Using MATLAB: 1. The charged parallel plate capacitor shown below creates a pote
ID: 3854073 • Letter: U
Question
Using MATLAB:
1. The charged parallel plate capacitor shown below creates a potential:
V = 9z/d for 0<=z/d<=1.
a) Using the meshgrid command, generate a rectangular grid in the y-z plane in the range 0<=y/l<=1, 0<=z/d<=1, and in steps of y/l = z/d = .05. Calculate the potential in this region. Using the imagesc and colorbar commands, plot the potential.
b) Using the gradient command, calculate the electric field E between the plates. Using the quiver command, plot the field.
Explanation / Answer
66
FUNDAMENTAL PARAMETERS OF ANTENNAS
account the efciency of the antenna as well as its directional capabilities. Rememberthat directivity is a measure that describes only the directional properties of the antenna,and it is therefore controlled only by the pattern.
Gain
of an antenna (in a given direction) is dened as “the ratio of the intensity, in agiven direction, to the radiation intensity that would be obtained if the power acceptedby the antenna were radiated isotropically. The radiation intensity corresponding tothe isotropically radiated power is equal to the power accepted (input) by the antennadivided by 4
.” In equation form this can be expressed asGain
=
4
radiation intensitytotal input (accepted) power
=
4
U(,)P
in
(
dimensionless
) (
2-46
)
In most cases we deal with
relative gain
, which is dened as “the ratio of thepower gain in a given direction to the power gain of a reference antenna in its refer-enced direction.” The power input must be the same for both antennas. The referenceantenna is usually a dipole, horn, or any other antenna whose gain can be calculatedor it is known. In most cases, however, the reference antenna is a
lossless isotropicsource
. Thus
G
=
4
U(,)P
in
(
lossless isotropic source
)(
dimensionless
) (
2-46a
)
When the direction is not stated, the power gain is usually taken in the direction of maximum radiation
.Referring to Figure 2.22(a), we can write that the total radiated power
(P
rad
)
isrelated to the total input power
(P
in
)
by
P
rad
=
e
cd
P
in
(
2-47
)
where
e
cd
is the antenna radiation efciency (dimensionless) which is dened in (2-44),(2-45) and Section 2.14 by (2-90). According to the IEEE Standards, “gain does notinclude losses arising from impedance mismatches (reection losses) and polarizationmismatches (losses).”In this edition of the book we dene two gains; one, referred to as
gain
(
G
),and the other, referred to as
absolute gain
(G
abs
)
, that also takes into account thereection/mismatch losses represented in both (2-44) and (2-45).Using (2-47) reduces (2-46a) to
G(,)
=
e
cd
4
U(,)P
rad
(
2-48
)
which is related to the directivity of (2-16) and (2-21) by
G(,)
=
e
cd
D(,) (
2-49
)
In a similar manner, the maximum value
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