Digital Signal Processing Reference
In-Depth Information
x
E
x
e
−g
z
E
x
(
z,t
)
=
y
1
h
E
x
e
−g
z
H
y
(
z,t
)
=
z
Figure 2-13
Time-harmonic TEM plane wave propagating down the
z
-axis.
it forms the basis of fundamental signal integrity theory and promotes an intu-
itive understanding of how electric fields behave. In this chapter we (1) define
the electric field, (2) describe how energy is stored in the electric field, and (3)
define capacitance, which is the circuit element used in circuit models to repre-
sent the energy stored in an electric field. The vast majority of signal integrity
analysis performed in the industry today uses electrostatic techniques to calculate
critical design variables such as transmission-line impedance, phase velocities,
and effective dielectric permittivities. The concepts introduced in this section are
expanded on in later chapters to describe a myriad of concepts.
When a weightlifter hoists a barbell over his head, the energy expended (or the
work done against the gravitational field) is stored in the form of potential energy.
The gravitational potential energy can be recovered by lowering the barbell to the
ground. Similarly, when two infinitely separated charges of the same polarity are
brought together, the charges will experience a repulsive force whose magnitude
depends on the distance between the charges. The existence of this force is
described by saying that a charge
q
with units of coulombs (C) produces an
electric field in the region surrounding it. When the electric fields of two charges
of the same polarity begin to interact, a force will be generated that will push the
charges apart. Therefore, the region surrounding a charge is permeated by a force
field known as the
electric field
,defined fundamentally as force per unit charge,
with units of newtons per coulomb (N/C). Note that because a volt is defined as
joules per coulomb (J/C), newtons per coulomb is equivalent to volts per meter
(V/m), which are the units commonly used to describe an electric field.
J
C
→
J
V
V
=
C
=
m
2
/
s
2
1J
=
1kg
·
m
/
s
2
1N
=
1kg
·
m
/
s
2
N
C
=
N
·
V
1kg
·
·
V
V
m
=
=
m
2
/
s
2
J
1kg
·
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