This preview shows pages 1–5. Sign up to view the full content.
Determination of Antenna Radiation Fields
Using Potential Functions
6
J
 vector electric current density (A/m
2
)
M
 vector magnetic current density (V/m
2
)
Some problems involving electric currents can be cast in equivalent forms
involving magnetic currents (the use of magnetic currents is simply a
mathematical tool, they have never been proven to exist).
A
 magnetic vector potential (due to
J
)
F
 electric vector potential (due to
M
)
In order to account for both electric current and/or magnetic current
sources, the symmetric form of Maxwell’s equations must be utilized to
determine the resulting radiation fields.
The symmetric form of Maxwell’s
equations include additional radiation sources (electric charge density 
D
and magnetic charge density
D
m
).
However, these charges can always be
related directly to the current via conservation of charge equations.
Sources of Antenna
Radiation Fields
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Maxwell’s equations
(symmetric, timeharmonic form)
The use of potentials in the solution of radiation fields employs the concept
of superposition of fields.
Electric current
Y
Magnetic vector
Y
Radiation fields
source (
J
,
D
)
potential (
A
)
(
E
A
,
H
A
)
Magnetic current
Y
Electric vector
Y
Radiation fields
source (
M
,
D
m
)
potential (
F
)
(
E
F
,
H
F
)
The total radiation fields (
E
,
H
) are the sum of the fields due to electric
currents (
E
A
,
H
A
) and the fields due to the magnetic currents (
E
F
,
H
F
).
Maxwell’s Equations
(electric sources only
Y
F
=
0
)
Maxwell’s Equations
(magnetic sources only
Y
A
=
0
)
Based on the vector identity,
any vector with zero divergence (rotational or solenoidal field) can be
expressed as the curl of some other vector.
From Maxwell’s equations with
electric or magnetic sources only [Equations (1d) and (2c)], we find
so that we may define these vectors as
where
A
and
F
are the magnetic and electric vector potentials, respectively.
The flux density definitions in Equations (3a) and (3b) lead to the
following field definitions:
Inserting (3a) into (1a) and (3b) into (2b) yields
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Equations (5a) and (5b) can be rewritten as
Based on the vector identity
the bracketed terms in (6a) and (6b) represent nonsolenoidal (lamellar or
irrotational
fields) and may each be written as the gradient of some scalar
where
N
e
is the electric scalar potential and
N
m
is the magnetic scalar
potential.
Solving equations (7a) and (7b) for the electric and magnetic
fields yields
Equations (4a) and (8a) give the fields (
E
A
,
H
A
) due to electric sources
while Equations (4b) and (8b) give the fields (
E
F
,
H
F
) due to magnetic
sources.
Note that these radiated fields are obtained by differentiating the
respective vector and scalar potentials.
The integrals which define the vector and scalar potential can be
This is the end of the preview. Sign up
to
access the rest of the document.
This document was uploaded on 04/11/2010.
 Spring '09

Click to edit the document details