UNIT - I

MICROWAVE FREQUENCY BANDS:

MICROWAVE FREQUENCY BANDS IN IEEE STANDARDS:

 Waveguides
The microwave portion of the radio spectrum covers frequencies from about 300 MHz to
300 GHz, with wavelengths in free-space ranging from 1m down to 1 mm. Transmission
lines are used at frequencies from dc to about 50 or 60 GHz, but anything above 5 GHz
only short runs are practical, because attenuation increases dramatically as frequency
increases. There are three types of losses in conventional transmission lines: ohmic,
dielectric, and radiation. The ohmic losses are caused by the current flowing in the
resistance of the conductors making up the transmission lines. The skin effect will
increase the resistance at higher frequencies; therefore the losses tend to increase in the
microwave region. Dielectric losses are caused by the electric field acting on the
molecules of the insulator and thus, will cause heating through molecular agitation.
Radiation losses are the loss of energy as the electromagnetic wave propagates away
from the surface of the transmission line conductor.
Losses on long runs of commonly used coaxial transmission line causes concern as low
as 400 MHz. Because of the increased losses the power handling capability decreases at
higher frequencies, therefore, at higher microwave frequencies, or where long runs make
coax attenuation losses unacceptable, or where high power levels causes the coax to
overheat, waveguides are used instead of the transmission lines.
The internal walls of the waveguide are not mirrored surfaces, but instead electrical
conductors. Most waveguides are made of aluminum, brass, or copper. Some
waveguides internal surfaces are electroplated with either gold or silver to reduce ohmic
losses. The gold or silver have lower resistivities than most other metals.
Waveguides are hollow pipes, and may have either circular or rectangular cross sections.
Rectangular are, by far, the most common. These waveguides are used for high
frequency transmission in the gigahertz (microwave) range. The TEM mode cannot
propagate in these single conductor transmission lines. Only higher modes in the form of
transverse electric (TE) and transverse magnetic (TM) modes can propagate in the
waveguide.
Transverse and Axial Fields

The waveguide is positioned with the longitudinal direction along the z axis.

y Ø

b r
0 a
0 x
a
+z
+z
(a)
(b)
Figure 8.1

Waveguide characteristics:
 guide walls have  c   (perfect conductor)
 dielectric-filled hollow has:
1.  c  0 (perfect conductor)
2.   o r
3.    o  r
4. assumed   0 (no free charge)
The dimensions for the cross section are inside dimensions. Figure 8.1(a) is a rectangular
waveguide shown in Cartesian coordinate system; Figure 8.1(b) shows a circular or
cylindrical waveguide of radius a in a cylindrical coordinate system.

The time dependence e jt will be assumed for the electromagnetic field in the dielectric
core. The following expressions for the field vector F (which stands for either E or H),
assuming the wave is propagating in the +z direction.

Rectangular coordinates F = F(x, y) e-jkz where:

F ( x, y)  Fx ( x, y)a x  Fy ( x, y)a y  Fz ( x, y)a z  F ( x, y)  Fz ( x, y)a z

Cylindrical coordinates F  f (r ,  )e  jkz where:

F (r ,  )  Fr (r ,  )ar  F (r ,  )a  Fz (r ,  )a z  F (r ,  )  Fr (r ,  )a z

The wave will propagate without attenuation, because the dielectric is lossless (σ = 0).
 2 
Let k   (in rad/m) be the wave number and is constrained to be real and positive.
  
Propagation Modes in Waveguide

In a waveguide a signal will propagate as an electromagnetic wave. Even in a

transmission line the signal propagates as a wave because the current in motion down the
line gives rise to the electric and magnetic fields that behaves as an electromagnetic field.
The transverse electromagnetic (TEM) field is the specific type of field found in
transmission lines. We also know that the term “transverse” implies to things at right
angles to each other, so the electric and magnetic fields are perpendicular to the direction
of travel. These right angle waves are said to be “normal” or “orthogonal “to the
direction of travel.
The boundary conditions that apply to waveguides will not allow a TEM wave to
propagate. However, the wave in the waveguide will propagate through air or inert gas
dielectric in a manner similar to free space propagation, the phenomena is bounded by the
walls of the waveguide and that implies certain conditions that must be met. The
boundary conditions for waveguides are:

1. The electric field must be orthogonal to the conductor in order to exist at the
surface of that conductor.
2. The magnetic field must not be orthogonal to the surface of the waveguide.

The waveguide has two different types of propagation modes to satisfy these boundary
conditions:

1. TE – transverse electric (Ez = 0)

2. TM – transverse magnetic (Hz = 0)

The transverse electric field requirement means that the E-field must be perpendicular to
the conductor wall of the waveguide. This requirement can be met with proper coupling
at the input end of the waveguide. A vertically polarized coupling radiator will provide
the necessary transverse field.
One boundary condition will require the magnetic (H) field not to be orthogonal to the
conductor surface. Since it is at right angles to the E-field, the requirement will be met.
The planes that are formed by the H-field will be parallel to the direction of propagation
and to the surface.

Dominant Mode

The dominant mode of any waveguide is that of the lowest cutoff frequency. Now, for a
rectangular guide, the coordinate system may always be oriented to make a ≥ b.
Velocity and Wavelength in Waveguides:

Figure 8.3 illustrates the geometry for two wave components simplified for sake of
illustration. There are three different wave velocities to consider with respect to
waveguides: free space velocity (c), group velocity (Vg), and phase velocity (Vp).
The space velocity of propagation in unbounded free-space, i.e., the speed of light
(c = 3 * 108 m/s).
The group velocity is the straight line velocity of propagation of the wave down the
center-line (z-axis) of the waveguides. The value of Vg is always less than c, because the
actual path length taken as the wave bounces back and forth is longer than the straight
line path (i.e., path ABC is longer than path AC). The relationship between c and V g is:
 Vg = c sin a

*Note: Vg is the group velocity in (m/s), c is the free space velocity (3 * 108 m/s), and a
is the angle of incidence in the waveguide.
The phase velocity is the velocity of propagation of the spot on the waveguide wall where
the wave impinges (e.g., point “B” in Figure1). This velocity is actually faster than both
the group velocity and the speed of light. The relationship between the phase and group
velocities can be seen in the “Beach analogy.” If we consider an ocean beach that waves
will arrive from offshore at an angle other than 90°, meaning the arriving wave fronts will
not be parallel to the shore. The arriving waves at V g as it hits the shore will strike a
point down the beach first, and the “point of strike” races up the beach at a faster phase
velocity, Vp, that is faster than Vg. In a microwave waveguide the phase velocity can be
greater than c.


a
A a 4 C
Vg
 g0
4

Figure 1 Wave propagation in a waveguide

Mode Cutoff Frequencies

The propagation of signals in a waveguide depends in part upon the operating frequency
of the applied signal. The angle of incidence made by the plane wave to the waveguide
wall is a function of frequency. As the frequency drops, the angle of incidence increases
towards 90°.