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TM MODE
The longitudinal electric field of the TM modes within the rectangular waveguide must satisfy the wave
equation
. Expansion and simplification leads to:
With
. By a similar nature to the TE mode then:
Applying the boundary conditions:
Wh
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Example
In AM, the sum of signal frequencies and carrier frequency
forms an envelope representing the signal
information. The carrier signal exhibits a phase velocity of
group velocity
while the envelope propagates at the
. Determine the group v
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R ADIATION P ATTERN
The radiation pattern is a graphical representation of the angular variation of the radiation level around
the antenna.
If we represent the angular variation of the amplitude of the field the pattern is called a field pattern
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R ADIATION I NTENSITY
Recall that:
We define the radiation intensity as the power radiation in a given direction per unit solid angle as:
Thus the total power radiation density and power pattern are given as:
We define the Directive gain as
the
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I DEAL D IPOLE
To begin with, we shall consider a very short and thin piece of wire
oriented along the z-axis and carrying an infinitesimal current element
, directed in the positive z direction, as the source of radiation in an
infinite lossles
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To summarise, the following equations of transverse field components are valid for all modes defined
previously:
TEM W AVES
TEM waves are characterized by the lack of longitudinal components
. We find that
the transverse fields of a TEM mode are
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ANTENNAS
An antenna is a device which acts as a transition between circuitry and space and aids in the transmission
of signals that are unguided and that can be received by several users simultaneously. An antenna makes
use of the electromagneti
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A NALYSIS OF TE AND TM W AVEGUIDES
In the next section we shall present the analysis for TE and TM waveguides by following the given
procedures:
1.
2.
3.
4.
Solve the reduced Helmholtz equation for
or which will contain unknown constants
includi
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WAVEGUIDES
Waveguiding structures are called waveguides and may consist of a single conductor. Transmission lines
tend to guide TEM waves using two or more conductors waves with no field component in the direction
of the propagation. However, wa
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T RANSVERSE E LECTRIC
In transverse electric waves,
and can be supported inside closed conductors and two or more
conductors. Substitution into the general solutions for the four transverse field components yields:
In this case
and the propagati
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M AGNITUDE OF N ORMALISED E LECTRIC F IELD
We define the magnitude of the normalised electric field as:
For the ideal dipole since:
Is a maximum at
then,
.
E NERGY P ROPAGATION
Recall the Poynting vector:
The significance of this vector is that
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Example
Determine the electric field intensity at a distance of 10 km from the antenna having a directive
gain of 5 dB and radiating a total power of 20 kW.
A NTENNA E FFICIENCY , P OWER G AIN
We define the radiation efficient as a ratio between