n i t v e c t o r aN
disp ( teta_Ga , ’ p h a s e a n g l e b e t w e e n G and u n i t v e c t o r
aN i n d e g r e e s = ’ )
// R e s u l t
// G( rQ ) =
5. − 10.
3.
// G. aN =
− 2.
// (G. aN ) aN =
− 1.3333333 − 0.6666667
1.3333333
// p h a s e a n g l e b e t w e e n G and u n i t v e c t o r aN i n
degrees =
99.956489
Refer to the following for dot ARC 6 Refer to the following for phase angel
ARC 16
Scilab code Exa 1.3 Transform the vector of Rectangular coordinates into
cylindrical coordinates
1
2
3
4
5
6
7
// C a p t i o n : T r a n s f o r m t h e v e c t o r o f R e c t a n g u l a r
coordinates into cylindrical coordinates
// Example1 . 3
// p a g e 18
clc ;
y = sym ( ’ y ’ ) ;
x = sym ( ’ x ’ ) ;
z = sym ( ’ z ’ ) ;
3
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
ar = sym ( ’ a r ’ ) ;
aphi = sym ( ’ a p h i ’ ) ;
phi = sym ( ’ p h i ’ ) ;
B = y * ax - x * ay + z * az ;
disp (B , ’ Given v e c t o r i n c a r t e s i a n co−o r d i a n t e s y s t e m
B= ’ )
Br = B * ar ;
Bphi = B * aphi ;
Bz = B * az ;
disp ( ’ Components o f c y l i n d r i c a l v e c t o r B ’ )
disp ( Br , ’ Br= ’ )
disp ( Bphi , ’ Bphi= ’ )
disp ( Bz , ’ Bz= ’ )
// R e s u l t
// Given v e c t o r i n c a r t e s i a n co−o r d i a n t e s y s t e m B=
// a z ∗ z+ax ∗y−ay ∗ x
// Components o f c y l i n d r i c a l v e c t o r B
// Br=
// a r ∗ ( a z ∗ z+ax ∗y−ay ∗ x )
// Bphi=
// a p h i ∗ ( a z ∗ z+ax ∗y−ay ∗ x )
// Bz=
// a z ∗ ( a z ∗ z+ax ∗y−ay ∗ x )
//
Scilab code Exa 1.4 Transform the vector of Rectangular coordinates into
spherical coordinates
1
2
3
4
5
6
// C a p t i o n : T r a n s f o r m t h e v e c t o r o f R e c t a n g u l a r
coordinates into spherical coordinates
// Example1 . 4
// p a g e 22
clc ;
y = sym ( ’ y ’ ) ;
x = sym ( ’ x ’ ) ;
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
z = sym ( ’ z ’ ) ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
ar = sym ( ’ a r ’ ) ;
aTh = sym ( ’ aTh ’ ) ;
aphi = sym ( ’ a p h i ’ ) ;
G = ( x * z / y ) * ax ;
disp (G , ’ Given v e c t o r i n c a r t e s i a n co−o r d i a n t e s y s t e m
B= ’ )
r = sym ( ’ r ’ ) ;
teta = sym ( ’ t e t a ’ )
phi = sym ( ’ p h i ’ )
x1 = r * sin ( teta ) * cos ( phi ) ;
y1 = r * sin ( teta ) * sin ( phi ) ;
z1 = r * cos ( teta ) ;
G1 = ( x1 * z1 / y1 ) * ax ;
Gr = G1 * ar ;
GTh = G1 * aTh ;
Gphi = G1 * aphi ;
Gsph = [ Gr , GTh , Gphi ];
disp ( Gr , ’ Gr= ’ )
disp ( GTh , ’GTh= ’ )
disp ( Gphi , ’ Gphi= ’ )
// R e s u l t
// Given v e c t o r i n c a r t e s i a n co−o r d i a n t e s y s t e m B =
ax ∗ x ∗ z / y
// Gr =
a r ∗ ax ∗ c o s ( p h i ) ∗ r ∗ c o s ( t e t a ) / s i n ( p h i )
//GTh =
ax ∗ c o s ( p h i ) ∗ r ∗ c o s ( t e t a ) ∗aTh/ s i n ( p h i )
// Gphi =
a p h i ∗ ax ∗ c o s ( p h i ) ∗ r ∗ c o s ( t e t a ) / s i n ( p h i )
//
5
Chapter 2
Columb’s Law and Electric
Field Intensity
Scilab code Exa 2.1 Program to Calculate force exerted on Q2 by Q1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
// C a p t i o n : Program t o C a c u l a t e f o r c e e x e r t e d on Q2 by
Q1
// Example2 . 1
// p a g e 29
clc ;
r2 = [2 ,0 ,5];
r1 = [1 ,2 ,3];
R12 = norm ( r2 - r1 ) ;
aR12 = UnitVector ( r2 - r1 ) ;
disp ( R12 , ’ R12= ’ )
disp ( aR12 , ’ aR12= ’ )
Q1 = 3e -04; // c h a r g e 1 i n Coulombs
Q2 = -1e -04; // c h a r g e 2 i n Coulombs
Eps = 8.854 e -12; // f r e e s p a c e p e r m i t t i v i t y
F2 = (( Q1 * Q2 ) /(4* %pi * Eps * R12 ^2) ) * aR12 ;
F1 = - F2 ;
disp ( F2 , ’ F o r c e e x e r t e d on Q2 by Q1 i n N/m F2 = ’ )
disp ( F1 , ’ F o r c e e x e r t e d on Q1 by Q2 i n N/m F1 = ’ )
// R e s u l t
// R12=
//
3.
6
21
22
23
24
25
26
// aR12=
//
0.3333333 − 0.6666667
0.6666667
// F o r c e e x e r t e d on Q2 by Q1 i n N/m F2 =
// − 9 . 9 8 6 3 8 0 5
19.972761 − 19.972761
// F o r c e e x e r t e d on Q1 by Q2 i n N/m F1 =
//
9.9863805 − 19.972761
19.972761
Refer to the following Scilab code for UnitVector ARC 27
Scilab code Exa 2.2 Program to Calculate Electric Field E at P due to 4
identical charges
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
// C a p t i o n : Program t o C a c u l a t e E l e c t r i c F i e l d E a t P
due t o 4 i d e n t i c a l c h a r g e s
// Example2 . 2
// p a g e 33
clc ;
P = [1 ,1 ,1];
P1 = [1 ,1 ,0];
P2 = [ -1 ,1 ,0];
P3 = [ -1 , -1 ,0];
P4 = [1 , -1 ,0];
R1 = norm (P - P1 ) ;
aR1 = UnitVector (P - P1 ) ;
R2 = norm (P - P2 ) ;
aR2 = UnitVector (P - P2 ) ;
R3 = norm (P - P3 ) ;
aR3 = UnitVector (P - P3 ) ;
R4 = norm (P - P4 ) ;
aR4 = UnitVector (P - P4 ) ;
disp ( R1 , ’ R1= ’ )
disp ( aR1 , ’ aR1= ’ )
disp ( R2 , ’ R2= ’ )
disp ( aR2 , ’ aR2= ’ )
disp ( R3 , ’ R3= ’ )
disp ( aR3 , ’ aR3= ’ )
disp ( R4 , ’ R4= ’ )
7
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
disp ( aR4 , ’ aR4= ’ )
Q = 3e -09; // c h a r g e
i n Coulombs
Eps = 8.854 e -12; // f r e e s p a c e p e r m i t t i v i t y
E1 = ( Q /(4* %pi * Eps * R1 ^2) ) * aR1 ;
E2 = ( Q /(4* %pi * Eps * R2 ^2) ) * aR2 ;
E3 = ( Q /(4* %pi * Eps * R3 ^2) ) * aR3 ;
E4 = ( Q /(4* %pi * Eps * R4 ^2) ) * aR4 ;
E = E1 + E2 + E3 + E4 ;
disp (E , ’ E l e c t r i c F i e l d I n t e s n i t y a t any p o i n t P due
t o f o u r i d e n t i c a l C h a r g e s i n V/m= ’ )
// R e s u l t
//R1=
1.
// aR1=
0.
0.
1.
//R2=
2.236068
// aR2=
0.8944272
0.
0.4472136
//R3=
3.
// aR3=
0.6666667
0.6666667
0.3333333
//R4=
2.236068
// aR4=
0.
0.8944272
0.4472136
// E l e c t r i c F i e l d I n t e s n i t y a t any p o i n t P due t o
f o u r i d e n t i c a l C h a r g e s i n V/m=
// 6 . 8 2 0 6 0 4 8
6.8206048
32.785194
//
Refer to the following Scilab code for UnitVector ARC 27
Scilab code Exa 2.3 Program to find the total charge enclosed in a volume
1
2
3
4
5
6
7
8
9
// Example2 . 3
// p a g e 35
clc ;
r = sym ( ’ r ’ ) ;
z = sym ( ’ z ’ ) ;
phi = sym ( ’ p h i ’ ) ;
rv = -5e -06* exp ( -1 e05 * r * z ) ;
disp ( rv , ’ Volume Charge d e n s i t y i n C/ c u b i c . m e t r e r v= ’
8
10
11
12
13
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15
16
17
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22
23
24
25
)
Q1 = integ ( rv *r , phi ) ;
Q1 = limit ( Q1 , phi ,2* %pi ) ;
Q2 = integ ( Q1 , z ) ;
Q2 = limit ( Q2 ,z ,0.04) - limit ( Q2 ,z ,0.02) ;
Q3 = integ ( Q2 , r ) ;
Q3 = limit ( Q3 ,r ,0.01) - limit ( Q3 ,r ,0) ;
disp ( Q1 , ’ Q1= ’ )
disp ( Q2 , ’ Q2= ’ )
disp ( Q3 , ’ T o t a l Charge E n c l o s e d i n a 2cm l e n g t h
of
e l e c t r o n beam i n c o u l o m b s Q= ’ )
// R e s u l t
// Volume Charge d e n s i t y i n C/ c u b i c . m e t r e r v = −%e
ˆ −(100000∗ r ∗ z ) / 2 0 0 0 0 0
//Q1=
−103993∗ r ∗%eˆ −(100000∗ r ∗ z ) / 3 3 1 0 2 0 0 0 0 0
//Q2=
−103993∗%eˆ −(2000∗ r ) / 3 3 1 0 2 0 0 0 0 0 0 0 0 0 0
// T o t a l Charge E n c l o s e d i n a 2cm l e n g t h
of electron
beam i n c o u l o m b s Q=
// 1 0 3 9 9 3 / 1 3 2 4 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 − 1 0 3 9 9 3 ∗ %e
ˆ −40/1324080000000000000
//Q a p p r o x i m a t e l y e q u a l t o
1 0 3 9 9 3 / 1 3 2 4 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 = 7 . 8 5 4D−14 c o u l o m b s
9
Chapter 3
Electric Flux Density, Gauss’s
Law and Divergence
Scilab code Exa 3.1 Program to find Electric Flux density ’D’ of a uniform
line charge
1
2
3
4
5
6
7
8
9
10
11
12
13
// C a p t i o n : Program t o f i n d E l e c t r i c Flux d e n s i t y ’D’
of a uniform l i n e charge
// Example3 . 1
// p a g e 54
clc ;
e0 = 8.854 e -12; // f r e e s p a c e p e r m i t t i v i t y i n F/m
rL = 8e -09; // l i n e c h a r g e d e n s i t y c /m
r = 3; // d i s t a n c e i n m e t r e
E = Electric_Field_Line_Charge ( rL , e0 , r ) ; // e l e c t r i c
f i e l d i n t e n s i t y of l i n e charge
D = e0 * E ;
disp (D , ’ E l e c t r i c Flux D e n s i t y i n Coulombs p e r s q u a r e
metre D = ’ )
// R e s u l t
// E l e c t r i c Flux D e n s i t y i n Coulombs p e r s q u a r e
metre D =
//
4 . 2 4 4D−10
Refer to the following for ElectricalFieldLineCharge ARC 8
10
Scilab code Exa 3.2 Program to calculate surface charge density, Flux
density, Field Intensity of coaxial cable
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
// C a p t i o n : Program t o c a l c u l a t e s u r f a c e c h a r g e
d e n s i t y , Flux d e n s i t y , F i e l d I n t e n s i t y o f c o a x i a l
cable
// Example3 . 2
// p a g e 64
clc ;
Q_innercyl = 30 e -09; // t o t a l c h a r g e on t h e i n n e r
conductor i n coulombs
a = 1e -03; // i n n e r r a d i u s o f c o a x i a l c a b l e i n m e t r e
b = 4e -03; // o u t e r r a d i u s o f c o a x i a l c a b l e i n m e t r e
L = 50 e -02; // l e n g t h o f c o a x i a l c a b l e
rs_innercyl = Q_innercyl /(2* %pi * a * L ) ;
rs_outercyl = Q_innercyl /(2* %pi * b * L ) ;
e0 = 8.854 e -12; // f r e e s p a c e r e l a t i v e p e r m i t t i v i t y F
/m
r = sym ( ’ r ’ ) ;
Dr = a * rs_innercyl / r ;
Er = Dr / e0 ;
disp ( rs_innercyl , ’ S u r f a c e c h a r g e d e n s i t y o f i n n e r
c y l i n d e r o f c o a x i a l c a b l e i n C/ s q u a r e . metre ,
r s i n n e r c y l= ’ )
disp ( rs_outercyl , ’ S u r f a c e c h a r g e d e n s i t y o f o u t e r
c y l i n d e r o f c o a x i a l c a b l e i n C/ s q u a r e . metre ,
r s o u t e r c y l= ’ )
disp ( Dr , ’ E l e c t r i c Flux D e n s i t y i n C/ s q u a r e . m e t r e Dr=
’)
disp ( Er , ’ E l e c t r i c F i e l d I n t e n s i t y i n V/m Er= ’ )
// R e s u l t
// S u r f a c e c h a r g e d e n s i t y o f i n n e r c y l i n d e r o f
c o a x i a l c a b l e i n C/ s q u a r e . metre , r s i n n e r c y l =
//
0.0000095
// S u r f a c e c h a r g e d e n s i t y o f o u t e r c y l i n d e r o f
c o a x i a l c a b l e i n C/ s q u a r e . metre , r s o u t e r c y l =
11
23
24
25
26
27
//
0.0000024
// E l e c t r i c Flux D e n s i t y i n C/ s q u a r e . m e t r e Dr=
// 9 . 5 4 8 8 1 8 3 3 3 7 3 1 2 0 1 1 E−9/ r
// E l e c t r i c F i e l d I n t e n s i t y i n V/m Er=
// 1 0 7 8 . 4 7 5 0 7 7 2 2 2 8 6 / r
Scilab code Exa 3.3 Program to calculate the total charge enclosed in a
volume at the origin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
// C a p t i o n : Program t o c a l c u l a t e t h e t o t a l c h a r g e
e n c l o s e d i n a volume a t t h e o r i g i n
// Example3 . 3
// p a g e 67
clc ;
V = 1e -09; // volume i n c u b i c m e t r e
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
// Components o f E l e c t r i c Flux D e n s i t y i n c a r t e s i a n
c o o r d i n a t e system
Dx = exp ( - x ) * sin ( y ) ;
Dy = - exp ( - x ) * cos ( y ) ;
Dz = 2* z ;
// D i v e r g e n c e o f e l e c t r i c f l u x d e n s i t y ’D’
dDx = diff ( Dx , x ) ;
dDy = diff ( Dy , y ) ;
dDz = diff ( Dz , z ) ;
// T o t a l c h a r g e e n c l o s e d i n a g i v e n volume
del_Q = ( dDx + dDy + dDz ) * V ;
disp ( del_Q , ’ T o t a l c h a r g e e n c l o s e d i n an i n c r e m e n t a l
volume i n coulombs , d e l Q = ’ )
// T o t a l Charge e n c l o s e d i n a g i v e n volume a t o r i g i n
(0 ,0 ,0)
del_Q = limit ( del_Q ,x ,0) ;
del_Q = limit ( del_Q ,y ,0) ;
del_Q = limit ( del_Q ,z ,0) ;
disp ( del_Q *1 e09 , ’ T o t a l c h a r g e e n c l o s e d i n an
i n c r e m e n t a l volume i n nano c o u l o m b s a t o r i g i n ,
12
25
26
27
28
del Q = ’ )
// R e s u l t
// T o t a l c h a r g e e n c l o s e d i n an i n c r e m e n t a l volume i n
2 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E−9
coulombs , d e l Q =
// T o t a l c h a r g e e n c l o s e d i n an i n c r e m e n t a l volume i n
nano c o u l o m b s a t o r i g i n , d e l Q =
// 2 . 0
Scilab code Exa 3.4 Program to Find the Divergence of ’D’ at the origin
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7
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18
19
20
21
22
23
// C a p t i o n : Program t o Find t h e D i v e r g e n c e o f ’D’ a t
the o r i g i n
// Example3 . 4
// p a g e 70
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
// Components o f E l e c t r i c Flux D e n s i t y i n c a r t e s i a n
c o o r d i n a t e system
Dx = exp ( - x ) * sin ( y ) ;
Dy = - exp ( - x ) * cos ( y ) ;
Dz = 2* z ;
// D i v e r g e n c e o f e l e c t r i c f l u x d e n s i t y ’D’
dDx = diff ( Dx , x ) ;
dDy = diff ( Dy , y ) ;
dDz = diff ( Dz , z ) ;
divD = dDx + dDy + dDz
disp ( divD , ’ D i v e r g e n c e o f E l e c t r i c Flux D e n s i t y D i n
C/ c u b i c . metre , divD = ’ )
divD = limit ( divD ,x ,0) ;
divD = limit ( divD ,y ,0) ;
divD = limit ( divD ,z ,0) ;
disp ( divD , ’ D i v e r g e n c e o f E l e c t r i c Flux D e n s i t y D i n
C/ c u b i c . m e t r e a t o r i g i n , divD = ’ )
// R e s u l t
// D i v e r g e n c e o f E l e c t r i c Flux D e n s i t y D i n C/ c u b i c .
metre , divD =
13
// 2
// D i v e r g e n c e o f E l e c t r i c Flux D e n s i t y D i n C/ c u b i c .
