Practical_Antenna_Handbook_0071639586

452 P a r t V I : A n t e n n a s f o r O t h e r F r e q u e n c i e s
E- and H-fields are said to be “normal” or “orthogonal” to the direction of travel—three
different ways of saying the same thing: right-angledness.
Boundary Conditions
In contrast, a TEM wave will not propagate in a waveguide because different constraints,
called boundary conditions, apply. Although the wave in the waveguide propagates
through the air (or inert gas dielectric) in a manner similar to free-space
propagation, the phenomenon is bounded by the walls of the waveguide—clearly a far
different situation than for a TEM wave in free space! The boundary conditions for
waveguides are these:
• The electric field must be orthogonal to the conductor in order to exist at the
surface of that conductor.
• The magnetic field must not be orthogonal to the surface of the waveguide.
In order to satisfy these boundary conditions the waveguide supports two types of
propagation modes: transverse electric mode (TE mode) and transverse magnetic mode (TM
mode). The TEM mode for radio waves propagating through free space violates the
boundary conditions because the magnetic field is not parallel to the surface and so
does not occur in waveguides.
The transverse electric field requirement means that the E-field must be perpendicular
to the conductor wall of the waveguide. This requirement is met by use of a
proper coupling scheme at the input end of the waveguide. A vertically polarized coupling
radiator will provide the necessary transverse field.
One boundary condition requires that the magnetic (H) field must not be orthogonal
to the conductor surface. An H-field that is at right angles to the E-field (which is
orthogonal to the conductor surface) meets this requirement (see Fig. 20.6). The planes
formed by the magnetic field are parallel to both the direction of propagation and the
wide surface dimension of the waveguide.
As the wave propagates away from the input radiator, it resolves into two components
that are not along the axis of propagation and are not orthogonal to the walls. The
component along the waveguide axis violates the boundary conditions, so it is rapidly
attenuated. For the sake of simplicity, only one component is shown in Fig. 20.7. Three
cases are shown in Fig. 20.7A, B, and C, respectively: high, medium, and low frequency.
Top
view
"a"
Dim.
Weak
H-field
"a"
Dim.
Side
view
"b"
Dim.
Strong H-field
Cross sectional view at center of side view
/ 2 End view
Cross sectional
view / 4
from end
Figure 20.6 Magnetic fields in waveguide.