Electromagnetic Theory discussions .ppt

IMPORTANCE OF
ELECTROMAGNETICS
IN ELECTRONICS
by
Prof (Dr) Annapurna Das
Director, GNIT

• Electromagnetic (EM) theory was started developing since late
1800’s because of
 Need of wireless communication
 Development of high resolution radars and
 Need of increased bandwidth (huge information through a
communication channel).
• Low frequency circuit analysis is based on
 Ohms’ law
 Kirchhoff’s law and
 Voltage-current concepts.
Introduction

At high frequencies these are not hold good
since
•Throughout the physical dimension of lumped parameters (R, L, G,
and C), voltage/current fluctuates.


High frequency/RF >100MHz
• Behavior of Lumped Components at Radio Frequency
 Nature of Lumped (physical) resistors, capacitors, and inductors
are “pure” components at lower frequencies.
 As the frequency of operation of any RF/MW circuit begins to
increase, physical length of the components becomes longer than
λ, and effects of unwanted reactances associated to lead inductance
and stray capacitance appear.
 At microwave frequencies even the PC board traces, that connect
the passive components, are longer than approximately , and must
be considered as transmission line structures.

IMPORTANCE OF
ELECTROMAGNETICS
IN ELECTRONICS
by
Director, GNIT
Resistors
he magnitude and phase of the resistor’s impedance as a function of frequenc

IMPORTANCE OF
ELECTROMAGNETICS
IN ELECTRONICS
by
Director, GNIT
Capacitors
Inductive

IMPORTANCE OF
ELECTROMAGNETICS
IN ELECTRONICS
by
Director, GNIT
Inductors
• Approximate model for a practical inductor

Element radiates whenever physical dimension is >
λ/2:
• Conductor resonates to give maximum response
• Thus at high frequencies signal flow considers the concept of fields (E,
H) which are integrated effect of voltage and current: These fields are
function of space co-ordinates:
Rectangular co-ordinate
(x,y,z)
Cylindrical co-ordinate
(ρ,φ,z)
Spherical co-ordinate
(r,θ,φ)









z
z
y
x




sin
cos












z
z
x
y
y
x
1
2
2
tan













2
2
2
2
cos
sin
y
x
x
y
x
y















cos
sin
r
z
r

















z
z
r
1
2
2
tan











2
2
2
2
cos
sin
z
z
z


















cos
sin
sin
cos
sin
r
z
r
y
r
x

















x
y
z
y
x
z
y
x
r
1
2
2
1
2
2
2
tan
tan
















2
2
2
2
2
2
2
2
cos
sin
z
y
x
z
z
y
x
y
x


Relations between Cartesian, Cylindrical, and
Spherical Coordinates
Cartesian Cylindrical
Cylindrical Spherical
Cartesian Spherical
P
)
,
,
(
)
,
,
(
)
,
,
(
z
r
z
y
x




x
Y
Z
y
x
z
r




a) (3, π/3, -4) from cylindrical to Cartesian.
b) (-2, 2, 3) from Cartesian to cylindrical.
c) (8, π/4, π/6) from spherical to Cartesian.
d) (2√3, 6, -4) from Cartesian to spherical.
e) (1, π/2, 1) from cylindrical to spherical.
EX 1 Convert the coordinates as indicated

Applications of Electromagnetic
signals (RF and MW)

The differential (Del ) operator can
completely specify any physical field problem
with three possible operations
1) Space variation (gradient) a vector
2) Converging and diverging (divergent) a scalar
3) Rotational behavior (curl) a vector
V

A

.

A
x


z
z
y
y
x
x









 ˆ
ˆ
ˆ

Gradient:
k
z
V
j
y
V
i
x
V
V










The gradient, at any point P(x, y, z), of a scalar point function v(x, y,
z) is a vector. The magnitude of the gradient vector is the maximum
rate of change of scalar function. The direction of the gradient
vector is the direction in which the change in scalar function is
maximum.
Divergence:
It is a scalar function.

Curl: Curl of a vector function ‘a’ is the rotational tendency of the vecto
Whose magnitude is the maximum rotation of ‘a’ per unit area and the
Direction is normal to the area where the rotational tendency is maximum
a. b.
a. b.

Theorems in EM
• Similar to Thevenin and Norton Theorems as applied at Low frequency
two fundamental theorems are used here to equate two integrants at two
different domain
1 Divergence Theorem
2 Stokes’ Theorem
 Classification of media
 The free space is characterized by the electrical medium parameters:
• Permittivity F/m
• Permeability H/m and
• Conductivity S/m
• Intrinsic impedance , and
• Velocity of wave propagation (light) c=2.9979x108
m/S.
S
d
F
x
d
F
S






.
)
(
.
 

S
d
F
x
d
F
S






.
)
(
.
 




 377
120π
ε
μ
η
o
o
o
π
εo
36
10 9


7
10
4 
 x
π
μo
14
10

o
σ

• General medium is characterized as:
 linear if it’s electrical parameters( ) are independent of field
strength or source current density,
 homogeneous if its electrical parameters are independent of position
within the medium,
 isotropic if it’s electrical parameters are independent of direction of E
• Electromagnetic is the study of the effect of
 charges at rest Electrostatics;
 charges in constant motion ( or DC) Magneto statics, and
 charges in time varying motion Electromagnetic wave.