m e t r e a t o r i g i n , divD =
26 // 2
24
25
Scilab code Exa 3.5 Program to verify the Divergence theorem for the
field ’D’
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3
4
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7
8
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11
12
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16
17
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22
23
24
// C a p t i o n : Program t o v e r i f y t h e D i v e r g e n c e t h e o r e m
f o r t h e f i e l d ’D’
// Example3 . 5
// p a g e 74
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
// Components o f E l e c t r i c Flux D e n s i t y i n c a r t e s i a n
c o o r d i n a t e system
Dx = 2* x * y ;
Dy = x ^2;
Dz = 0;
// D i v e r g e n c e o f e l e c t r i c f l u x d e n s i t y ’D’
dDx = diff ( Dx , x ) ;
dDy = diff ( Dy , y ) ;
dDz =0;
divD = dDx + dDy + dDz
disp ( divD , ’ D i v e r g e n c e o f E l e c t r i c Flux D e n s i t y D i n
C/ c u b i c . metre , divD = ’ )
// E v a l u a t e volume i n t e g r a l on d i v e r g e n c e o f ’D’
Vol_int_divD = integ ( divD , x ) ;
Vol_int_divD = limit ( Vol_int_divD ,x ,1) - limit (
Vol_int_divD ,x ,0) ;
Vol_int_divD = integ ( Vol_int_divD , y ) ;
Vol_int_divD = limit ( Vol_int_divD ,y ,2) - limit (
Vol_int_divD ,y ,0) ;
Vol_int_divD = integ ( Vol_int_divD , z ) ;
Vol_int_divD = limit ( Vol_int_divD ,z ,3) - limit (
Vol_int_divD ,z ,0) ;
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42
disp ( Vol_int_divD , ’ Volume I n t e g r a l o f d i v e r g e n c e o f
D, i n c o u l o m b s v o l i n t ( divD )= ’ )
// E v a l u a t e s u r f a c e i n t e g r a l on f i e l d D
Dx = limit ( Dx ,x ,1) ;
sur_D = integ ( Dx , y ) ;
sur_D = limit ( sur_D ,y ,2) - limit ( sur_D ,y ,0) ;
sur_D = integ ( sur_D , z ) ;
sur_D = limit ( sur_D ,z ,3) - limit ( sur_D ,z ,0) ;
disp ( sur_D , ’ S u r f a c e I n t e g r a l o f f i e l d D, i n c o u l o m b s
s u r i n t (D . d s )= ’ )
if ( sur_D == Vol_int_divD )
disp ( ’ D i v e r g e n c e Theorem v e r i f i e d ’ )
end
// R e s u l t
// D i v e r g e n c e o f E l e c t r i c Flux D e n s i t y D i n C/ c u b i c .
metre , divD =
// 2∗ y
// Volume I n t e g r a l o f d i v e r g e n c e o f D, i n c o u l o m b s
v o l i n t ( divD )=
// 12
// S u r f a c e I n t e g r a l o f f i e l d D, i n c o u l o m b s s u r i n t (
D . d s )=
// 12
15
Chapter 4
Energy and Potential
Scilab code Exa 4.1 Program to find the work involved ’W’ in moving a
charge ’Q’ along shorter arc of a circle
1
2
3
4
5
6
7
8
9
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19
20
// C a p t i o n : Program t o f i n d t h e work i n v o l v e d ’W’ i n
moving a c h a r g e ’Q’ a l o n g s h o r t e r a r c o f a c i r c l e
// Example4 . 1
// p a g e 84
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
y1 = sym ( ’ y1 ’ ) ;
y = sqrt (1 - x ^2) ;
Q = 2; // c h a r g e i n c o u l o m b s
Edot_dL1 = integ (y , x ) ;
disp ( Edot_dL1 , ’E . dx ∗ ax = ’ )
Edot_dL1 = limit ( Edot_dL1 ,x ,0.8) - limit ( Edot_dL1 ,x ,1)
;
disp ( Edot_dL1 , ’ V a l u e o f E . dx ∗ ax = ’ )
Edot_dL2 = 0;
disp ( Edot_dL2 , ’ V a l u e o f E . dz ∗ a z= ’ )
x = sqrt (1 - y1 ^2) ;
Edot_dL3 = integ (x , y1 )
disp ( Edot_dL3 , ’E . dy ∗ ay= ’ )
Edot_dL3 = limit ( Edot_dL3 , y1 ,0.6) - limit ( Edot_dL3 , y1
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29
30
31
32
33
,0) ;
disp ( Edot_dL3 , ’ V a l u e o f E . dy ∗ ay = ’ )
W = -Q *( Edot_dL1 + Edot_dL2 + Edot_dL3 ) ;
disp (W , ’ Work done i n moving a p o i n t c h a r g e a l o n g
s h o r t e r a r c o f c i r c l e i n J o u l e s , W= ’ )
// R e s u l t
// E . dx ∗ ax =
a s i n ( x ) /2+x ∗ s q r t (1−x ˆ 2 ) /2
// V a l u e o f E . dx ∗ ax =
( 2 5 ∗ a s i n ( 4 / 5 ) +12) /50−%pi /4
// V a l u e o f E . dz ∗ a z =
0.
// E . dy ∗ ay =
a s i n ( y1 ) /2+ y1 ∗ s q r t (1− y1 ˆ 2 ) /2
// V a l u e o f E . dy ∗ ay =
( 2 5 ∗ a s i n ( 3 / 5 ) +12) /50
// Work done i n moving a p o i n t c h a r g e a l o n g s h o r t e r
arc of c i r c l e in Joules , W =
// −2∗((25∗ a s i n ( 4 / 5 ) +12) /50+(25∗ a s i n ( 3 / 5 ) +12) /50−%pi
/4)
// Which i s e q u i v a l e n t t o
// − 2 ∗ ( ( 2 5 ∗ 0 . 9 2 7 2 9 5 2 + 1 2 ) / 5 0 + ( 2 5 ∗ 0 . 6 4 3 5 0 1 1 + 1 2 ) /50−%pi
/ 4 ) = −0.96 J o u l e s
Scilab code Exa 4.2 Program to find the work involved ’W’ in moving a
charge ’Q’ along straight line
1
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3
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5
6
7
8
9
10
11
12
13
14
// C a p t i o n : Program t o f i n d t h e work i n v o l v e d ’W’ i n
moving a c h a r g e ’Q’ a l o n g s t r a i g h t l i n e
// Example4 . 2
// p a g e 84
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
y1 = sym ( ’ y1 ’ ) ;
y = -3*( x -1) ;
Q = 2; // c h a r g e i n c o u l o m b s
Edot_dL1 = integ (y , x ) ;
disp ( Edot_dL1 , ’E . dx ∗ ax = ’ )
Edot_dL1 = limit ( Edot_dL1 ,x ,0.8) - limit ( Edot_dL1 ,x ,1)
;
disp ( Edot_dL1 , ’ V a l u e o f E . dx ∗ ax = ’ )
17
15 Edot_dL2 = 0;
16 disp ( Edot_dL2 , ’ V a l u e o f E . dz ∗ a z= ’ )
17 x = (1 - y1 /3) ;
18 Edot_dL3 = integ (x , y1 )
19 disp ( Edot_dL3 , ’E . dy ∗ ay= ’ )
20 Edot_dL3 = limit ( Edot_dL3 , y1 ,0.6) - limit ( Edot_dL3 , y1
,0) ;
21 disp ( Edot_dL3 , ’ V a l u e o f E . dy ∗ ay = ’ )
22 W = -Q *( Edot_dL1 + Edot_dL2 + Edot_dL3 ) ;
23 disp (W , ’ Work done i n moving a p o i n t c h a r g e a l o n g
24
25
26
27
28
29
30
s h o r t e r a r c o f c i r c l e i n J o u l e s , W= ’ )
// R e s u l t
//E . dx ∗ ax = −3∗( x ˆ2/2 − x )
// V a l u e o f E . dx ∗ ax = −3/50
// V a l u e o f E . dz ∗ a z =
0.
//E . dy ∗ ay = y1−y1 ˆ 2 / 6
// V a l u e o f E . dy ∗ ay =
27/50
// Work done i n moving a p o i n t c h a r g e a l o n g s h o r t e r
a r c o f c i r c l e i n J o u l e s , W = −24/25 = −0.96
Joules
Scilab code Exa 4.3 Program to calculate E, D and volume charge density
using divergence of D
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2
3
4
5
6
7
8
9
10
11
12
// C a p t i o n : Program t o c a l c u l a t e E , D and volume
charge density using divergence of D
// Example4 . 3
// p a g e 100
clc ;
x = -4;
y = 3;
z = 6;
V = 2*( x ^2) *y -5* z ;
disp ( float ( V ) , ’ P o t e n t i a l V a t p o i n t P( − 4 , 3 , 6 ) i n
v o l t s i s Vp = ’ )
x1 = sym ( ’ x1 ’ ) ;
y1 = sym ( ’ y1 ’ ) ;
z1 = sym ( ’ z 1 ’ ) ;
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46
47
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
V1 = 2*( x1 ^2) * y1 -5* z1 ;
// E l e c t r i c F i e l d I n t e n s i t y from g r a d i e n t o f V
Ex = - diff ( V1 , x1 ) ;
Ey = - diff ( V1 , y1 ) ;
Ez = - diff ( V1 , z1 ) ;
Ex1 = limit ( Ex , x1 , -4) ;
Ex1 = limit ( Ex1 , y1 ,3) ;
Ex1 = limit ( Ex1 , z1 ,6) ;
Ey1 = limit ( Ey , x1 , -4) ;
Ey1 = limit ( Ey1 , y1 ,3) ;
Ey1 = limit ( Ey1 , z1 ,6) ;
Ez1 = limit ( Ez , x1 , -4) ;
Ez1 = limit ( Ez1 , y1 ,3) ;
Ez1 = limit ( Ez1 , z1 ,6) ;
E = Ex1 * ax + Ey1 * ay + Ez1 * az ;
Ep = sqrt ( float ( Ex1 ^2+ Ey1 ^2+ Ez1 ^2) ) ;
disp ( Ep , ’ E l e c t r i c F i e l d I n t e n s i t y E a t p o i n t P
( −4 ,3 ,6) in v o l t s E = ’ )
aEp = float ( E / Ep ) ;
disp ( aEp , ’ D i r e c t i o n o f E l e c t r i c F i e l d E a t p o i n t P
( − 4 , 3 , 6 ) aEp= ’ )
Dx = float (8.854* Ex ) ;
Dy = float (8.854* Ey ) ;
Dz = float (8.854* Ez ) ;
D = Dx * ax + Dy * ay + Dz * az ;
disp (D , ’ E l e c t r i c Flux D e n s i t y i n p i c o . C/ s q u a r e . m e t r e
D =’)
dDx = diff ( Dx , x1 ) ;
dDx = limit ( dDx , x1 , -4) ;
dDx = limit ( dDx , y1 ,3) ;
dDx = limit ( dDx , z1 ,6) ;
dDy = diff ( Dy , y1 ) ;
dDy = limit ( dDy , x1 , -4) ;
dDy = limit ( dDy , y1 ,3) ;
dDy = limit ( dDy , z1 ,6) ;
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48
49
50
51
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54
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61
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63
dDz = diff ( Dz , z1 ) ;
dDz = limit ( dDz , x1 , -4) ;
dDz = limit ( dDz , y1 ,3) ;
dDz = limit ( dDz , z1 ,6) ;
rV = dDx + dDy + dDz ;
disp ( rV , ’ Volume Charge d e n s i t y from d i v e r g e n c e o f D
i n pC/ c u b i c . m e t r e i s rV= ’ )
// R e s u l t
// P o t e n t i a l V a t p o i n t P( − 4 , 3 , 6 ) i n v o l t s i s Vp =
66.
// E l e c t r i c F i e l d I n t e n s i t y E a t p o i n t P( − 4 , 3 , 6 ) i n
v o l t s E = 57.9050947672137
// D i r e c t i o n o f E l e c t r i c F i e l d E a t p o i n t P( − 4 , 3 , 6 )
aEp=
// 0 . 0 1 7 2 6 9 6 3 7 5 6 8 5 1 ∗ ( 5 ∗ az −32∗ ay +48∗ ax )
// e q u i v a l e n t t o aEp= 0 . 0 8 6 3 4 8 2 ∗ az − 0 . 5 5 2 6 2 8 4 ∗ ay
+ 0 . 8 2 8 9 4 2 6 ∗ ax
// E l e c t r i c Flux D e n s i t y i n p i c o . C/ s q u a r e . m e t r e D =
//
−35.416∗ ax ∗ x1 ∗ y1 − 1 7 . 7 0 8 ∗ ay ∗ x1 ˆ 2 + 4 4 . 2 7 ∗ a z
// Volume Charge d e n s i t y from d i v e r g e n c e o f D i n pC/
c u b i c . m e t r e i s rV=
//
−106.248
20
Chapter 5
Current and Conductors
Scilab code Exa 5.1 Program to find the resistance, current and current
density
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// C a p t i o n : Program t o f i n d t h e r e s i s t a n c e , c u r r e n t
and c u r r e n t d e n s i t y
// Example5 . 1
// p a g e 123
clc ;
clear ;
D = 0.0508; // d i a m e t e r o f c o n d u c t o r i n i n c h e s
D = 0.0508*0.0254; // d i a m e t e r i n m e t r e s
r = D /2; // r a d i u s i n m e t r e s
A = %pi * r ^2; // a r e a o f t h e c o n d u c t o r i n s q u a r e m e t r e
L = 1609; // l e n g t h o f t h e c o p p e r w i r e i n m e t r e
sigma = 5.80 e07 ; // c o n d u c t i v i t y i n s i e m e n s / m e t r e
R = L /( sigma * A ) ; // r e s i s t a n c e i n ohms
I = 10; // c u r r e n t i n a m p e r e s
J = I / A ; // c u r r e n t d e n s i t y i n amps / s q u a r e . m e t r e
disp (R , ’ R r e s i s t a n c e i n ohms o f g i v e n c o p p e r w i r e R =
’)
disp (J , ’ C u r r e n t d e n s i t y i n A/ s q u a r e . m e t r e J = ’ )
// R e s u l t
// R r e s i s t a n c e i n ohms o f g i v e n c o p p e r w i r e R =
//
21.215013
// C u r r e n t d e n s i t y i n A/ s q u a r e . m e t r e J =
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21
//
7647425.6
Scilab code Exa 5.2 Program to find potential at point P, Electric Field
Intensity E, Flux density D
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// C a p t i o n : Program t o f i n d p o t e n t i a l a t p o i n t P ,
E l e c t r i c f F i e l d I n t e n s i t y E , Flux d e n s i t y D
// Example5 . 2
// p a g e 126
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
V = 100*( x ^2 - y ^2) ;
disp (V , ’ P o t e n t i a l i n V o l t s V = ’ )
Ex = diff (V , x ) ;
Ey = diff (V , y ) ;
Ez = diff (V , z ) ;
E = -( Ex * ax + Ey * ay + Ez * az ) ;
disp (E , ’ E l e c t r i c F i e l d I n t e n s i t y i n V/m E = ’ )
E = limit (E ,x ,2) ;
E = limit (E ,y , -1) ;
V = limit (V ,x ,2) ;
V = limit (V ,y , -1) ;
disp (V , ’ P o t e n t i a l a t p o i n t P i n V o l t s Vp = ’ )
disp (E , ’ E l e c t r i c F i e l d I n t e n s i t y a t p o i n t P i n V/m
Ep = ’ )
D = 8.854 e -12* E ;
disp ( D *1 e09 , ’ E l e c t r i c FLux D e n s i t y a t p o i n t P i n nC/
s q u a r e . m e t r e Dp = ’ )
// R e s u l t
// P o t e n t i a l i n V o l t s V = 1 0 0 ∗ ( xˆ2−y ˆ 2 )
// E l e c t r i c F i e l d I n t e n s i t y i n V/m E = 2 00 ∗ ay ∗y −200∗
ax ∗ x
// P o t e n t i a l a t p o i n t P i n V o l t s Vp =
300
22
// E l e c t r i c F i e l d I n t e n s i t y a t p o i n t P i n V/m Ep =
−200∗ ay −400∗ ax
31 // E l e c t r i c FLux D e n s i t y a t p o i n t P i n nC/ s q u a r e .
