Radar System Engineering

SEC. 11.4] RESONANT CAVITIES 405
could be used for the wavelength carried by the waveguide. Since, however,
the distortion of the normal field by the stub supports of the coaxial
line makes it impossible to realize the calculated limit, the factor of two
does not represent the full superiority of waveguide. In either waveguide
or coaxial line, small nicks, burrs, or solder fillets can easily cause breakdown
at a fifth of the calculated maximum power. Table 11.1 summarizes
the properties of the waveguides widely used in microwave radar,
and for comparison those of some standard coaxial lines and cable.
Attenuation in waveguide is seen to be about half that in the largest
coaxial line suitable for a given wavelength. For smaller coaxial lines
of a given impedance the attenuation is inversely proportional t6
diameter. The conclusion to be drawn is that waveguides are superior
electrically to coaxial line in nearly every respect. They are easier to
fabricate because the inner conductor and its precisely machined stub
supports are simply omitted. For these reasons, waveguide is almost
universally used for wavelengths below 8~cm. In the lo-cm region where
the size and weight of the Ii- by 3-in. waveguide are awkward and the
power-carrying capacity is not needed, coaxial line is frequently used.
For ‘(long wave” radars (wavelengths of 50 cm and greater) wave guide
is never used because of its relatively enormous size.
11.4. Resonant Cavities.-If both ends of a waveguide are closed
by a short-circuiting plate, and energy is introduced by a probe so small
that it does not appreciably change the properties of the enclosure, the
amplitude of the standing-wave pattern in the waveguide will show a
sharp maximum when the frequency is such that the length of the
enclosure is an integral number of half guide-wavelengths. The reflections
will then be in the proper phase to reinforce each other and cause a
resonant buildup. (This is the property used in wavemeters.) For
standard rectangular guide, reference to Eq. (4) shows that if the broad
dimension is taken to be 0.707~ then half a guide-wavelength is also
0.707A. The shortest resonant piece of such a waveguide is therefore
square. The height does not affect the resonant wavelength, though if
it is greater than A/2, modes polarized at right angles to the desired mode
become possible. Rounding off the corners of the square box shortens
the resonant wavelength slightly; exact calculation shows that for a
cylindical box the resonance occurs when X = 1.30 times the diameter, as
opposed to 1.41 times the side of the square.
These round and square boxes are examples of resonunt cam”ties, which
play the same role in microwave transmission circuits as do resonant circuits
involving lumped inductance and capacity in traditional circuit
theory. Any hollow metal enclosure is capable of supporting oscillations
in a large number of modes. In practice the geometry is usually chosen
so only a single mode, often the lowest, is excited.
For simple geometn-