 ,
,

Electromagnetism (Time
invariant)
(A) Electrostatic fields E(r) generated by stationary
electric charge(s) at a distance r
1)Coulomb’s Law
Electric Field: The electric field at r due to the charge q2 at origin is force on a
unit charge q1=1, placed at r
2
2
1
ˆ
4 r
r
q
q
F
E
o
πε




(N/C or V/m)
E field E = - V
Here the electric potential



v
r
dv
V


2) Gauss Law for Electricity
The flux out of any closed surface S is proportional to the total
charge enclosed within the surface :
Q
D
d
S
n
 


S
V
dv
Q
dS
D ρ
. 

D
.
3) Gauss' Law for Magnetism
Thus magnetic flux exits always in close loop.

(B)Magneto static fields H(r) generated by steady
motion of electric charge(s) or by DC current
1) Amperes law for steady current:
 




S
dS
J
I
d
H .
.
where J is current density. Using Stoke’s theorem
J
xH 

In static field theory E and H fields are time invariant and both are
independent to each other

C ) Electromagnetism (Time varying
1. Conservation of Charge and Equation of Continuity
dt
dQ
ds
J
I
S


 .
t
J






.
me varying electromagnet fields E(r,t) & H (r,t) generated by time
arying motion of electric charge or AC/RF current flow.
isplacement current and Inconsistence of Ampère's Circuital law for
me varying field
S
d
t
D
J
d
H
S





).
(
.
  




4. Faraday's Law
A time-varying voltage is produced in a circuit whenever
time varying magnetic fields are linked the circuit.
In the differential form of Faraday’s law can be expressed as
)
(t
Vo
S
d
t
B
S
d
B
dt
d
d
E
S S








.
.
.  
 






•Time varying fields both E and H fields are inter-dependent or
one is associated with each other.
•Time varying EM fields propagate in a medium as EM waves as a
function of space coordinates r, and time t.

,
Maxwell's Equations

Boundary Conditions at Interface between two
media 1 and 2: Singularities of the fields
The solution of Maxwell’s equations in a region can be solved
completely with the consideration of singularities of the field.
Medium 1
Medium 2
n
t
A
dS=n dS
dS
n.A=Normal component of A

nXA= Tangential component of A

Electromagnetic Theory discussions .ppt

Characteristics of uniform Plane
Waves in Unbounded Medium
• The solution E=E0Cos (wt – kz)
• Plane wave where phase kz = constant over a set of planes
called equiphase surfaces
• Uniform plane wave where amplitude Eo= constant over the
equiphase planes.
Electric field at different instant of time

a. Travelling waves
• The electric and magnetic fields are mutually perpendicular to
each other and also perpendicular to the direction of
propagation. Thus the wave is called transverse
electromagnetic (TEM).
• Signal Wave has Impedance called Wave Impedance
E/H ohm =120π ohm in free space
• The power transmitted by the two fields in the direction
of
propagation =P= ½(EXH) watts /sq.m



Wave Impedance and E field and
H field Impedances
Ohm
Amp
Volt
m
A
H
m
V
E


)
/
(
)
/
(

η



 377
120π
ε
μ
η
EM wave has impedance:
In free
space

• For electric field source (electric current in dipoles or straight
conductors) the wave impedance is larger than the free space
impedance (377 ohm).
• Reverse is the case for magnetic field source (electric current in
coils or loops).
• As one moves away from the source, E-field impedance decreases
and H-field impedance increases to the free space value in the far-
field range which is defined by a distance

b. Standing waves
Linearly polarized uniform plane standing wave

Polarization of Plane waves
• In EM wave propagation, at a given position, the electric field
vector tip traces a curve as time elapses, as shown in Fig.
Plane wave propagation in +z direction

Wavefront
• The phase distribution in the medium exhibits locus of
constant phase surfaces, called the wave front as shown in Fig.
A linear current source
Different nature of Wave fronts
Both the wave fronts at a very large (ideally infinite) distance appear
plane over a practical size observation

Phase and group velocities
• Phase velocity
Equiphase surface travels with the phase velocity for which
t
cons
kz
t tan


ω
Phase velocity


1
/ 

 k
dt
dz
vp
; με
ω

k
• Group velocity
The velocity at which the energy is propagated is expressed
by
group velocity


d
d
g 
v

Propagation through
transmission lines (bounded
medium)
• Electromagnetic signal or waves are transmitted through
different form of guided lines, called transmission lines:
 Co-axial lines

Wave guides Planner tx line
Microstrip lines

Applications of EM wave
 Wireless signal propagation in free space
(unbounded medium)
• Mobile phone communication

• Satellite communication and TV broast cast
• Radar communication

• Radio broast cast- AM and FM
N
fc 9
 ; fc maximum kHz frequency which reflects from
ionosphere having electron density N per cm3
.

P
)
,
,
(
)
,
,
(
)
,
,
(
z
r
z
y
x




x
Y
Z
y
x
z
r




Electromagnetic Theory discussions .ppt

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