m e t r e Dp = 0 . 0 0 8 8 5 4 ∗ ( − 2 0 0 ∗ ay −400∗ ax )
32 // which i s e q u i v a l e n t t o Dp = −3.5416∗ ax −1.7708∗ ay
30
Scilab code Exa 5.3 Program to determine the equation of the streamline
passing through any point
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// C a p t i o n : Program t o d e t e r m i n e t h e e q u a t i o n o f t h e
s t r e a m l i n e p a s s i n g t h r o u g h any p o i n t P
// Example5 . 3
// p a g e 128
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
C1 = integ (1/ y , y ) + integ (1/ x , x ) ;
disp ( C1 , ’ C1 = ’ )
C2 = exp ( C1 ) ;
disp ( C2 , ’ The Stream l i n e E q u a t i o n C2 = ’ )
C2 = limit ( C2 ,x ,2) ;
C2 = limit ( C2 ,y , -1) ;
disp ( C2 , ’ The v a l u e o f c o n s t a n t i n t h e s t r e a m l i n e
e q u a t i o n p a s s i n g t h r o u g h t h e p o i n t P i s C2= ’ )
// R e s u l t
//C1 = l o g ( y )+l o g ( x )
// The Stream l i n e E q u a t i o n C2 = x ∗ y
// The v a l u e o f c o n s t a n t i n t h e s t r e a m l i n e e q u a t i o n
p a s s i n g t h r o u g h t h e p o i n t P i s C2 = −2
23
Chapter 6
Dielectrics and Capacitance
Scilab code Exa 6.1 Program to calculate D, E and Polarization P for
Teflon slab
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// C a p t i o n : Program t o c a l c u l a t e D, E and P o l a r i z a t i o n
P for Teflon slab
// Example6 . 1
// p a g e 142
clc ;
ax = sym ( ’ ax ’ ) ;
e0 = sym ( ’ e 0 ’ ) ;
E0 = sym ( ’ E0 ’ ) ;
Ein = sym ( ’ Ein ’ ) ;
er = 2.1; // r e l a t i v e p e r m i t t i v i t y o f t e f l o n
chi = er -1; // e l e c t r i c s u s c e p t i b i l i t y
Eout = E0 * ax ;
Dout = float ( e0 * Eout ) ;
Din = float ( er * e0 * Ein ) ;
Pin = float ( chi * e0 * Ein ) ;
disp ( Dout , ’ Dout i n c / s q u a r e . m e t r e = ’ )
disp ( Din , ’ Din i n c / s q u a r e . m e t r e = ’ )
disp ( Pin , ’ P o l a r i z a t i o n i n c o u l o m b s p e r s q u a r e m e t r e
Pin = ’ )
// R e s u l t
// Dout i n c / s q u a r e . m e t r e =
ax ∗ e 0 ∗E0
// Din i n c / s q u a r e . m e t r e =
2 . 1 ∗ e 0 ∗ Ein
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// P o l a r i z a t i o n i n c o u l o m b s p e r s q u a r e m e t r e Pin =
1 . 1 ∗ e 0 ∗ Ein
Scilab code Exa 6.2 Program to calculate E and Polarization P for Teflon
slab
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// C a p t i o n : Program t o c a l c u l a t e E and P o l a r i z a t i o n P
for Teflon slab
// Example6 . 2
// p a g e 146
clc ;
ax = sym ( ’ ax ’ ) ;
e0 = sym ( ’ e 0 ’ ) ;
E0 = sym ( ’ E0 ’ ) ;
er = 2.1; // r e l a t i v e p e r m i t t i v i t y o f t e f l o n
chi = er -1; // e l e c t r i c s u s c e p t i b i l i t y
Eout = E0 * ax ;
Ein = float ( Eout / er ) ;
Din = float ( e0 * Eout ) ;
Pin = float ( Din - e0 * Ein ) ;
disp ( Ein , ’ Ein i n V/m = ’ )
disp ( Pin , ’ P o l a r i z a t i o n i n c o u l o m b s p e r s q u a r e m e t r e
Pin = ’ )
// R e s u l t
// Ein i n V/m = 0 . 4 7 6 1 9 0 4 7 6 1 9 0 4 8 ∗ ax ∗E0
// P o l a r i z a t i o n i n c o u l o m b s p e r s q u a r e m e t r e Pin =
0 . 5 2 3 8 0 9 5 2 3 8 0 9 5 2 ∗ ax ∗ e 0 ∗E0
Scilab code Exa 6.3 Program to calculate the capacitance of a parallel
plate capacitor
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// C a p t i o n : Program t o c a l c u l a t e t h e c a p a c i t a n c e o f a
parallel plate capacitor
// Example6 . 3
// p a g e 151
clc ;
S = 10; // a r e a i n s q u a r e i n c h
S = 10*(0.0254) ^2; // a r e a i n s q u a r e m e t r e
25
7 d = 0.01; // d i s t a n c e b e t w e e n t h e p l a t e s i n i n c h
8 d = 0.01*0.0254; // d i s t a n c e b e t w e e n t h e p l a t e s i n
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metre
e0 = 8.854 e -12; // f r e e s p a c e p e r m i t t i v i t y i n F/m
er = 6; // r e l a t i v e p e r m i t t i v i t y o f mica
e = e0 * er ;
C = parallel_capacitor (e ,S , d ) ;
disp ( C *1 e09 , ’ C a p a c i t a n c e o f a p a r a l l e l p l a t e
capacitor in pico farads C =’)
// R e s u l t
// C a p a c i t a n c e o f a p a r a l l e l p l a t e c a p a c i t o r i n p i c o
farads C = 1.3493496
Refer to the following for parallelcapacitor ARC 14
26
Chapter 7
Poisson’s and Laplace’s
Equation
Scilab code Exa 7.1 Derivation of capacitance of a parallel plate capacitor
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// C a p t i o n : D e r i v a t i o n o f c a p a c i t a n c e o f a p a r a l l e l
plate capacitor
// Example7 . 1
// p a g e 177
clc ;
x = sym ( ’ x ’ ) ;
d = sym ( ’ d ’ ) ;
Vo = sym ( ’ Vo ’ ) ;
e = sym ( ’ e ’ ) ;
ax = sym ( ’ ax ’ ) ;
A = sym ( ’A ’ ) ;
B = sym ( ’B ’ ) ;
S = sym ( ’ S ’ ) ;
V = integ (A , x ) + B ;
V = limit (V ,A , Vo / d ) ;
V = limit (V ,B ,0) ;
disp (V , ’ P o t e n t i a l i n V o l t s V = ’ )
E = - diff (V , x ) * ax ;
disp (E , ’ E l e c t r i c F i e l d i n V/m E = ’ )
D = e*E;
DN = D / ax ;
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disp (D , ’ E l e c t r i c Flux D e n s i t y i n C/ s q u a r e m e t r e D = ’
)
Q = - DN * S ;
disp (Q , ’ Charge i n Coulombs Q = ’ )
C = Q / Vo ;
disp (C , ’ C a p a c i t a n c e o f p a r a l l e l p l a t e c a p a c i t o r C = ’
)
// R e s u l t
// P o t e n t i a l i n V o l t s V =
Vo∗ x / d
// E l e c t r i c F i e l d i n V/m E =
−ax ∗Vo/d
// E l e c t r i c Flux D e n s i t y i n C/ s q u a r e m e t r e D = −ax ∗ e
∗Vo/d
// Charge i n Coulombs Q =
e ∗Vo∗S /d
// C a p a c i t a n c e o f p a r a l l e l p l a t e c a p a c i t o r C = e ∗S /d
Scilab code Exa 7.2 Capacitance of a Cylindrical Capacitor
// C a p t i o n : C a p a c i t a n c e o f a C y l i n d r i c a l C a p a c i t o r
// Example7 . 2
// p a g e 179
clc ;
A = sym ( ’A ’ ) ;
B = sym ( ’B ’ ) ;
r = sym ( ’ r ’ ) ;
ar = sym ( ’ a r ’ ) ;
ruo = sym ( ’ r u o ’ ) ;
a = sym ( ’ a ’ ) ;
b = sym ( ’ b ’ ) ;
L = sym ( ’ L ’ ) ;
Vo = sym ( ’ Vo ’ ) ;
V = integ ( A /r , r ) + B ;
disp (V , ’ P o t e n t i a l V = ’ )
V = limit (V ,A , Vo / log ( a / b ) ) ;
V = limit (V ,B , - Vo * log ( b ) / log ( a / b ) ) ;
disp (V , ’ P o t e n t i a l V by s u b s t i t u t e t h e v a l u e s o f
constant A & B = ’)
19 V = Vo * log ( b / r ) / log ( b / a ) ;
20 E = - diff (V , r ) * ar ;
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disp (E , ’E = ’ ) ;
E = limit (E ,r , a ) ;
disp (E , ’E a t r =a i s = ’ )
D = e*E;
DN = D / ar ;
disp ( DN , ’DN = ’ )
S = float (2* %pi * a * L ) ; // a r e a o f c y l i n d e r
Q = DN * S
disp (Q , ’Q = ’ )
C = Q / Vo ;
disp (C , ’ C a p a c i t a n c e o f a c y l i n d r i c a l C a p a c i t o r C = ’ )
// R e s u l t
// P o t e n t i a l V = B+l o g ( r ) ∗A
// P o t e n t i a l V by s u b s t i t u t e t h e v a l u e s o f c o n s t a n t
A & B =( l o g ( r )−l o g ( b ) ) ∗Vo/ l o g ( a / b )
// E = a r ∗Vo / ( l o g ( b / a ) ∗ r )
// E a t r =a i s = a r ∗Vo / ( a ∗ l o g ( b / a ) )
// DN = e ∗Vo / ( a ∗ l o g ( b / a ) )
// Q = 6 . 2 8 3 1 8 5 3 0 6 0 2 3 8 0 5 ∗ e ∗Vo∗L/ l o g ( b/ a )
// C a p a c i t a n c e o f a c y l i n d r i c a l C a p a c i t o r C =
6 . 2 8 3 1 8 5 3 0 6 0 2 3 8 0 5 ∗ e ∗L/ l o g ( b/ a )
Scilab code Exa 7.3 Program to determine the electric field of a two infinite radial planes with an interior angle alpha
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// C a p t i o n : Program t o D e t e r m i n e t h e e l e c t r i c f i e l d
o f a two i n f i n i t e r a d i a l p l a n e s w i t h an i n t e r i o r
angle alpha
// Example 7 . 3
// p a g e 180
clc ;
phi = sym ( ’ p h i ’ ) ;
A = sym ( ’A ’ ) ;
B = sym ( ’B ’ ) ;
Vo = sym ( ’ Vo ’ ) ;
alpha = sym ( ’ a l p h a ’ ) ;
aphi = sym ( ’ a p h i ’ ) ;
r = sym ( ’ r ’ ) ;
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12 V = integ (A , phi ) + B ;
13 disp (V , ’V = ’ ) ;
14 V = limit (V ,B ,0) ;
15 V = limit (V ,A , Vo / alpha ) ;
16 disp (V , ’ P o t e n t i a l V a f t e r
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a p p l y i n g boundary
conditions =’)
E = -(1/ r ) * diff (V , phi ) * aphi ;
disp (E , ’E = ’ )
// R e s u l t
// V = B+p h i ∗A
// P o t e n t i a l V a f t e r a p p l y i n g boundary c o n d i t i o n s =
p h i ∗Vo/ a l p h a
// E =
−a p h i ∗Vo / ( a l p h a ∗ r )
Scilab code Exa 7.4 Derivation of capacitance of a spherical capacitor
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// C a p t i o n : D e r i v a t i o n o f c a p a c i t a n c e o f a s p h e r i c a l
capacitor
// Example7 . 4
// p a g e 181
clc ;
a = sym ( ’ a ’ ) ;
b = sym ( ’ b ’ ) ;
Vo = sym ( ’ Vo ’ ) ;
r = sym ( ’ r ’ ) ;
e = sym ( ’ e ’ ) ;
V = Vo *((1/ r ) -(1/ b ) ) /((1/ a ) -(1/ b ) ) ;
disp (V , ’V = ’ )
E = - diff (V , r ) * ar ;
disp (E , ’E = ’ )
D = e*E;
DN = D / ar ;
disp ( DN , ’DN = ’ )
S = float (4* %pi * r ^2) ; // a r e a o f s p h e r e
Q = DN * S ;
disp (Q , ’Q = ’ )
C = Q / Vo ;
disp (C , ’ C a p a c i t a n c e o f a s p h e r i c a l c a p a c i t o r = ’ )
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// R e s u l t
//V = ( 1 / r −1/b ) ∗Vo / ( 1 / a −1/b )
//E =
a r ∗Vo / ( ( 1 / a −1/b ) ∗ r ˆ 2 )
//DN =
e ∗Vo / ( ( 1 / a −1/b ) ∗ r ˆ 2 )
//Q =
1 2 . 5 6 6 3 7 0 6 0 4 6 9 6 4 3 ∗ e ∗Vo / ( 1 / a −1/b )
// C a p a c i t a n c e o f a s p h e r i c a l c a p a c i t o r =
1 2 . 5 6 6 3 7 0 6 0 4 6 9 6 4 3 ∗ e / ( 1 / a −1/b )
Scilab code Exa 7.5 Potential in spherical coordinates as a function of teta
V(teta)
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// C a p t i o n : P o t e n t i a l i n s p h e r i c a l c o o r d i n a t e s a s a
f u n c t i o n o f t e t a V( t e t a )
// Example7 . 5
// p a g e 182
clc ;
teta = sym ( ’ t e t a ’ ) ;
A = sym ( ’A ’ ) ;
B = sym ( ’B ’ ) ;
V = integ ( A / float ( sin ( teta ) ) , teta ) + B ;
disp (V , ’V = ’ )
// R e s u l t
//V = B+( l o g ( c o s ( t e t a ) −1)/2− l o g ( c o s ( t e t a ) +1) / 2 ) ∗A
// E q u i v a l e n t t o V = B+l o g ( t a n ( t e t a / 2 ) ) ∗A
31
Chapter 8
The Steady Magnetic Field
Scilab code Exa 8.1 Program to find the magnetic field intensity of a current carrying filament
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// C a p t i o n : Program t o f i n d t h e m a g n e t i c f i e l d
intensity of a current carrying filament
// Example8 . 1
// p a g e 217
clc ;
I = 8; // c u r r e n t i n amps
alpha1x = -90/57.3; // p h a s e a n g l e a l o n g w i t h x−a x i s
x = 0.4;
y = 0.3;
z =0;
alpha2x = atan ( x / y ) ;
aphi = sym ( ’ a p h i ’ ) ;
az = sym ( ’ a z ’ ) ;
rx = y ; // d i s t a n c e i n m e t r e s i n c y n l i n d r i c a l
c o o r d i a n t e system
H2x = float (( I /(4* %pi * rx ) ) *( sin ( alpha2x ) - sin ( alpha1x
) ) ) * - az ;
disp ( H2x , ’ H2x = ’ )
alpha1y = - atan ( y / x ) ;
alpha2y = 90/57.3;
ry = 0.4;
H2y = float (( I /(4* %pi * ry ) ) *( sin ( alpha2y ) - sin ( alpha1y
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) ) ) * - az ;
disp ( H2y , ’ H2y = ’ )
H2 = H2x + H2y ;
disp ( H2 , ’ H2 = ’ )
// R e s u l t
// H2x = − 3 . 8 1 9 7 1 8 6 1 7 0 7 9 2 8 9 ∗ a z
// H2y =
−2.546479080730701∗ az
//H2 =
−6.36619769780999∗ az
Scilab code Exa 8.2 Program to find the curlH of a square path of side
’d’
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// C a p t i o n : Program t o f i n d t h e c u r l H o f a s q u a r e
path o f s i d e ’ d ’
// Example8 . 2
// p a g e 230
clc ;
ax = sym ( ’ ax ’ ) ;
az = sym ( ’ a z ’ ) ;
ay = sym ( ’ ay ’ ) ;
z = sym ( ’ z ’ ) ;
y = sym ( ’ y ’ ) ;
d = sym ( ’ d ’ ) ;
H = 0.2* z ^2* ax ;
Hx = float ( H / ax ) ;
HdL = float (0.4* z * d ^2) ;
// c u r l H e v a l u a t e d from t h e d e f i n i t i o n o f c u r l
curlH = ( HdL /( d ^2) ) * ay ;
// c u r l H e v a l u a t e d from t h e d e t e r m i n a n t
del_cross_H = - ay *( - diff ( Hx , z ) ) + az *( - diff ( Hx , y ) ) ;
disp ( curlH , ’ c u r l H = ’ )
disp ( del_cross_H , ’ d e l c r o s s H = ’ )
// R e s u l t
// c u r l H = 0 . 4 ∗ ay ∗ z
// d e l c r o s s H = 0 . 4 ∗ ay ∗ z
Scilab code Exa 8.3 Program to verify Stokes theorem
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// C a p t i o n : Program t o v e r i f y S t o k e s t h e o r e m
// Example8 . 3
// p a g e 233
clc ;
teta = sym ( ’ t e t a ’ ) ;
phi = sym ( ’ p h i ’ ) ;
ar = sym ( ’ a r ’ ) ;
aphi = sym ( ’ a p h i ’ ) ;
az = sym ( ’ a z ’ ) ;
r = sym ( ’ r ’ ) ;
curlH = float (36* cos ( teta ) * cos ( phi ) * r ^2* sin ( teta ) ) ;
curlH_S = integ ( curlH , teta ) ;
curlH_S = float ( limit ( curlH_S ,r ,4) ) ;
curlH_S = float ( limit ( curlH_S , teta ,0.1* %pi ) ) - float (
limit ( curlH_S , teta ,0) ) ;
curlH_S = integ ( curlH_S , phi ) ;
curlH_S = float ( limit ( curlH_S , phi ,0.3* %pi ) ) - float (
limit ( curlH_S , phi ,0) ) ;
disp ( curlH_S , ’ S u r f a c e I n t e g r a l o f c u r l H i n Amps = ’ )
Hr = 6* r * sin ( phi ) ;
Hphi = 18* r * sin ( teta ) * cos ( phi ) ;
HdL = float ( limit ( Hphi * r * sin ( teta ) ,r ,4) ) ;
HdL = float ( limit ( HdL , teta ,0.1* %pi ) ) ;
HdL = float ( integ ( HdL , phi ) )
HdL = float ( limit ( HdL , phi ,0.3* %pi ) ) ;
disp ( HdL , ’ C l o s e d L i n e I n t e g r a l o f H i n Amps = ’ )
// R e s u l t
// S u r f a c e I n t e g r a l o f c u r l H i n Amps =
22.24922359441324
// C l o s e d L i n e I n t e g r a l o f H i n Amps =
22.24922359441324
34
Chapter 9
Magnetic Forces, Materials and
Inductance
Scilab code Exa 9.1 Program to find magnetic field and force produced in
a square loop
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// C a p t i o n : Program t o f i n d m a g n e t i c f i e l d and f o r c e
produced in a square loop
// Example9 . 1
// p a g e 263
clc ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
I = 15; // f i l a m e n t c u r r e n t i n amps
I1 = 2e -03; // c u r r e n t i n s q u a r e l o o p
u0 = 4* %pi *1 e -07; // f r e e s p a c e p e r m e a b i l i t y i n H/m
H = float ( I /(2* %pi * x ) ) * az ;
disp (H , ’ M a g n e t i c F i e l d I n t e n s i t y i n A/m H = ’ )
B = float ( u0 * H ) ;
disp (B , ’ M a g n e t i c Flux D e n s i t y i n T e s l a B = ’ )
Bz = B / az ;
// B c r o s s d L = ay ∗ d i f f ( Bz , x ) ;
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F1 = float ( - I1 * integ ( ay * Bz , x ) ) ;
F1 = float ( limit ( F1 ,x ,3) - limit ( F1 ,x ,1) ) ;
F2 = float ( - I1 * integ ( ax * - Bz , y ) ) ;
F2 = float ( limit ( F2 ,x ,3) ) ;
F2 = float ( limit ( F2 ,y ,2) - limit ( F2 ,y ,0) ) ;
F3 = float ( - I1 * integ ( ay * Bz , x ) ) ;
F3 = float ( limit ( F3 ,x ,1) - limit ( F3 ,x ,3) ) ;
F4 = float ( - I1 * integ ( ax * - Bz , y ) ) ;
F4 = float ( limit ( F4 ,x ,1) ) ;
F4 = float ( limit ( F4 ,y ,0) - limit ( F4 ,y ,2) ) ;
F = float (( F1 + F2 + F3 + F4 ) *1 e09 ) ;
disp (F , ’ T o t a l F o r c e a c t i n g on a s q u a r e l o o p i n nN F
= ’)
// R e s u l t
// M a g n e t i c F i e l d I n t e n s i t y i n A/m H =
2.387324146817574∗ az /x
