Radar System Engineering

400 R-F COMPONENTS [SEC.11.3
walls are also shown. At all microwave frequencies, the skin effect
confines the current to a microscopically thin layer on the inner surface.
As the dimensions of the waveguide are increased, the frequency being
fixed, propagation becomes possible by modes—that is, by particular
types of “vibration” in the electromagnetic field, other than the fundamental
mode illustrated in Fig. 11.9. Each of these higher modes has
its own characteristic electromagnetic field configuration. ordinarily
it is advisable to avoid propagation in more than one mode, and this is
most easily done by choosing the dimensions of the guide so that the
lowest mode, and the lowest mode only, can propagate. However, for
certain applications some of the higher modes are useful. A notable
example, to which we shall return later, is the second mode”in waveguide
of circular cross section. This has axial symmetry and is thus useful in
waveguide rotary joints.
For each type of waveguide there exists a critical, or cutoff, frequency
for propagation in the lowest mode. Waves of higher than critical frequent
y are transmitted; those of lower frequency are rapidly attenuated. 1
Corresponding to the cutoff frequency f. is a cutoff wavelength A, related
to f. by L = c/f. where c is the velocity of light. That is, kc refers to the
wavelength in space. For rectangular guide, as shown from the stubsupported
two-wire line, the cutoff wavelength is twice the broad dimension.
In other words, a ewide that is to transmit a wave must have a
broad dimension greater t~an half a free-space wavelength. If the width
is more than a whole free-space wavelength, a higher mode of propagation
with a node in the electric field down the center becomes possible, which
adds most undesirable complications. Therefore, the broad dimension
must lie between a half and a whole free-space wavelength. The wavelength
inside the guide is longer than that in free space and is given by the
relation:
(4)
where x is the free-space wavelength and A. is the cutoff wavelength (here
equal to twice the broad dimension). When ACis only slightly greater
than A, the guide-wavelength becomes very long and varies rapidly with
changes in X. This greatly increases the frequency sensitivity of quarterwave
sections of guide used in duplexers and mixers (Sees. 115 and 11“8)
and handicaps broadband design. The other extreme of a close approach
to the boundary of the higher mode, corresponding to a wide dimension
of nearly a whole free-space wavelength, runs into difficulty because of
1In a waveguide beyond cutoff the voltiage or current falls off exponentially with
distance, with constants exactly calculable from the dimensions and frequency. One
form of standard attenuator utilizes this fact.