// M a g n e t i c Flux D e n s i t y i n T e s l a B =
3 . 0 0 0 0 0 0 0 0 0 3 3 4 0 7 7 1 E−6∗ a z / x
// T o t a l F o r c e a c t i n g on a s q u a r e l o o p i n nN F =
− 8 . 0 0 0 0 0 0 0 0 0 8 9 0 8 7 3 ∗ ax
Scilab code Exa 9.2 Program to determine the differential force between
two differential current elements
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// C a p t i o n : Program t o d e t e r m i n e t h e d i f f e r e n t i a l
f o r c e b e t w e e n two d i f f e r e n t i a l c u r r e n t e l e m e n t s
// Example9 . 2
// p a g e 265
clc ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
// p o s i t i o n o f f i l a m e n t i n c a r t e s i a n c o o r d i n a t e
system
P1 = [5 ,2 ,1];
P2 = [1 ,8 ,5];
// d i s t a n c e b e t w e e n f i l a m e n t 1 and f i l a m e n t 2
R12 = norm ( P2 - P1 ) ;
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disp ( R12 , ’ R12 = ’ )
I1dL1 = [0 , -3 ,0]; // c u r r e n t c a r r y i n g f i r s t f i l a m e n t
1
I2dL2 = [0 ,0 , -4]; // c u r r e n t c a r r y i n g s e c o n d f i l a m e n t
2
u0 = 4* %pi *1 e -07; // f r e e s p a c e p e r m e a b i l i t y i n H/m
aR12 = UnitVector ( P2 - P1 ) ; // u n i t v e c t o r
disp ( aR12 , ’ aR12 = ’ )
C1 = cross_product ( I1dL1 , aR12 ) ;
C2 = cross_product ( I2dL2 , C1 ) ;
dF2 = ( u0 /(4* %pi * R12 ^2) ) * C2 ;
dF2_y = float ( dF2 (2) *1 e09 ) ;
disp ( dF2_y * ay , ’ t h e d i f f e r e n t i a l f o r c e b e t w e e n two
d i f f e r e n t i a l c u r r e n t e l e m e n t s i n nN = ’ )
// R e s u l t
// R12 = 8 . 2 4 6 2 1 1 3
// aR12 = − 0 . 4 8 5 0 7 1 3
0.7276069
0.4850713
// t h e d i f f e r e n t i a l f o r c e b e t w e e n two d i f f e r e n t i a l
c u r r e n t e l e m e n t s i n nN = 8 . 5 6 0 0 8 0 8 7 8 1 0 5 1 4 2 ∗ ay
Refer to the following Scilab code for UnitVector ARC 27 Refer to the fol-
lowing for cross product ARC 4
Scilab code Exa 9.3 Program to calculate the total torque acting on a
planar rectangular current loop
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// C a p t i o n : Program t o c a l c u l a t e t h e t o t a l t o r q u e
a c t i n g on a p l a n a r r e c t a n g u l a r c u r r e n t l o o p
// Example9 . 3
// p a g e 271
clc ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
x = 1; // l e n g t h i n m e t r e
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9 y = 2; // w i d e i n m e t r e
10 S = [0 ,0 , x * y ]; // a r e a o f
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current loop in square
metre
I = 4e -03; // c u r r e n t i n Amps
B = [0 , -0.6 ,0.8];
T = I * cross_product (S , B ) ;
Tx = float ( T (1) ) ;
disp ( Tx * ax *1 e03 , ’ T o t a l Torque a c t i n g on t h e
r e c t a n g u l a r c u r r e n t l o o p i n m i l l i N/m= ’ )
// R e s u l t
// T o t a l Torque a c t i n g on t h e r e c t a n g u l a r c u r r e n t
l o o p i n m i l l i N/m = 4 . 8 ∗ ax
Refer to the following for cross product ARC 4
Scilab code Exa 9.4 Program to find the torque and force acting on each
side of planar loop
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// C a p t i o n : Program t o f i n d t h e t o r q u e and f o r c e
a c t i n g on e a c h s i d e o f p l a n a r l o o p
// Example9 . 4
// p a g e 271
clc ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
I = 4e -03; // c u r r e n t i n Amps
B = [0 , -0.6 ,0.8]; // M a g e n t i c F i e l d a c t i n g on c u r r e n t
loop in Tesla
L1 = [1 ,0 ,0]; // l e n g t h a l o n g x−a x i s
L2 = [0 ,2 ,0]; // l e n g t h a l o n g y−a x i s
F1 = I * cross_product ( L1 , B ) ;
F3 = - F1 ;
F2 = I * cross_product ( L2 , B ) ;
F4 = - F2 ;
R1 = [0 , -1 ,0]; // d i s t a n c e from c e n t e r o f l o o p f o r
side1
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17 R2 = [0.5 ,0 ,0]; // d i s t a n c e from c e n t e r
of loop for
side2
18 R3 = [0 ,1 ,0]; // d i s t a n c e from c e n t e r
of loop for
side3
19 R4 = [ -0.5 ,0 ,0]; // d i s t a n c e from c e n t e r
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of loop for
side4
T1 = cross_product ( R1 , F1 ) ;
T2 = cross_product ( R2 , F2 ) ;
T3 = cross_product ( R3 , F3 ) ;
T4 = cross_product ( R4 , F4 ) ;
T = T1 + T2 + T3 + T4 ;
Tx = float ( T (1) *1 e03 ) ;
disp ( F1 , ’ F1 = ’ )
disp ( F2 , ’ F2 = ’ )
disp ( F3 , ’ F3 = ’ )
disp ( F4 , ’ F4 = ’ )
disp ( T1 , ’ T1 = ’ )
disp ( T2 , ’ T2 = ’ )
disp ( T3 , ’ T3 = ’ )
disp ( T4 , ’ T4 = ’ )
disp ( Tx * ax , ’ T o t a l t o r q u e a c t i n g on t h e r e c t a n g u l a r
p l a n a r l o o p i n m i l l i N/m T = ’ )
// R e s u l t
// F1 =
//
0.
// − 0 . 0 0 3 2
// − 0 . 0 0 2 4
// F2 =
//
0.0064
//
0.
//
0.
// F3 =
//
0.
//
0.0032
//
0.0024
// F4 =
//
− 0.0064
//
0.
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//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
0.
T1 =
0.0024
0.
0.
T2 =
0.
0.
0.
T3 =
0.0024
0.
0.
T4 =
0.
0.
0.
T o t a l t o r q u e a c t i n g on t h e r e c t a n g u l a r p l a n a r
l o o p i n m i l l i N/m T = 4 . 8 ∗ ax
Refer to the following for cross product ARC 4
Scilab code Exa 9.5 Program to find Magnetic Susceptibility, H , Magnetization M
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// C a p t i o n : Program t o f i n d M a g n e t i c S u s c e p t i b i l i t y ,
H, M a g e n t i z a t i o n M
// Example9 . 5
// p a g e 279
clc ;
ur = 50; // r e l a t i v e p e r m e a b i l i t y o f f e r r i t e m a t e r i a l
u0 = 4* %pi *1 e -07; // f r e e s p a c e p e r m e a b i l i t y i n H/m
chim = ur -1; // m a g n e t i c s u s c e p t i b i l i t y
B = 0.05; // m a g n e t i c f l u x d e n s i t y i n t e s l a
u = u0 * ur ;
H = B / u ; // m a g n e t i c f i e l d i n t e n s i t y i n A/m
M = chim * ceil ( H ) ; // m a g n e t i z a t i o n i n A/m
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disp ( chim , ’ chim = ’ )
disp (H , ’H = ’ )
disp (M , ’M = ’ )
// R e u s l t
// chim = 4 9 .
//H =
795.77472
//M =
39004.
Scilab code Exa 9.6 Program to find the boundary conditions on magnetic field
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// C a p t i o n : Program t o f i n d t h e boundary c o n d i t i o n s
on m a g n e t i c f i e l d
// Example9 . 6
// p a g e 283
clc ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
u1 = 4e -06; // r e l a t i v e p e r m e a b i l i t y i n medium1
u2 = 7e -06; // r e l a t i v e p e r m e a b i l i t y i n medium2
k = [80 ,0 ,0]; // i n A/m
B1 = [2 e -03 , -3 e -03 ,1 e -03]; // f i e l d i n r e g i o n 1
aN12 = [0 ,0 , -1];
//To f i n d Normal Components o f M a g n e t i c F i e l d
Bz = dot ( B1 , aN12 ) ;
BN1 = [0 ,0 , - Bz ];
BN1 = float ( BN1 ) ;
BN2 = float ( BN1 ) ;
//To Find t h e T a n g e n t i a l Components o f M a g n e t i c
Field
Bt1 = float ( B1 - BN1 ) ;
Ht1 = float ( Bt1 / u1 ) ;
v = cross_product ( aN12 , k ) ;
Ht2 = float ( Ht1 -v ’) ;
Bt2 = float ( u2 * Ht2 ) ;
disp ( BN1 (1) * ax + BN1 (2) * ay + BN1 (3) * az , ’BN1 = ’ )
disp ( BN2 (1) * ax + BN2 (2) * ay + BN2 (3) * az , ’BN2 = ’ )
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26 disp ( Bt1 (1) * ax + Bt1 (2) * ay + Bt1 (3) * az , ’ Bt1 = ’ ) ;
27 disp ( Ht1 (1) * ax + Ht1 (2) * ay + Ht1 (3) * az , ’ Ht1 = ’ ) ;
28 disp ( Ht2 (1) * ax + Ht2 (2) * ay + Ht2 (3) * az , ’ Ht2 = ’ ) ;
29 disp ( Bt2 (1) * ax + Bt2 (2) * ay + Bt2 (3) * az , ’ Bt2 = ’ ) ;
30 // T o t a l M a g n e t i c F i e l d R e g i o n 2
31 B2 = ( BN2 + Bt2 ) *1 e03 ;
32 B2 = B2 (1) * ax + B2 (2) * ay + B2 (3) * az ;
33 disp ( B2 , ’ T o t a l M a g n e t i c F i e l d R e g i o n 2 i n m i l l i
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Tesla
B2 = ’ )
// R e s u l t
// BN1 =
// 0 . 0 0 1 ∗ a z
//BN2 =
// 0 . 0 0 1 ∗ a z
// Bt1 =
// 0 . 0 0 2 ∗ ax − 0 . 0 0 3 ∗ ay
// Ht1 =
// 5 0 0 . 0 ∗ ax − 7 5 0 . 0 ∗ ay
// Ht2 =
// 5 0 0 . 0 ∗ ax − 6 7 0 . 0 ∗ ay
// Bt2 =
// 0 . 0 0 3 5 ∗ ax − 0 . 0 0 4 6 9 ∗ ay
// T o t a l M a g n e t i c F i e l d R e g i o n 2 i n m i l l i T e s l a B2 =
// 1 . 0 ∗ az −4.69∗ ay +3.5∗ ax
Refer to the following for crossproduct ARC 4 Refer to the following for dot
ARC 6
Scilab code Exa 9.7 Program to find magnetomotive force ’Vm’ and reluctance ’R’
// C a p t i o n : Program t o f i n d f i n d m a g n e t o m o t i v e f o r c e
’Vm’ and r e l u c t a n c e ’R ’
2 // Example9 . 7
3 // p a g e 288
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clc ;
u0 = 4* %pi *1 e -07 ; // f r e e s p a c e p e r m e a b i l i t y i n H/m
ur = 1; // r e l a t i v e p e r m e a b i l i t y
u = u0 * ur ;
dair = 2e -03; // a i r gap i n t o r o i d
dsteel = 0.3* %pi ;
S = 6e -04; // a r e a o f c r o s s s e c t i o n i n s q u a r e m e t r e
B = 1; // f l u x d e n s i t y 1 t e s l a
N = 500; // number o f t u r n s
Rair = dair /( u * S ) ;
disp ( Rair , ’ R e l u c t a n c e i n A . t /Wb R a i r = ’ )
phi = B * S ;
disp ( phi , ’ M a g n e t i c Flux i n weber p h i = ’ )
Vm_air = S * Rair ;
disp ( Vm_air , ’mmf r e q u i r e d f o r t h e a i r gap i n A . t
Vm air = ’ )
Hsteel = 200; // m a g n e t i c f i e l d i n t e n s i t y o f s t e e l i n
A/m
Vm_steel = Hsteel * dsteel ;
disp ( Vm_steel , ’mmf r e q u i r e d f o r t h e s t e e l i n A . t
Vm steel =’ )
disp ( Vm_steel + Vm_air , ’ T o t l a mmf r e q u i r e d f o r t o r o i d
i n A . t Vm = ’ )
I = ( Vm_steel + Vm_air ) / N ;
disp (I , ’ T o t a l c o i l c u r r e n t i n Amps I = ’ )
// R e s u l t
// R e l u c t a n c e i n A . t /Wb R a i r = 2 6 5 2 5 8 2 . 4
// M a g n e t i c Flux i n weber p h i = 0 . 0 0 0 6
//mmf r e q u i r e d f o r t h e a i r gap i n A . t Vm air =
1591.5494
//mmf r e q u i r e d f o r t h e s t e e l i n A . t V m s t e e l =
188.49556
// T o t l a mmf r e q u i r e d f o r t o r o i d i n A . t Vm =
1780.045
// T o t a l c o i l c u r r e n t i n Amps I =
3.56009
Scilab code Exa 9.8 Program to find total Magnetic Flux Density in Weber
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// C a p t i o n : Program t o f i n d t o t a l M a g n e t i c Flux
D e n s i t y i n Weber
// Example9 . 8
// p a g e 289
clc ;
I = 4; // c u r r e n t t h r o u g h t o r o i d i n Amps
r = 1e -03; // a i r gap r a d i u s i n m e t r e
Hphi = I /(2* %pi * r ) ;
u0 = 4* %pi *1 e -07 ; // f r e e s p a c e p e r m e a b i l i t y i n H/m
ur = 1; // r e l a t i v e p e r m e a b i l i t y
u = u0 * ur ;
N = 500; // number o f t u r n s
S = 6e -04; // c r o s s s e c t i o n a r e a i n s q u a r e m e t r e
Rair = 2.65 e06 ; // r e l u c t a n c e i n a i r A . t /Wb
Rsteel = 0.314 e06 ; // r e l u c t a n c e i n s t e e l A . t /Wb
R = Rair + Rsteel ; // t o t a l r e l u c t a n c e i n A . t /Wb
Vm = I *500; // t o t a l mmf i n A . t
phi = Vm / R ; // t o t a l f l u x i n w e b e r s
B = phi / S ; // f l u x d e n s i t y i n Wb/ S q u a r e m e t r e
disp (B , ’ M a g e n t i c Flux D e n s i t y i n t e s l a B = ’ )
// R e s u l t
// M a g e n t i c Flux D e n s i t y i n t e s l a B = 1 . 1 2 4 6 0 6 4
Scilab code Exa 9.9 Program to calculate self inductances and Mutual Inductances between two coaxial solenoids
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// C a p t i o n : Program t o c a l c u l a t e s e l f i n d u c t a n c e s and
Mutual I n d u c t a n c e s b e t w e e n two c o a i x a l s o l e n o i d s
// Example9 . 9
// p a g e 297
clc ;
n1 = sym ( ’ n1 ’ ) ;
n2 = sym ( ’ n2 ’ ) ;
I1 = sym ( ’ I 1 ’ ) ;
I2 = sym ( ’ I 2 ’ ) ;
az = sym ( ’ a z ’ ) ;
R1 = sym ( ’ R1 ’ ) ;
R2 = sym ( ’ R2 ’ ) ;
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u0 = sym ( ’ u0 ’ ) ;
H1 = n1 * I1 * az ;
disp ( H1 , ’ H1 = ’ ) ;
H2 = n2 * I2 * az ;
disp ( H2 , ’ H2 = ’ ) ;
S1 = float ( %pi * R1 ^2) ;
S2 = float ( %pi * R2 ^2) ;
Hz = float ( H1 / az ) ;
phi12 = float ( u0 * Hz * S1 ) ;
disp ( phi12 , ’ p h i 1 2 = ’ )
M12 = n2 * phi12 / I1 ;
disp ( M12 , ’ M12 = ’ )
//R1 = 2 e −02;
//R2 = 3 e −02;
// n1 = 5 0 ∗ 1 0 0 ; // number o f t u r n s /m
// n2 = 8 0 ∗ 1 0 0 ; // number o f t u r n s /m
// u0 = 4∗ %pi ∗1 e −07;
M12 = float ( limit ( M12 , R1 ,2 e -02) ) ;
M12 = float ( limit ( M12 , R2 ,3 e -02) ) ;
M12 = float ( limit ( M12 , n1 ,5000) ) ;
M12 = float ( limit ( M12 , n2 ,8000) ) ;
M12 = float ( limit ( M12 , u0 ,4* %pi *1 e -07) ) ;
disp ( M12 *1 e03 , ’ Mutual I n d u c t a n c e i n mH/m M12= ’ )
L1 = u0 * n1 ^2* S1 ;
L1 = float ( limit ( L1 , u0 ,4* %pi *1 e -07) ) ;
L1 = float ( limit ( L1 , n1 ,5000) ) ;
L1 = float ( limit ( L1 , R1 ,2 e -02) ) ;
disp ( L1 *1 e3 , ’ S e l f I n d u c t a n c e o f s o l e n o i d 1 i n mH/m
L1 = ’ )
L2 = u0 * n2 ^2* S2 ;
L2 = float ( limit ( L2 , u0 ,4* %pi *1 e -07) ) ;
L2 = float ( limit ( L2 , n2 ,8000) ) ;
L2 = float ( limit ( L2 , R2 ,3 e -02) ) ;
disp ( L2 *1 e3 , ’ S e l f I n d u c t a n c e o f s o l e n o i d 1 i n mH/m
L2 = ’ )
// R e s u l t
// H1 =
a z ∗ n1 ∗ I 1
// H2 =
a z ∗ n2 ∗ I 2
45
phi12 =
3 . 1 4 1 5 9 2 6 5 3 0 1 1 9 0 3 ∗ n1 ∗ u0 ∗ I 1 ∗R1ˆ2
M12 =
3 . 1 4 1 5 9 2 6 5 3 0 1 1 9 0 3 ∗ n1 ∗ n2 ∗ u0 ∗R1ˆ2
Mutual I n d u c t a n c e i n mH/m M12=
63.16546815077
S e l f I n d u c t a n c e o f s o l e n o i d 1 i n mH/m L1 =
39.47841759423
52 // S e l f I n d u c t a n c e o f s o l e n o i d 1 i n mH/m L2 =
227.39568534276
48
49
50
51
//
//
//
//
46
Chapter 11
Transmission Lines
Scilab code Exa 11.1 Program to determine the total voltage as a function of time and position in a loss less transmission line
1
2
3
4
5
6
7
8
9
10
// C a p t i o n : Program t o d e t e r m i n e t h e t o t a l v o l t a g e a s
a function
// o f t i m e and p o s i t i o n i n a l o s s l e s s t r a n s m i s s o n
line
// Example11 . 1
// p a g e 3 4 2
// syms z , t , B , w , Vo ;
VST = sym ( ’ 2∗Vo∗ c o s (B∗ z ) ’ ) ;
V_zt = VST * sym ( ’ c o s (w∗ t ) ’ ) ;
disp ( V_zt , ’V( z , t )= ’ )
// R e s u l t
//V( z , t )= 2∗Vo∗ c o s ( t ∗w) ∗ c o s ( z ∗B)
Scilab code Exa 11.2 Program to find the characteristic impedance, the
phase constant an the phase velocity
// C a p t i o n : Program t o f i n d t h e c h a r a c t e r i s t i c
impedance , t h e p h a s e c o n s t a n t an t h e p h a s e
velocity
2 // Example11 . 2
3 // p a g e 3 4 4
4 clear ;
1
47
5
6
7
8
9
10
11
12
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14
15
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17
18
19
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21
22
23
clc ;
close ;
L = 0.25 e -6; // 0 . 2 5 uH/m
C = 100 e -12; // 100 pF/m
f = 600 e06 ; // f r e q u e n c y f = 100MHz
W = 2* %pi * f ; // a n g u l a r f r e q u e n c y
Zo = sqrt ( L / C ) ;
B = W * sqrt ( L * C ) ;
Vp = W / B ;
disp ( Zo , ’ C h a r a c t e r i s t i c Impedance i n ohms Zo = ’ )
disp (B , ’ Phase c o n s t a n t i n r a d /m B= ’ )
disp ( Vp , ’ Phase v e l o c i t y i n m/ s Vp= ’ )
// R e s u l t
// C h a r a c t e r i s t i c Impedance i n ohms Zo =
//
50.
// Phase c o n s t a n t i n r a d /m B=
//
18.849556
// Phase v e l o c i t y i n m/ s Vp=
//
2 . 0 0 0D+08
Scilab code Exa 11.3 Program to find the magnitude and phase of characteristic impedance Zo
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2
3
4
5
6
7
8
9
10
11
12
13
// C a p t i o n : Program t o f i n d t h e m a g n i t u d e and p h a s e o f
characteristic
// i m p e d a n c e Zo
// Example11 . 3
// p a g e 3 4 7
Zo = sym ( ’ s q r t ( L/C) ∗(1 − s q r t ( −1) ∗R/ ( 2 ∗W∗L ) ) ’ ) ;
teta = sym ( ’ a t a n (−R/ ( 2 ∗W∗L ) ) ’ ) ;
disp ( Zo , ’ C h a r a c t e r i s t i c i m p e d a n c e Zo = ’ )
disp ( teta , ’ The p h a s e a n g l e t e t a= ’ )
// R e s u l t
// C h a r a c t e r i s t i c i m p e d a n c e Zo =
// s q r t ( L/C) ∗(1 − %i ∗R/ ( 2 ∗ L∗W) )
// The p h a s e a n g l e t e t a=
// −a t a n (R/ ( 2 ∗ L∗W) )
48
Scilab code Exa 11.4 Program to find the output power and attenuation
coefficient
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2
3
4
5
6
7
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9
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12
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15
16
17
18
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20
21
22
// C a p t i o n : Program t o f i n d t h e o u t p u t power and
attenuation c o e f f i c i e n t
// Example11 . 4
// p a g e 3 4 9
clear ;
clc ;
close ;
z = 20; // d i s t a n c e i n m e t e r s
Pz_P0_dB = -2; // f r a c t i o n o f power d r o p i n dB
Pz_P0 = 10^( Pz_P0_dB /10) ;
disp ( Pz_P0 , ’ F r a c t i o n o f i n p u t power r e a c h e s o u t p u t P
( z ) /P ( 0 )= ’ )
P0_mid_dB = -1; // f r a c t i o n o f power d r o p a t m i d p o i n t
i n dB
P0_mid = 10^( P0_mid_dB /10) ;
disp ( P0_mid , ’ F r a c t i o n o f t h e i n p u t power r e a c h e s t h e
m i d p o i n t P ( 1 0 ) /P ( 0 )= ’ )
alpha = - Pz_P0_dB /(8.69* z ) ;
disp ( alpha , ’ a t t e n u a t i o n i n Np/m a l p h a= ’ )
// R e s u l t
// F r a c t i o n o f i n p u t power r e a c h e s o u t p u t P( z ) /P ( 0 )=
//
0.6309573
// F r a c t i o n o f t h e i n p u t power r e a c h e s t h e m i d p o i n t P
( 1 0 ) /P ( 0 )=
//
0.7943282
// a t t e n u a t i o n i n Np/m a l p h a=
//
0.0115075
Scilab code Exa 11.5 Program to find the power dissipated in the lossless
transmission line
// C a p t i o n : Program t o f i n d t h e power d i s s i p a t e d i n
the l o s s l e s s
2 // t r a n s m i s s i o n l i n e
3 // Example11 . 5
1
49
// p a g e 3 5 2
clc ;
close ;
ZL = 50 - %i *75; // l o a d i m p e d a n c e i n ohms
Zo = 50; // c h a r a c t e r i s t i c i m p e d a n c e i n ohms
R = reflection_coeff ( ZL , Zo ) ;
Pi = 100 e -03; // i n p u t power i n m i l l i w a t t s
Pt = (1 - abs ( R ) ^2) * Pi ; // power d i s s i p a t e d by t h e l o a d
disp (R , ’ R e f l e c t i o n c o e f f i c i e n t R = ’ )
disp ( Pt *1000 , ’ power d i s s i p a t e d by t h e l o a d i n m i l l i
w a t s s Pt= ’ )
14 // R e s u l t
15 // R e f l e c t i o n c o e f f i c i e n t R =
0.36 − 0.48 i
16 // power d i s s i p a t e d by t h e l o a d i n m i l l i w a t s s Pt =
64.
4
5
6
7
8
9
10
11
12
13
Refer to the following for reflection coeff ARC 23
Scilab code Exa 11.6 Program to find the total loss in lossy lines
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2
3
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5
6
7
8
9
10
11
12
13
14
15
// C a p t i o n : Program t o f i n d t h e t o t a l l o s s i n l o s s y
lines
// Example11 . 6
// page352 −353
clc ;
close ;
L1 = 0.2*10; // l o s s ( dB ) i n f i r s t l i n e o f l e n g t h =10 m
L2 = 0.1*15; // l o s s ( dB ) i n s e c o n d l i n e o f l e n g t h =15m
R = 0.3; // r e f l e c t i o n c o e f f i c i e n t
Pi = 100 e -03; // i n p u t power i n m i l l i w a t t s
Lj = 10* log10 (1/(1 - abs ( R ) ^2) ) ;
Lt = L1 + L2 + Lj ;
Pout = Pi *(10^( - Lt /10) ) ;
disp ( Lt , ’ The t o t a l l o s s o f t h e l i n k i n dB i s Lt= ’ )
disp ( Pout *1000 , ’ The o u t p u t power w i l l be i n m i l l i
w a t s s Pout = ’ )
// R e s u l t
50
16
17
18
19
// The t o t a l l o s s o f t h e l i n k i n dB i s Lt=
//
3.9095861
// The o u t p u t power w i l l be i n m i l l i w a t s s Pout =
//
40.648207
Scilab code Exa 11.7 Program to find the load impedance of a slotted line
1
2
3
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5
6
7
8
9
10
11
12
13
// C a p t i o n : Program t o f i n d t h e l o a d i m p e d a n c e o f a
slotted line
// Example11 . 7
// p a g e 3 5 7
clear ;
clc ;
close ;
S = 5; // s t a n d i n g wave r a t i o
T = (1 - S ) /(1+ S ) ; // r e f l e c t i o n c o e f f i c i e n t
Zo = 50; // c h a r a c t e r i s t i c i m p e d a n c e
ZL = Zo *(1+ T ) /(1 - T ) ;
disp ( ZL , ’ Load i m p e d a n c e o f a s l o t t e d l i n e i n ohms ZL
=’)
// R e s u l t
// Load i m p e d a n c e o f a s l o t t e d l i n e i n ohms ZL = 1 0 .
Scilab code Exa 11.8 Program to find the input impedance and power
delivered to the load
1
2
3
4
5
6
7
8
9
10
11
// C a p t i o n : Program t o f i n d t h e i n p u t i m p e d a n c e and
power d e l i v e r e d t o
// t h e l o a d
// Example11 . 8
// p a g e 3 6 3
clc ;
close ;
ZR1 = 300; // i n p u t i m p e d a n c e o f f i r s t r e c e i v e r
ZR2 = 300; // i n p u t i m p e d a n c e o f s e c o n d r e c e i v e r
Zo = ZR1 ; // c h a r a c t e r i s t i c i m p e d a n c e = 300 ohm
Zc = - %i *300; // c a p a c i t i v e i m p e d a n c e
L = 80 e -02; // l e n g t h = 80 cm
51
12
13
14
15
16
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18
19
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21
22
23
24
25
26
27
28
29
30
31
32
Lambda = 1; // w a v e l e n g t h = 1m
Vth = 60; // v o l t a g e 300 v o l t s
Zth = Zo ;
ZL1 = parallel ( ZR1 , ZR2 ) ;
ZL = parallel ( ZL1 , Zc ) ; // n e t l o a d impedane
T = reflection_coeff ( ZL , ZR2 ) ; // r e f l e c t i o n
coefficient
[R , teta1 ] = polar ( T ) ; // r e f l e c t i o n c o e f f i c i e n t i n
p o l a r form
teta1 = real ( teta1 ) *57.3; // t e t a v a l u e i n d e g r e e s
S = VSWR ( R ) ; // v o l t a g e s t a n d i n g wave r a t i o
EL = electrical_length (L , Lambda ) ;
EL = EL /57.3; // e l e c t r i c a l l e n g t h i n d e g r e e s
Zin = Zo *( ZL * cos ( EL ) + %i * Zo * sin ( EL ) ) /( Zo * cos ( EL ) + %i *
ZL * sin ( EL ) ) ;
disp ( Zin , ’ I n p u t Impedance i n ohms Z i n = ’ )
Is = Vth /( Zth + Zin ) ; // s o u r c e c u r r e n t i n amps
[ Is , teta2 ] = polar ( Is ) ; // s o u r c e c u r r e n t i n p o l a r
form
Pin = (1/2) *( Is ^2) * real ( Zin ) ;
PL = Pin ; // f o r l o s s l e s s l i n e
disp ( Pin , ’ Power d e l i v e r e d t o a l o s s l e s s l i n e i n
w a t s s PL = ’ )
// R e s u l t
// I n p u t Impedance i n ohms Z i n =
755.49551 −
138.46477 i
// Power d e l i v e r e d t o a l o s s l e s s l i n e i n w a t s s PL =
1.2
Refer to the following for electrical length ARC 7
Refer to the following for parallel ARC 15
Refer to the following for reflection coeff ARC 23
52
Refer to the scilab code for VSWR ??ARC 28)
Scilab code Exa 11.9 Program to find the input impedance for a line terminated with pure capacitive impedance
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2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
// C a p t i o n : Program t o f i n d t h e i n p u t i m p e d a n c e f o r a
l i n e t e r m i n a t e d with pure c a p a c i t i v e impedance
// Example11 . 9
// p a g e 3 6 3
clc ;
close ;
ZL = - %i *300; // l o a d impdance i s p u r e l y c a p a c i t i v e
impedance
ZR = 300;
T = reflection_coeff ( ZL , ZR ) ; // r e f l e c t i o n c o e f f i c i e n t
i n r e c t a n d u l a r form
[R , teta ] = polar ( T ) ; // r e f l e c t i o n c o e f f i c i e n t i n
p o l a r form
S = VSWR ( R )
if ( S == %inf )
Zo = ZR ;
end
Zin = Zo *( ZL * cos ( EL ) + %i * Zo * sin ( EL ) ) /( Zo * cos ( EL ) + %i * ZL
* sin ( EL ) ) ;
disp (T , ’ R e f l e c t i o n c o e f f i c i e n t i n r e c t a n g u l a r form ’ )
disp (S , ’ V o l t a g e S t a n d i n g Wave R a t i o S= ’ )
disp ( Zin , ’ I n p u t i m p e d a n c e i n ohms Z i n = ’ )
// R e s u l t
// R e f l e c t i o n c o e f f i c i e n t i n r e c t a n g u l a r form
//
− i
// V o l t a g e S t a n d i n g Wave R a t i o S=
//
Inf
// I n p u t i m p e d a n c e i n ohms Z i n =
//
588.78315 i
Refer to the scilab code for VSWR ??ARC 28)
53
Refer to the following for reflection coeff ARC 23
Scilab code Exa 11.10 Program to find the input impedance for a line
terminated with impedance (with inductive reactance)
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2
3
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5
6
7
8
9
10
11
12
13
14
15
16
17
18
// C a p t i o n : Program t o f i n d t h e i n p u t i m p e d a n c e f o r a
l i n e t e r m i n a t e d with impedance ( with i n d u c t i v e
reactance )
// Example11 . 1 0
// p a g e 3 6 9
clc ;
close ;
ZL = 25+ %i *50; // l o a d impdance i n ohms
Zo = 50; // c h a r a c t e r i s t i c i m p e d a n c e i n ohms
T = reflection_coeff ( ZL , Zo ) ; // r e f l e c t i o n c o e f f i c i e n t
i n r e c t a n d u l a r form
[R , teta ] = polar ( T ) ; // r e f l e c t i o n c o e f f i c i e n t i n
p o l a r form
L = 60 e -02; // l e n g t h 60 cm
Lambda = 2; // w a v e l e n g t h = 2m
EL = electrical_length (L , Lambda ) ;
EL = EL /57.3; // e l e c t r i c a l l e n g t h i n r a d i a n s
Zin =(1+ T * exp ( - %i *2* EL ) ) /(1 - T * exp ( - %i *2* EL ) ) ;
disp ( Zin , ’ I n p u t i m p e d a n c e i n ohms Z i n = ’ )
// R e s u l t
// I n p u t i m p e d a n c e i n ohms Z i n =
//
0.2756473 − 0.4055013 i
Refer to the following for electrical length ARC 7 Refer to the following for
reflection coeff ARC 23
Scilab code Exa 11.11 Program to find the voltage at the load resistor
and the current in the battery
54
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
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21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
// C a p t i o n :
// Example11 . 1 1
// p a g e 3 8 1
clc ;
close ;
Rg = 50; // s e r i e s r e s i s t a n c e w i t h b a t t e r y i n ohms
Zo = Rg ; // c h a r a c t e r i s t i c i m p e d a n c e
RL = 25; // l o a d r e s i s t a n c e
Vo = 10; // b a t t e r y v o l t a g e i n v o l t s
V1_S = ( Rg /( Zo + Rg ) ) * Vo ;
T = reflection_coeff ( RL , Zo ) ;
V1_R = T * V1_S ;
I1_S = V1_S / Zo ;
I1_R = - V1_R / Zo ;
IB = Vo /( Zo + RL ) ;
VL = Vo *( RL /( Rg + RL ) ) ;
disp ( V1_S , ’ V o l t a g e a t s o u r c e i n v o l t s V 1 p l u s = ’ )
disp ( V1_R , ’ V o l t a g e r e t u r n s t o b a t t e r y i n v o l t s
V1minus= ’ )
disp ( I1_S , ’ C u r r e n t a t b a t t e r y i n amps I 1 p l u s= ’ )
disp ( I1_R , ’ C u r r e n t a t b a t t e r y i n amps I 1 m i n u s= ’ )
disp ( IB , ’ S t e a d y s t a t e c u r r e n t t h r o u g h b a t t e r y i n
amps IB= ’ )
disp ( VL , ’ S t e a d y s t a t e l o a d v o l t a g e i n v o l t s VL= ’ )
// R e s u l t
// V o l t a g e a t s o u r c e i n v o l t s V 1 p l u s =
//
5.
// V o l t a g e r e t u r n s t o b a t t e r y i n v o l t s V1minus=
// − 1 . 6 6 6 6 6 6 7
// C u r r e n t a t b a t t e r y i n amps I 1 p l u s=
//
0.1
// C u r r e n t a t b a t t e r y i n amps I 1 m i n u s=
//
0.0333333
// S t e a d y s t a t e c u r r e n t t h r o u g h b a t t e r y i n amps IB=
//
0.1333333
// S t e a d y s t a t e l o a d v o l t a g e i n v o l t s VL=
//
3.3333333
55
Refer to the following for reflection coeff ARC 23
Scilab code Exa 11.12 Program to plot the voltage and current through
a resistor
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14
15
16
17
18
19
// C a p t i o n : Program t o p l o t t h e v o l t a g e and c u r r e n t
through a r e s i s t o r
// Example11 . 1 2
// p a g e 386
clear ;
close ;
clc ;
t1 = 0:0.1:2;
t2 = 2:0.1:4;
t3 = 4:0.1:6;
t4 = 6:0.1:8;
VR =[40* ones (1 , length ( t1 ) ) , -20* ones (1 , length ( t2 ) ) ,10*
ones (1 , length ( t3 ) ) , -5* ones (1 , length ( t4 ) ) ];
IR =[ -1.2* ones (1 , length ( t1 ) ) ,0.6* ones (1 , length ( t2 ) )
, -0.3* ones (1 , length ( t3 ) ) ,0.15* ones (1 , length ( t4 ) )
];
subplot (2 ,1 ,1)
a = gca () ;
a . x_location = ” o r i g i n ” ;
a . y_location = ” o r i g i n ” ;
a . data_bounds = [0 , -100;10 ,100];
plot2d ([ t1 , t2 , t3 , t4 ] , VR ,5)
xlabel ( ’
20
21
22
23
24
25
t ’)
ylabel ( ’
VR ’ )
title ( ’ R e s i s t o r V o l t a g e a s a f u n c t i o n o f t i m e ’ )
subplot (2 ,1 ,2)
a = gca () ;
a . x_location = ” o r i g i n ” ;
a . y_location = ” o r i g i n ” ;
1
2
3
4
5
6
7
8
9
10
11
12
56
Figure 11.1: To be provided
26 a . data_bounds = [0 , -1.4;10 ,1.4];
27 plot2d ([ t1 , t2 , t3 , t4 ] , IR ,5)
28 xlabel ( ’
29
30
t ’)
ylabel ( ’
IR ’ )
title ( ’ C u r r e n t t h r o u g h R e s i s t o r a s a f u n c t i o n o f
time ’ )
57
Chapter 12
The Uniform Plane Wave
Scilab code Exa 12.1 Program to determine the phasor of forward propagating field
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2
3
4
5
6
7
8
9
10
11
12
// C a p t i o n : Program t o d e t e r m i n e t h e p h a s o r o f f o r w a r d
propagating f i e l d
// Example12 . 1
// p a g e 4 0 0
clc ;
close ;
Eyzt = sym ( ’ 1 00 ∗ exp ( %i ∗ 1 0 ˆ 8 ∗ t−%i ∗ 0 . 5 ∗ z +30) ’ ) ;
Eysz = sym ( ’ 1 00 ∗ exp ( %i ∗ 1 0 ˆ 8 ∗ t−%i ∗ 0 . 5 ∗ z +30) ∗ exp (−%i
∗10ˆ8∗ t ) ’ );
disp ( Eyzt )
disp ( Eysz , ’ Forward P r o p a g a t i n g F i e l d i n p h a s o r form
=’)
// R e s u l t
// 100 ∗ exp ( −0.5∗ %i ∗ z +100000000∗ %i ∗ t +30)
// Forward P r o p a g a t i n g F i e l d i n p h a s o r form =100∗ exp
( 3 0 − 0 . 5 ∗ %i ∗ z )
Scilab code Exa 12.2 Program to determine the instantaneous field of a
plane wave
1
// C a p t i o n : Program t o d e t e r m i n e t h e i n s t a n t e o u s f i e l d
o f a wave
58
// Example12 . 2
// page400 −401
clc ;
t = sym ( ’ t ’ ) ;
z = sym ( ’ z ’ ) ;
Ezt1 = sym ( ’ 1 00 ∗ c o s ( − 0 . 2 1 ∗ z +2∗%pi ∗1 e 0 7 ∗ t ) ’ ) ;
Ezt2 = sym ( ’ 20∗ c o s ( − 0 . 2 1 ∗ z +30+2∗%pi ∗1 e 0 7 ∗ t ) ’ ) ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
Ezt = Ezt1 * ax + Ezt2 * ay ;
disp ( Ezt , ’ The r e a l i n s t a n t a n e o u s f i e l d Ezt = ’ )
// R e s u l t
// The r e a l i n s t a n t a n e o u s f i e l d Ezt =
// 100 ∗ ax ∗ c o s ( 0 . 2 1 ∗ z −2.0E+7∗%pi ∗ t ) +20∗ ay ∗ c o s ( 0 . 2 1 ∗ z
−2.0E+7∗%pi ∗ t −30)
16 //
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Scilab code Exa 12.3 Program to find the Phase constant, Phase velocity,
Electric Field Intensity and Intrinsic ratio
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
// C a p t i o n : Program t o f i n d t h e Phase c o n s t a n t , Phase
v e l o c i t y , E l e c t r i c F i e l d I n t e n s i t y and I n t r i n s c i
ratio .
// Example12 . 3
// p a g e 4 0 8
clc ;
syms t ;
z = %z ;
[ uo , eo ] = muo_epsilon () ;
ur = 1;
f = 10^6;
er1 = 81;
er2 =0;
etta0 = 377;
Ex0 = 0.1;
beta1 = phase_constant_dielectric ( uo , eo ,f , er1 , er2 , ur
);
disp ( beta1 , ’ p h a s e c o n s t a n t i n r a d /m b e t a= ’ )
59
16 Lambda = 2* %pi / beta1 ;
17 Vp = phase_velocity (f , beta1 ) ;
18 disp ( Vp , ’ Phase v e l o c i t y i n m/ s e c ’ )
19 etta =
intrinsic_dielectric ( etta0 , er1 , er2 )
20 disp ( etta , ’ I n t r i n s i c i m p e d a n c e i n ohms = ’ )
21 Ex = 0.1* cos (2* %pi * f *t - beta1 * z )
22 disp ( Ex , ’ E l e c t r i c f i e l d i n V/m Ex= ’ )
23 Hy = Ex / etta ;
24 disp ( Hy , ’ M a g n e t i c F i e l d i n A/m Hy= ’ )
25 // R e s u l t
26 // p h a s e c o n s t a n t i n r a d /m b e t a=
0.1886241
27 // Phase v e l o c i t y i n m/ s e c =
33310626.
28 // I n t r i n s i c i m p e d a n c e i n ohms =
41.888889
29 // E l e c t r i c f i e l d i n V/m Ex=
cos (58342∗ z
/309303 −81681409∗ t / 1 3 ) /10
30 // e q u i v a l e n t t o Ex = 0 . 1 ∗ c o s ( 0 . 1 9 ∗ z − 6 2 8 3 1 8 5 . 3 ∗ t )
31 // M a g n e t i c F i e l d i n A/m Hy = 9∗ c o s ( 5 8 3 4 2 ∗ z
/309303 −81681409∗ t / 1 3 ) / 3 7 7 0
32 // e q u i v a l e n t t o Hy = 0 . 0 0 2 3 8 7 3 ∗ c o s ( 0 . 1 9 ∗ z − 6 2 8 3 1 8 5 . 3 ∗
t)
Refer to the following for intrinsic dielectric ARC 11
Refer to the following for intrinsi dielectric ARC 11 Refer to the following
for mu epsilon ARC 13
Refer to the following for phase constant dielectric ARC 17
Refer to the following for phase velocity ARC 19
Scilab code Exa 12.4 Program to find the penetration depth and intrinsic
impedance
60
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
// C a p t i o n : Program t o f i n d t h e p e n e t r a t i o n d e p t h and
i n t r i n s i c impedance
// Example12 . 4
// p a g e 4 0 9
clc ;
f = 2.5 e09 ; // h i g h m i c r o w a v e f r e q u e n c y = 2 . 5 GHz
er1 = 78; // r e l a t i v e p e r m i t t i v i t y
er2 = 7;
C = 3 e08 ; // f r e e s p a c e v e l o c i t y i n m/ s e c
[ uo , eo ] = muo_epsilon () ; // f r e e s p a c e p e r m i t t i v i t y
and p e r m e a b i l i t y
ur = 1; // r e l a t i v e p e r m e a b i l i t y
etta0 = 377; // f r e e s p a c e i n t r i n s i c i m e d a n c e i n ohms
alpha = attenuation_constant_dielectric ( uo , eo ,f , er1 ,
er2 , ur ) ;
etta = intrinsic_dielectric ( etta0 , er1 , er2 ) ;
disp ( alpha , ’ a t t e n u a t i o n c o n s t a n t i n Np/m a l p h a= ’ )
disp ( etta , ’ I n t r i n s i c c o n s t a n t i n ohms e t t a= ’ )
// R e s u l t
// a t t e n u a t i o n c o n s t a n t i n Np/m a l p h a=
20.727602
// I n t r i n s i c c o n s t a n t i n ohms e t t a=
42.558673
+ 1.9058543 i
Refer to the following for attenuation constant gooddie ARC 1
Refer to the following for intrinsic dielectric ARC 11
Refer to the following for mu epsilon ARC 13
Scilab code Exa 12.5 Program to find the attenuation constant, propagation constant and intrinsic impedance
// C a p t i o n : Program t o f i n d t h e a t t e n u a t i o n c o n s t a n t ,
p r o p a g a t i o n c o n s t a n t and i n t r i n s i c i m p e d a n c e
2 // Example12 . 5
1
61
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
// p a g e 4 1 2
clc ;
f = 2.5 e09 ; // h i g h m i c r o w a v e f r e q u e n c y = 2 . 5 GHz
er1 = 78; // r e l a t i v e p e r m i t t i v i t y
er2 = 7;
C = 3 e08 ; // f r e e s p a c e v e l o c i t y i n m/ s e c
[ uo , eo ] = muo_epsilon () ; // f r e e s p a c e p e r m i t t i v i t y
and p e r m e a b i l i t y
ur = 1; // r e l a t i v e p e r m e a b i l i t y
etta0 = 377; // f r e e s p a c e i n t r i n s i c i m e d a n c e i n ohms
alpha = attenuation_constant_gooddie ( uo , eo ,f , er1 , er2
, ur ) ;
etta = intrinsic_good_dielectric ( etta0 , er1 , er2 ) ;
beta1 = phase_constant_gooddie ( uo , eo ,f , er1 , er2 , ur ) ;
disp ( alpha , ’ a t t e n u a t i o n c o n s t a n t p e r cm a l p h a= ’ )
disp ( beta1 , ’ p h a s e c o n s t a n t i n r a d /m b e t a 1 = ’ )
disp ( etta , ’ I n t r i n s i c c o n s t a n t i n ohms e t t a= ’ )
// R e s u l t
// a t t e n u a t i o n c o n s t a n t p e r cm a l p h a=
//
20.748417
// p h a s e c o n s t a n t i n r a d /m b e t a 1 =
//
462.3933
// I n t r i n s i c c o n s t a n t i n ohms e t t a=
//
42.558673 + 1.9058543 i
Refer to the following for attenuation constant gooddie ARC 1
Refer to the following for intrinsic good dielectric ARC 12
Refer to the following for mu epsilon ARC 13 Refer to the following for
phase constant gooddie ARC 18
62
Scilab code Exa 12.6 Program to find skin depth, loss tangent and phase
velocity
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
// C a p t i o n : Program t o f i n d s k i n depth , l o s s t a n g e n t
and p h a s e v e l o c i t y
// Example12 . 6
// p a g e 4 1 9
clc ;
f1 = 1 e06 ; // f r e q u e n c y i n Hz
// e r 1 = 8 1 ;
ur = 1;
[ uo , eo ] = muo_epsilon () ; // f r e e s p a c e p e r m i t t i v i t y
and p e r m e a b i l i t y
sigma = 4; // c o n d u c t i v i t y o f a c o n d u c t o r i n s /m
[ del ] = SkinDepth ( f1 , uo , ur , sigma ) ;
pi = 22/7;
Lambda = 2* pi * del ;
Vp = 2* pi * f1 * del ;
disp ( del *100 , ’ s k i n d e p t h i n cm d e l t a = ’ )
disp ( Lambda , ’ Wavelength i n m e t r e Lambda = ’ )
disp ( Vp , ’ Phase v e l o c i t y i n m/ s e c Vp = ’ )
// R e s u l t
// s k i n d e p t h i n cm d e l t a =
//
25.17737
// Wavelength i n m e t r e Lambda =
//
1.5825775
// Phase v e l o c i t y i n m/ s e c Vp =
//
1582577.5
Refer to the following for mu epsilon ARC 13 Refer to the following Scilab
code for SkinDepth ARC 24
Scilab code Exa 12.7 Program to find the electric field of linearly polarized wave
63
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
//
clc ;
s = sym ( ’ s ’ ) ;
B = sym ( ’B ’ ) ;
Eo = sym ( ’ Eo ’ ) ;
z = sym ( ’ z ’ ) ;
ax = sym ( ’ ax ’ ) ;
EsL = Eo *( ax + %i * ay ) * exp ( %i * s ) * exp ( - %i * B * z ) ;
EsR = Eo *( ax - %i * ay ) * exp ( - %i * B * z ) ;
Est = Eo * exp ( %i * s /2) *(2* cos ( s /2) * ax - %i *2* %i * sin ( s /2)
* ay ) * exp ( - %i * B * z ) ;
disp ( EsL , ’ L e f t c i r c u l a r l y p o l a r i z e d f i e l d EsL= ’ )
disp ( EsR , ’ R i g h t c i r c u l a r l y p o l a r i z e d f i e l d EsR= ’ )
disp ( Est , ’ T o t a l E l e c e t r i c f i e l d o f a l i n e a r l y
p o l a r i z e d wave EsT = ’ )
// R e s u l t
// L e f t c i r c u l a r l y p o l a r i z e d f i e l d EsL=
// ( %i ∗ ay+ax ) ∗Eo∗ exp ( %i ∗ s−%i ∗ z ∗B)
// R i g h t c i r c u l a r l y p o l a r i z e d f i e l d EsR=
// ( ax−%i ∗ ay ) ∗Eo∗%eˆ−(%i ∗ z ∗B)
// T o t a l E l e c e t r i c f i e l d o f a l i n e a r l y p o l a r i z e d wave
EsT =
// Eo ∗ ( 2 ∗ ay ∗ s i n ( s / 2 ) +2∗ ax ∗ c o s ( s / 2 ) ) ∗ exp ( %i ∗ s /2−%i ∗ z ∗
B)
64
Chapter 13
Plane Wave Reflection and
Dispersion
Scilab code Exa 13.1 Program to find the electric field of incident, reflected and transmitted waves
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
// C a p t i o n : Program t o f i n i d t h e e l e c t r i c f i e l d o f
i n c i d e n t , r e f l e c t e d and t r a n s m i t t e d waves
// Example13 . 1
// p a g e 4 3 9
etta1 = 100;
etta2 = 300; // i n t r i n s i c i m p e d a n c e i n ohms
T = reflection_coefficient ( etta1 , etta2 ) ;
Ex10_i = 100; // i n c i d e n t e l e c t r i c f i e l d i n v /m
Ex10_r = T * Ex10_i ; // r e f l e c t e d e l e c t r i c f i e l d i n v /m
Hy10_i = Ex10_i / etta1 ; // i n c i d e n t m a g n e t i c f i e l d A/m
Hy10_r = - Ex10_r / etta1 ; // r e f l e c t e d m a g n e t i c f i e l d A
/m
Si = (1/2) * Ex10_i * Hy10_i ; // a v e r a g e i n c i d e n t power
d e n s i t y i n W/ s q u a r e m e t r e
Sr = -(1/2) * Ex10_r * Hy10_r ; // a v e r a g e r e f l e c t e d power
d e n s t i y i n W/ s q u a r e m e t r e
tuo = 1+ T ; // t r a n s m i s s i o n c o e f f i c i e n t
Ex20_t = tuo * Ex10_i ; // t r a n s m i t t e d e l e c t r i c f i e l d v /
m
Hy20_t = Ex20_t / etta2 ; // t r a n s m i t t e d m a g n e t i c f i e l d
65
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
A/m
St = (1/2) * Ex20_t * Hy20_t ; // a v e r a g e power d e n s i t y
transmitted
disp (T , ’ r e f l e c t i o n c o e f f i c i e n t t = ’ ) ;
disp ( Ex10_i , ’ i n c i d e n t e l e c t r i c f i e l d i n v /m E x 1 0 i =
’)
disp ( Ex10_r , ’ r e f l e c t e d e l e c t r i c f i e l d i n v /m E x 1 0 r
=’)
disp ( Hy10_i , ’ i n c i d e n t m a g n e t i c f i e l d A/m H y 1 0 i = ’ )
disp ( Hy10_r , ’ r e f l e c t e d m a g n e t i c f i e l d A/m H y 1 0 r= ’ )
disp ( Si , ’ a v e r a g e i n c i d e n t power d e n s i t y i n W/ s q u a r e
m e t r e S i= ’ )
disp ( Sr , ’ a v e r a g e r e f l e c t e d power d e n s t i y i n W/ s q u a r e
m e t r e S r= ’ )
disp ( St , ’ a v e r a g e power d e n s i t y t r a n s m i t t e d i n W/
s q u a r e m e t r e S t= ’ )
// R e s u l t
// r e f l e c t i o n c o e f f i c i e n t t =
0.5
100.
// i n c i d e n t e l e c t r i c f i e l d i n v /m E x 1 0 i =
// r e f l e c t e d e l e c t r i c f i e l d i n v /m E x 1 0 r =
50.
1.
// i n c i d e n t m a g n e t i c f i e l d A/m H y 1 0 i =
− 0.5
// r e f l e c t e d m a g n e t i c f i e l d A/m H y 1 0 r=
// a v e r a g e i n c i d e n t power d e n s i t y i n W/ s q u a r e m e t r e
S i=
50.
// a v e r a g e r e f l e c t e d power d e n s t i y i n W/ s q u a r e m e t r e
S r= 1 2 . 5
// a v e r a g e power d e n s i t y t r a n s m i t t e d i n W/ s q u a r e
m e t r e S t=
37.5
Refer to the following for reflection coefficient ARC 22 Refer to the following
Scilab code for reflection coeffcient ARC 28
Scilab code Exa 13.2 Program to find the maxima and minima electric
field
66
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
// C a p t i o n : Program t o f i n d t h e maxima and minma
electric field
// Example13 . 2
// p a g e 4 4 3
clc ;
er1 = 4;
ur1 = 1;
er2 = 9;
ur2 = 1;
[ uo , eo ] = muo_epsilon () ; // f r e e s p a c e p e r m i t t i v i t y
and p e r m e a b i l i t y
u1 = uo * ur1 ; // p e r m e a b i l i t y o f medium 1
u2 = uo * ur2 ; // p e r m e a b i l i t y o f medium 2
e1 = eo * er1 ; // p e r m i t t i v i t y o f medium 1
e2 = eo * er2 ; // p e r m i t t i v i t y o f medium 2
etta1 = sqrt ( u1 / e1 ) ;
etta2 = sqrt ( u2 / e2 ) ;
T = reflection_coefficient ( etta1 , etta2 )
Exs1_i = 100; // i n c i d e n t e l e c t r i c f i e l d i n v /m
Exs1_r = -20; // r e f l e c t e d e l e c t r i c f i e l d i n v /m
Ex1T_max = (1+ abs ( T ) ) * Exs1_i ; //maximum t r a n s m i t t e d
e l e c t r i c f i e l d i n v /m
Ex1T_min = (1 - abs ( T ) ) * Exs1_i ; // minimum t r a n s m i t t e d
e l e c t r i c f i e l d i n v /m
S = VSWR ( T ) ; // v o l t a g e s t a n d i n g wave r a t i o
disp ( Ex1T_max , ’ maximum t r a n s m i t t e d e l e c t r i c f i e l d i n
v /m = ’ )
disp ( Ex1T_min , ’ minimum t r a n s m i t t e d e l e c t r i c f i e l d i n
v /m = ’ )
disp (S , ’ v o l t a g e s t a n d i n g wave r a t i o S= ’ )
// R e s u l t
//maximum t r a n s m i t t e d e l e c t r i c f i e l d i n v /m =
//
120.
// minimum t r a n s m i t t e d e l e c t r i c f i e l d i n v /m =
//
80.
// v o l t a g e s t a n d i n g wave r a t i o S=
//
1.5
67
Refer to the following for mu epsilon ARC 13 Refer to the following for
reflection coefficient ARC 22
Refer to the scilab code for VSWR ARC 28
Scilab code Exa 13.3 Program to determine the intrinsic impedance of
the unknown material
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
// C a p t i o n : Program t o d e t e r m i n e t h e i n t r i n s i c
i m p e d a n c e o f t h e unkonwn m a t e r i a l
// Eample13 . 3
// p a g e 4 4 1
clc ;
maxima_spacing = 1.5; // Lambda /2 i n m e t r e s
Lambda = 2* maxima_spacing ; // w a v e l e n g t h i n m e t r e s
C = 3 e08 ; // f r e e s p a c e v e l o c i t y i n m/ s e c
f = C / Lambda ; // f r e q u e n c y i n Hz
S = 5; // v o l t a g e s t a n d i n g wave r a t i o
T = (1 - S ) /(1+ S ) ; // r e f l e c t i o n c o e f f i c i e n t
etta0 = 377; // i n t r i n s i c i m p e d a n c e i n ohms
ettau = etta0 / S ; // i n t r i n s i c i m p e d a n c e o f unkonwn
m a t e r i a l i n ohms
disp (T , ’ r e f l e c t i o n c o e f f i c i e n t T= ’ )
disp ( ettau , ’ i n t r i n s i c i m p e d a n c e i n ohms = ’ )
// R e s u l t
// r e f l e c t i o n c o e f f i c i e n t T =
− 0.6666667
// i n t r i n s i c i m p e d a n c e i n ohms =
75.4
Scilab code Exa 13.4 Program to determine the required range of glass
thickness for Fabry-perot interferometer
1
// C a p t i o n : Program t o d e t e r m i n e t h e r e q u i r e d r a n g e o f
g l a s s t h i c k n e s s f o r Fabry−p e r o t i n t e r f e r o m e t e r
68
2 // Example13 . 4
3 // p a g e 4 5 0
4 clear ;
5 clc ;
6 Lambda0 = 600 e -09; // w a v e l e n g t h o f r e d p a r t o f
7
8
9
10
11
12
v i s i b l e s p e c t r u m 600nm
n = 1.45; // r e f r a c t i v e i n d e x o f g l a s s p l a t e
delta_Lambda = 50 e -09; // o p t i c a l s p e c t r u m o f f u l l
w i d t h = 50nm
l = Lambda0 ^2/(2* n * delta_Lambda ) ;
disp ( l *1 e06 , ’ r e q u i r e d r a n g e o f g l a s s t h i c k n e s s i n
m i c r o m e t e r l= ’ )
// R e s u l t
// r e q u i r e d r a n g e o f g l a s s t h i c k n e s s i n m i c r o m e t e r l
= 2.4827586
Scilab code Exa 13.5 Program to find the required index for the coating
and its thickness
1
2
3
4
5
6
7
8
9
10
11
12
13
14
// C a p t i o n : Program t o f i n d t h e r e q u i r e d i n d e x f o r t h e
c o a t i n g and i t s t h i c k n e s s
// Example13 . 5
// p a g e 4 5 1
clear ;
clc ;
etta1 = 377; // i n t r i n s i c i m p e d a n c e o f f r e e s p a c e i n
ohms
n3 = 1.45; // r e f r a c t i v e i n d e x o f g l a s s
etta3 = etta1 / n3 ; // i n t r i n s i c i m p e d a n c e i n g l a s s
etta2 = sqrt ( etta1 * etta3 ) ; // i n t r i n s i c i m p e d a n c e i n
ohms f o r c o a t i n g
n2 = etta1 / etta2 ; // r e f r a c t i v e i n d e x o f r e g i o n 2
Lambda0 = 570 e -09; // f r e e s p a c e w a v e l e n g t h
Lambda2 = Lambda0 / n2 ; // w a v e l e n g t h i n r e g i o n 2
l = Lambda2 /4; // minimum t h i c k n e s s o f t h e d i e l e c t r i c
layer
disp ( l *1 e06 , ’ minimum t h i c k n e s s o f t h e d i e l e c t r i c
l a y e r i n um = ’ )
69
15
16
17
// R e s u l t
// minimum t h i c k n e s s o f t h e d i e l e c t r i c l a y e r i n um =
//
0.1183398
Scilab code Exa 13.6 Program to find the phasor expression for the electric field
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
// C a p t i o n : Program t o f i n d t h e p h a s o r e x p r e s s i o n f o r
the e l e c t r i c f i e l d
// Example13 . 6
// p a g e 4 5 6
clc ;
ax = sym ( ’ ax ’ ) ;
ay = sym ( ’ ay ’ ) ;
az = sym ( ’ a z ’ ) ;
x = sym ( ’ x ’ ) ;
y = sym ( ’ y ’ ) ;
z = sym ( ’ z ’ ) ;
teta = 30; // p h a s e a n g l e i n d e g r e e s
teta = 30/57.3; // p h a s e a n g l e i n r a d i a n s
Eo = 10; // E l e c t r i c f i e l d i n v /m
f = 50 e06 ; // f r e q u e n c y i n Hz
er = 9.0; // r e l a t i v e p e r m i t t i v i t y
ur = 1; // r e l a t i v e p e r m e a b i l i t y
[ uo , eo ] = muo_epsilon () ;
k = propagation_constant (f , uo , ur , eo , er ) ;
K = k *( cos ( teta ) * ax + sin ( teta ) * ay ) ;
r = x * ax + y * ay ;
Es = Eo * exp ( - sqrt ( -1) * K * r ) * az ;
disp (K , ’ p r o p a g a t i o n c o n s t a n t p e r m e t r e K= ’ )
disp (r , ’ d i s t a n c e i n m e t r e r= ’ )
disp ( Es , ’ P h a s o r e x p r e s s i o n f o r t h e e l e c t r i c f i e l d o f
t h e u n i f o r m p l a n e wave Es= ’ )
// R e s u l t
//K= 5 6 0 7 ∗ ( 1 4 9 6 9 ∗ ay /29940+25156∗ ax / 2 9 0 4 7 ) / 1 7 8 4
// r= ay ∗ y+ax ∗ x
// Es =10∗ a z ∗%eˆ −(5607∗ %i ∗ ( 1 4 9 6 9 ∗ ay /29940+25156∗ ax
/ 2 9 0 4 7 ) ∗ ( ay ∗ y+ax ∗ x ) / 1 7 8 4 )
70
Refer to the following for mu epsilon ARC 13 Refer to the following for
propagation constant ARC 21
Scilab code Exa 13.7 Program to find the fraction of incident power that
is reflected and transmitted
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
// C a p t i o n : Program t o f i n d t h e f r a c t i o n o f i n c i d e n t
power t h a t i s r e f l e c t e d and t r a n s m i t t e d
// Example13 . 7
// p a g e 4 6 0
clc ;
teta1 = 30; // i n c i d e n t a n g l e i n d e g r e e s
n2 = 1.45; // r e f r a c t i v e i n d e x o f g l a s s
teta2 = snells_law ( teta1 , n2 ) ;
etta1 = 377* cos ( teta1 /57.3) ; // i n t r i n s i c i m p e d a n c e
i n medium 1 i n ohms
etta2 = (377/ n2 ) * cos ( teta2 ) ; // i n t r i n s i c i m p e d a n c e
i n medium2 i n ohms
Tp = reflection_coefficient ( etta1 , etta2 ) ; //
r e f l e c t i o n c o e f f i c i e n t f o r p− p o l a r i z a t i o n
Reflected_Fraction_p = ( abs ( Tp ) ) ^2;
Transmitted_Fraction_p = 1 -( abs ( Tp ) ) ^2;
etta1s = 377* sec ( teta1 /57.3) ; // i n t r i n s i c i m p e d a n c e
f o r s− p o l a r i z a t i o n
etta2s = (377/ n2 ) * sec ( teta2 ) ;
Ts = reflection_coefficient ( etta1s , etta2s ) ; //
r e f l e c t i o n c o e f f i c i e n t f o r s− p o l a r i z a t i o n
Reflected_Fraction_s = ( abs ( Ts ) ) ^2;
Transmitted_Fraction_s = 1 -( abs ( Ts ) ) ^2;
disp ( teta2 *57.3 , ’ T r a n s m i s s i o n a n g l e u s i n g s n e l l s law
in degrees teta2 =’)
disp ( Tp , ’ R e f l e c t i o n c o e f f i c i e n t f o r p− p o l a r i z a t i o n
Tp= ’ )
disp ( Reflected_Fraction_P , ’ F r a c t i o n o f i n c i d e n t
71
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
power t h a t i s r e f l e c t e d f o r p− p o l a r i z a t i o n = ’ )
disp ( Transmitted_Fraction_p , ’ F r a c t i o n o f power
t r a n s m i t t e d f o r p− p o l a r i z a t i o n = ’ )
disp ( Ts , ’ R e f l e c t i o n c o e f f i c i e n t f o r s− p o l a r i z a t i o n
Tp= ’ )
disp ( Reflected_Fraction_s , ’ F r a c t i o n o f i n c i d e n t
power t h a t i s r e f l e c t e d f o r s− p o l a r i z a t i o n = ’ )
disp ( Transmitted_Fraction_s , ’ F r a c t i o n o f power
t r a n s m i t t e d f o r s− p o l a r i z a t i o n = ’ )
// R e s u l t
// T r a n s m i s s i o n a n g l e u s i n g s n e l l s law i n d e g r e e s
teta2 =
//
20.171351
// R e f l e c t i o n c o e f f i c i e n t f o r p− p o l a r i z a t i o n Tp=
// − 0 . 1 4 4 4 9 7 2
// F r a c t i o n o f i n c i d e n t power t h a t i s r e f l e c t e d f o r
−p o l a r i z a t i o n =
//
0.0337359
// F r a c t i o n o f power t r a n s m i t t e d f o r p− p o l a r i z a t i o n
//
0.9791206
// R e f l e c t i o n c o e f f i c i e n t f o r s− p o l a r i z a t i o n Tp=
//
− 0.2222748
// F r a c t i o n o f i n c i d e n t power t h a t i s r e f l e c t e d f o r
− p o l a r i z a t i o n = //
0.0494061
// F r a c t i o n o f power t r a n s m i t t e d f o r s− p o l a r i z a t i o n
//
0.9505939
p
=
s
=
Refer to the following for reflection coefficient ARC 22
Refer to the following Scilab code for snells law ARC 25
Scilab code Exa 13.8 Program to find the refractive index of the prism
material
1
// C a p t i o n : Program t o f i n d t h e r e f r a c t i v e i n d e x o f
the prism m a t e r i a l
72
2 // Example13 . 8
3 // p a g e 4 6 3
4 clear ;
5 clc ;
6 n2 =1.00; // r e f r a c t i v e i n d e x o f a i r
7 teta1 = 45; // i n c i d e n t a n g l e i n d e g r e e s
8 teta1 = 45/57.3; // i n c i d e n t a n g l e i n r a d i a n s
9 n1 = n2 / sin ( teta1 ) ;
10 disp ( n1 , ’ r e f r a c t i v e i n d e x o f p r i s m m a t e r i a l n1= ’ )
11 // R e s u l t
12 // r e f r a c t i v e i n d e x o f p r i s m m a t e r i a l n1=
13 //
1.4142954
Scilab code Exa 13.9 Program to determine incident and transmitted anlges
1
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6
7
8
9
10
11
12
13
14
15
16
17
// C a p t i o n : Program t o d e t e r m i n e i n c i d e n t and
transmitted anlges
// Example13 . 9
// p a g e 4 6 4
clear ;
clc ;
n1 =1.00; // r e f r a c t i v e i n d e x o f a i r
n2 =1.45; // r e f r a c t i v e i n d e x o f g l a s s
teta1 = asin ( n2 / sqrt ( n1 ^2+ n2 ^2) ) ;
teta2 = asin ( n1 / sqrt ( n1 ^2+ n2 ^2) ) ;
Brewster_Condition = teta1 + teta2 ;
disp ( teta1 *57.3 , ’ I n c i d e n t a n g l e i n d e g r e e s t e t a 1 = ’ )
disp ( teta2 *57.3 , ’ t r a n s m i t t e d a n g l e i n d e g r e e s t e t a 2=
’)
disp ( Brewster_Condition *57.3 , ’ sum o f t h e i n c i d e n t
a n g l e and t r a n s m i t t e d a n g l e , B r e w s t e r C o n d i t i o n= ’
)
// R e s u l t
// I n c i d e n t a n g l e i n d e g r e e s t e t a 1 = 5 5 . 4 1 1 7 9 3
// t r a n s m i t t e d a n g l e i n d e g r e e s t e t a 2 = 3 4 . 5 9 4 8 3 7
// sum o f t h e i n c i d e n t a n g l e and t r a n s m i t t e d a n g l e ,
B r e w s t e r C o n d i t i o n=
90.00663
73
Scilab code Exa 13.10 Program to determine group velocity and phase
velocity of a wave
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2
3
4
5
6
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11
12
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22
23
24
25
26
27
// C a p t i o n : Program t o d e t e r m i n e g r o u p v e l o c i t y and
p h a s e v e l o c i t y o f a wave
// Example13 . 1 0
// p a g e 4 7 0
clc ;
w = sym ( ’w ’ ) ;
wo = sym ( ’ wo ’ ) ;
no = sym ( ’ no ’ ) ;
c = sym ( ’ c ’ ) ;
beta_w = ( no * w ^2) /( wo * c ) ;
disp ( beta_w , ’ Phase c o n s t a n t= ’ )
d_beta_w = diff ( beta_w , w ) ;
disp ( d_beta_w , ’ D i f f e r e n t i a t i o n o f p h a s e c o n s t a n t w . r
. to w =’ )
Vg = 1/ d_beta_w ;
Vg = limit ( Vg ,w , wo ) ;
Vp = w / beta_w ;
Vp = limit ( Vp ,w , wo ) ;
disp ( Vg , ’ Group v e l o c i t y = ’ )
disp ( Vp , ’ Phase v e l o c i t y = ’ )
// R e s u l t
// Phase c o n s t a n t=
// no ∗wˆ 2 / ( c ∗wo )
// D i f f e r e n t i a t i o n o f p h a s e c o n s t a n t w . r . t o w =
// 2∗ no ∗w/ ( c ∗wo )
// Group v e l o c i t y =
// c / ( 2 ∗ no )
// Phase v e l o c i t y =
// c / no
Scilab code Exa 13.11 Program to determine the pulse width at the optical fiber output
1
// C a p t i o n : Program t o d e t e r m i n e t h e p u l s e w i d t h a t
the o p t i c a l f i b e r output
74
2 // Example13 . 1 1
3 // p a g e 4 7 4
4 clear ;
5 clc ;
6 T = 10; // w i d t h o f
7
8
9
10
11
12
13
14
15
16
17
l i g h t pulse at the o p t i c a l f i b e r
input in pico secs
beta2 = 20; // d i s p e r s i o n i n p i c o s e c o n d s s q u a r e p r e
kilometre
z = 15; // l e n g t h o f o p t i c a l f i b e r i n k i l o m e t r e
delta_t = beta2 * z / T ;
T1 = sqrt ( T ^2+ delta_t ^2) ;
disp ( delta_t , ’ P u l s e s p r e a d i n p i c o s e c o n d s d e l t a t =
’)
disp ( ceil ( T1 ) , ’ Output p u l s e w i d t h i n p i c o s e c o n d s T1
=’)
// R e s u l t
// P u l s e s p r e a d i n p i c o s e c o n d s d e l t a t =
//
30.
// Output p u l s e w i d t h i n p i c o s e c o n d s T1 =
//
32.
75
Chapter 14
Guided Wave and Radiation
Scilab code Exa 14.1 Program to determine the cutoff frequency for the
first waveguide mode(m=1)
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2
3
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5
6
7
8
9
10
11
12
13
14
15
// C a p t i o n : Program t o d e t e r m i n e t h e c u t o f f f r e q u e n c y
f o r t h e f i r s t w a v e g u i d e mode (m=1)
// Example14 . 1
// p a g e 499
clear ;
clc ;
er1 = 2.1; // d i e l e c t r i c c o n s t a n t o f t e f l o n m a t e r i a l
er0 = 1; // d i e l e c t r i c c o n s t a n t o f a i r
d = 1e -02; // p a r a l l e l p l a t e w a v e g u i d e s e p a r a t i o n i n
metre
C = 3 e08 ; // f r e e s p a c e v e l o c i t y i n m/ s e c
n = sqrt ( er1 / er0 ) ; // r e f r a c t i v e i n d e x
fc1 = C /(2* n * d ) ;
disp ( fc1 , ’ c u t o f f f r e q u e n c y f o r t h e f i r s t w a v e g u i d e
mode i n Hz f c 1 = ’ )
// R e s u l t
// c u t o f f f r e q u e n c y f o r t h e f i r s t w a v e g u i d e mode i n
Hz f c 1 =
//
1 . 0 3 5D+10
Scilab code Exa 14.2 Program to determine the number of modes propagate in waveguide
76
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
// C a p t i o n : Program t o d e t e r m i n e t h e number o f modes
propagate in waveguide
// Example14 . 2
// p a g e 499
clear ;
clc ;
er1 = 2.1; // d i e l e c t r i c c o n s t a n t o f t e f l o n m a t e r i a l
er0 = 1; // d i e l e c t r i c c o n s t a n t o f a i r
n = sqrt ( er1 / er0 ) ; // r e f r a c t i v e i n d e x
Lambda_cm = 2e -03; // o p e r a t i n g c u t o f f w a v e l e n g t h i n
metre
d = 1e -02; // p a r a l l e l −p l a t e w a v e g u i d e s e p a r a t i o n
m = (2* n * d ) / Lambda_cm ;
disp ( floor ( m ) , ’ Number o f w a v e g u i d e s modes p r o p a g a t e
m =’)
// R e s u l t
// Number o f w a v e g u i d e s modes p r o p a g a t e m =
//
14.
Scilab code Exa 14.3 Program to determine the group delay and difference in propagation times
1
2
3
4
5
6
7
8
9
10
11
12
// C a p t i o n : Program t o d e t e r m i n e t h e g r o u p d e l a y and
d i f f e r e n c e in propagation times
// Example14 . 3
// p a g e 502
clc ;
C = 3 e08 ; // f r e e s p a c e v e l o c i t y i n m/ s e c
er = 2.1; // d i e l e c t r i c c o n s t a n t o f t e f l o n m a t e r i a l
fc1 = 10.3 e09 ; // c u t o f f f r e q u e n c y f o r mode m =1
fc2 = 2* fc1 ; // c u t o f f f r e q u e n c y f o r mode m =2
f = 25 e09 ; // o p e r a t i n g f r e q u e n c y i n Hz
Vg1 = group_delay (C , er , fc1 , f ) ; // g r o u p d e l a y f o r mode
m = 1
Vg2 = group_delay (C , er , fc2 , f ) ; // g r o u p d e l a y f o r mode
m = 2
del_t = group_delay_difference ( Vg1 , Vg2 ) ;
77
disp ( ceil ( del_t *1 e10 ) , ’ g r o u p d e l a y d i f f e r e n c e i n p s /
cm d e l t = ’ )
14 // R e s u l t
15 // g r o u p d e l a y d i f f e r e n c e i n p s /cm d e l t =
16 //
33.
13
Refer to the following for group delay ARC 10
Refer to the following for group delay difference ARC 9
Scilab code Exa 14.4 Program to determine the operating range of frequency for TE10 mode of air filled rectangular waveguide
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
// C a p t i o n : Program t o d e t e r m i n e t h e o p e r a t i n g r a n g e
o f f r e q u e n c y f o r TE10 mode o f a i r f i l l e d
r e c t a n g u l a r waveguide
// Example14 . 4
// p a g e 509
clear ;
clc ;
// d i m e n s i o n s o f a i r f i l l e d r e c t a n g u l a r w a v e g u i d e
a = 2e -02;
b = 1e -02;
// F r e e s p a c e v e l o c i t y i n m/ s e c
C = 3 e08 ;
// t h e v a l u e o f m f o r TE10 mode
m = 1;
n = 1; // r e f r a c t i v e i n d e x f o r a i r f i l l e d w a v e g u i d e
fc = ( m * C ) /(2* n * a ) ;
disp ( fc *1 e -09 , ’ O p e r a t i n g r a n g e o f f r e q u e n c y f o r TE10
mode i n GHz f c= ’ )
// R e s u l t
// O p e r a t i n g r a n g e o f f r e q u e n c y f o r TE10 mode i n GHz
f c=
//
7.5
78
Scilab code Exa 14.5 Program to determine the maximum allowable refractive index of the slab material
1
2
3
4
5
6
7
8
9
10
11
12
13
// C a p t i o n : Program t o d e t e r m i n e t h e maximum
allowable r e f r a c t i v e index of the slab material
// Example14 . 5
// p a g e 517
clear ;
clc ;
Lambda = 1.30 e -06; // w a v e l e n g t h r a n g e o v e r which
s i n g l e −mode o p e r a t i o n
d = 5e -06; // s l a b t h i c k n e s s i n m e t r e
n2 = 1.45; // r e f r a c t i v e i n d e x o f t h e s l a b m a t e r i a l
n1 = sqrt (( Lambda /(2* d ) ) ^2+ n2 ^2) ;
disp ( n1 , ’ The maximum a l l o w a b l e r e f r a c t i v e i n d e x o f
t h e s l a b m a t e r i a l n1= ’ )
// R e s u l t
// The maximum a l l o w a b l e r e f r a c t i v e i n d e x o f t h e s l a b
m a t e r i a l n1=
//
1.4558159
Scilab code Exa 14.6 Program to find the V number of a step index fiber
1
2
3
4
5
6
7
8
9
10
11
12
// C a p t i o n : Program t o f i n d t h e V number o f a s t e p
index f i b e r
// Example14 . 6
// p a g e 524
clear ;
clc ;
Lambda = 1.55 e -06; // o p e r a t i n g w a v e l e n g t h i n m e t r e
LambdaC = 1.2 e -06; // c u t o f f w a v e l e n g t h i n m e t r e
V = ( LambdaC / Lambda ) *2.405;
disp (V , ’ t h e V number o f a s t e p i n d e x f i b e r V= ’ )
// R e s u l t
// t h e V number o f a s t e p i n d e x f i b e r V=
//
1.8619355
79
2
3
4
5
6
7
8
9
10
Scilab code ARC 11 // C a p t i o n : Program t o c a l c u l a t e t h e
a t t e n u a t i o n c o n s t a n t o f good d i e l e c t r i c
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example12 . 4 [ 2 ] . Example12 . 5
function [ beta1 ] = attenuation_constant_gooddie ( uo , eo
,f , er1 , er2 , ur )
W = 2*3.14* f ;
e1 = eo * er1 ;
e2 = eo * er2 ;
u = uo * ur ;
beta1 = ( W * e2 /2) * sqrt ( u / e1 ) ;
endfunction
2
3
4
5
6
Scilab code ARC 2
1 // C a p t i o n : Program u s e d t o c o n v e r t c a r t e s i a n
coordinates into cylindrical coordinates
// Not u s e d i n any e x a m p l e s
function [ th ,r , z ] = cart2cyl (x ,y , z )
th = atan (y , x ) ;
r = sqrt ( abs ( x ) .^2+ abs ( y ) .^2) ;
endfunction
2
3
4
5
6
7
Scilab code ARC 13 // C a p t i o n : Program u s e d t o c o n v e r t
cartesian coordinates into spherical coordinates
// Not u s e d i n any e x a m p l e s e x a m p l e s
function [ az , elev , r ] = cart2spher (x ,y , z )
r = sqrt ( abs ( x ) .^2+ abs ( y ) .^2+ abs ( z ) .^2) ;
elev = atan (z , sqrt ( abs ( x ) .^2+ abs ( y ) .^2) ) ;
az = atan (y , x ) ;
endfunction
Scilab code ARC 14 // C a p t i o n : Program u s e d t o f i n d t h e
c r o s s p r o d u c t o f two v e c t o r s
2 // The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
80
4
5
6
7
8
// [ 1 ] . Example9 . 2 [ 2 ] . Example9 . 3 [ 3 ] . Example9 . 4
Example9 . 6
function [ c ] = cross_product (a , b )
c = [ a (2) * b (3) -a (3) .* b (2)
a (3) * b (1) -a (1) * b (3)
a (1) * b (2) -a (2) * b (1) ];
endfunction
2
3
4
5
6
7
Scilab code ARC 15 // C a p t i o n : Program u s e d t o c o n v e r t
the c y l i n d r i c a l c o o r d i n a t e s into
// c a r t e s i a n c o o r d i n a t e s
// Not u s e d i n any e x a m p l e s
function [x ,y , z ] = cyl2cart (x ,y , z )
x = r .* cos ( th ) ;
y = r .* sin ( th ) ;
endfunction
2
3
4
5
6
Scilab code ARC 16 // C a p t i o n : Program t o f i n d t h e d o t
p r o d u c t o f two v e c t o r s
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example1 . 2 [ 2 ] . Example9 . 6
function [ C ] = dot (A , B )
C = sum ( A .* B ) ;
endfunction
2
3
4
5
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Scilab code ARC 7
1 // C a p t i o n : Program t o f i n d t h e e l e c t r i c a l l e n g t h
// R e f e r t h e f u n c t i o n f o r t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example11 . 8 [ 2 ] . Example11 . 1 0
function [ beta1 ] = electrical_length (L , Lambda )
beta1 = 2* %pi * L *57.3/ Lambda ;
endfunction
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[4].
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Scilab code ARC 18 // C a p t i o n : Program u s e d t o c a l c u l a t e
the e l e c t r i c f i e l d i n t e n s i t y of a l i n e charge
// The f u n c t i o n cna be u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example3 . 1
function [ E ] = Electric_Field_Line_Charge ( rL , e0 , r )
E = rL /(2* %pi * e0 * r ) ;
endfunction
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Scilab code ARC 19 // C a p t i o n : Program t o f i n i d t h e
group d e l a y d i f f e r e n c e
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example14 . 3
function [ del_t ] = group_delay_difference ( Vg1 , Vg2 )
del_t = ((1/ Vg2 ) -(1/ Vg1 ) )
endfunction
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Scilab code ARC 10
1 // C a p t i o n : Program t o f i n d t h e g r o u p d e l a y
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example14 . 3
function [ Vg ] = group_delay (C , er , fcm , f )
Vg = ( C / sqrt ( er ) ) * sqrt (1 -( fcm / f ) ^2) ;
endfunction
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Scilab code ARC 11
1 // C a p t i o n : Program t o f i n d t h e
i n t r i n s i c impedance o f d i e l e c t r i c
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example12 . 3 [ 2 ] . Example12 . 4
function [ etta ] = intrinsic_dielectric ( etta0 , er1 , er2 )
etta = ( etta0 / sqrt ( er1 ) ) *(1/ sqrt (1 - sqrt ( -1) *( er2 /
er1 ) ) )
endfunction
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Scilab code ARC 12
1 // C a p t i o n : Program t o f i n d t h e
i n t r i n s i c i m e d a n c e o f a good d i e l e c t r i c
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example12 . 5
function [ etta ] = intrinsic_good_dielectric ( etta0 , er1
, er2 )
etta = ( etta0 / sqrt ( er1 ) ) *(1/ sqrt (1 - sqrt ( -1) *( er2 /
er1 ) ) )
endfunction
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Scilab code ARC 13
1 // C a p t i o n : Program t o f i n d t h e f r e e
s p a c e p e r m i t t i v i t y and f r e e s p a c e p e r m e a b i l i t y
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example12 . 3 [ 2 ] . Example12 . 4 [ 3 ] . Example12 . 5
[ 4 ] . Example12 . 6
// [ 5 ] . Example13 . 2 [ 6 ] . Example13 . 6
function [ uo , eo ] = muo_epsilon ()
uo = 4*3.14*(10^ -7) ;
eo = 8.854*(10^ -12) ;
endfunction
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Scilab code ARC 14
1 // C a p t i o n : Program u s e d t o f i n d t h e
capacitance of a p a r a l l e l plate
// C a p a c i t o r
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example6 . 3
function [ C ] = parallel_capacitor (e ,S , d )
C = e*S/d;
endfunction
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Scilab code ARC 15
1 // C a p t i o n : Program t o f i n d t h e
impedance o f a p a r a l l e l c o n n e c t i o n
2 // R e f e r t h e f u n c t i o n f o r t h e f o l l o w i n g e x a m p l e s
3 // Example11 . 8
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function [ C ] = parallel (A , B )
C = A * B /( A + B )
endfunction
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Scilab code ARC 16
1 // C a p t i o n : Program u s e d t o
c a l c u l a t e the phase angle
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example1 . 2
function [ teta ] = Phase_Angle (A , B )
mod_A = sqrt ( A (1) ^2+ A (2) ^2+ A (3) ^2) ;
mod_B = sqrt ( B (1) ^2+ B (2) ^2+ B (3) ^2) ;
teta = acos ( dot (A , B ) /( mod_A * mod_B ) ) *57.3;
endfunction
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Scilab code ARC 17
1 // C a p t i o n : Program t o f i n d t h e
phase constant o f d i e l e c t r i c
// [ 1 ] . Example12 . 3
function [ beta1 ] = phase_constant_dielectric ( uo , eo ,f ,
er1 , er2 , ur )
W = 2* %pi * f ;
e1 = eo * er1 ;
e2 = eo * er2 ;
u = uo * ur ;
beta1 = W * sqrt ( u * e1 /2) * sqrt ( sqrt (1+( e2 / e1 ) ^2) +1) ;
endfunction
Scilab code ARC 18
1 // C a p t i o n : Program t o f i n d t h e
p h a s e c o n s t a n t o f a good d i e l e c t r i c
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// Example12 . 5
function [ beta1 ] = phase_constant_gooddie ( uo , eo ,f , er1
, er2 , ur )
W = 2*3.14* f ;
e1 = eo * er1 ;
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e2 = eo * er2 ;
u = uo * ur ;
beta1 = W * sqrt ( u * e1 ) ;
endfunction
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Scilab code ARC 19
1 // C a p t i o n : Program t o f i n d t h e p h a s e v e l o c i t y
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example12 . 3
function [ Vp ] = phase_velocity (f , beta1 )
W = 2* %pi * f ;
Vp = W / beta1 ;
endfunction
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Scilab code ARC 21
1 // C a p t i o n : Program t o f i n d t h e
propagation constant
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example13 . 6
function [ k ] = propagation_constant (f , uo , ur , eo , er )
W = 2* %pi * f ;
u = uo * ur ;
e = eo * er ;
k = W * sqrt ( u * e ) ;
endfunction
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Scilab code ARC 22
1 // C a p t i o n : Program t o f i n d t h e
reflection coefficient
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example13 . 1 [ 2 ] . Example13 . 2 [ 3 ] . Example13 . 7
function [ T ] = reflection_coefficient ( etta1 , etta2 )
T = ( etta2 - etta1 ) /( etta2 + etta1 ) ;
endfunction
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Scilab code ARC 23
1 // C a p t i o n : Program t o f i n d t h e
reflection coefficient
// R e f e r t h e f u n c t i o n f o r t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example11 . 5 [ 2 ] . Example11 . 8 [ 3 ] . Example11 . 9
[ 4 ] . Example11 . 1 0
// [ 5 ] . Example11 . 1 1
function [ T ] = reflection_coeff ( ZL , Zo )
T = ( ZL - Zo ) /( ZL + Zo ) ;
endfunction
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Scilab code ARC 24
1 // C a p t i o n : Program t o c a l c u l a t e t h e
s k i n d e p t h o f a good c o n d u c t o r
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example12 . 6
function [ del ] = SkinDepth (f , uo , ur , sigma )
del = sqrt (1/(3.14* f * ur * uo * sigma ) ) ;
endfunction
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Scilab code ARC 25
1 // C a p t i o n : Program t o f i n d t h e
r e f r a c t e d a n g l e u s i n g s n e l l ’ s law
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example13 . 7
function [ teta2 ] = snells_law ( teta1 , n2 )
teta1 = teta1 /57.3; // t e t a 1 i n r a d i a n s
teta2 = asin ( sin ( teta1 ) / n2 ) ;
endfunction
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Scilab code ARC 26
1 // C a p t i o n : Program u s e d t o c o n v e r t
spherical coordinates into cartesian coordinates
2 // Not u s e d i n any e x a m p l e s
3 function [x ,y , z ] = spher2cart ( az , elev , r )
4 // ” s p h e r 2 c a r t ” T r a n s f o r m s p h e r i c a l t o C a r t e s i a n
coordinates .
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//
[ x , y , z ] = s p h e r 2 c a r t (TH, PHI , R) t r a n s f o r m s
corresponding elements
o f data s t o r e d in
s p h e r i c a l c o o r d i n a t e s ( a z i m u t h TH, e l e v a t i o n PHI ,
//
r a d i u s R) t o C a r t e s i a n c o o r d i n a t e s X, Y, Z . TH and
PHI must be i n r a d i a n s .
z = r * sin ( elev ) ;
rcoselev = r * cos ( elev ) ;
x = rcoselev * cos ( az ) ;
y = rcoselev * sin ( az ) ;
endfunction
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Scilab code ARC 27
1 // C a p t i o n : Program u s e d t o f i n d t h e U n i t v e c t o r
// The f u n c t i o n u s e d i n t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example1 . 1 [ 2 ] . Example2 . 1 [ 3 ] . Example2 . 2 [ 4 ] .
Example9 . 2
function [ a ] = UnitVector ( A )
a = A / sqrt ( A (1) ^2+ A (2) ^2+ A (3) ^2) ;
endfunction
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Scilab code ARC 28
1 // C a p t i o n : Program t o f i n d t h e
V o l t a g e S t a n d i n g Wave R a t i o (VSWR)
// R e f e r t h e f u n c t i o n f o r t h e f o l l o w i n g e x a m p l e s
// [ 1 ] . Example 1 1 . 8 [ 2 ] . Example 1 1 . 9 [ 3 ] . Example13 . 2
function [ S ] = VSWR ( T )
// where T i s t h e r e f l e c t i o n c o e f f i c i e n t
if ((1 - abs ( T ) ) ==0)
S = %inf ;
else
S = (1+ abs ( T ) ) /(1 - abs ( T ) ) ;
end
endfunction
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