is a great treatise on waveguide theory put in layman's language.
Although written in 1948 at a time when microwave frequencies were
just coming into common use, the language and descriptive drawings
are similar to what you will find in modern textbooks. Waveguide
is not practical for use at lower frequencies because the physical
dimensions prohibitively large. For instance, for the FM radio band
(88-108 MHz), waveguide width for a TE10 cutoff
frequency at 88 MHz is around 67.5 inches. According to
Wikipedia, the first waveguide was proposed by
J. J. Thomson in 1893 and experimentally verified by
Oliver Lodge in 1894.
waveguide cutoff frequency formula.
Thanks to Terry W. for providing this article.
Microwave Plumbing Replaces Circuitry
By Samuel Freedman and DeMornay Budd
basic microwave transmitter in its simplest form need be no more
than a tube and some microwave plumbing or pipe!
whose past association with radio has been with frequencies below
about 1000 megacycles, microwaves are unique in every respect. The
basic difference between lower radio frequencies and microwaves
is that inductive and capacitive effects are utilized in lieu of
coils and condensers. It is achieved by direct action on the magnetic
and electric fields through the use of special structures such as
simple pipes (called wave guides) of suitable shape and dimension.
This is both a necessity and an advantage for microwaves.
At conventional radio frequencies, the physical dimensions of
inductance in the form of coils or conductors, and of capacitance
in the form of condensers are specially provided or "lumped." Their
physical size is very small with respect to the operating wavelength.
At microwave radio frequencies the physical dimensions of
any conductor or condenser are large with respect to the wavelength
involved. So little inductance and capacitance is required that
the circuit may work best, or only, when "distributed" rather than
lumped inductance and capacitance is provided. This may be little
more than that represented by the electrodes, their separation,
and the connections to the vacuum tube.
No wire is efficient
in conducting energy at extremely high a.c. frequencies as represented
by ultra or super high frequencies. Instead the wire behaves like
an a.c. insulator even though at d.c. or low radio frequencies it
is an excellent conductor. The reactance or a.c. impedance of any
wire or coil increases with increase of frequency. Specifically,
it must increase because the inductive reactance in ohms is always
equal to: 6.2832 x frequency in cycles x inductance in henrys.
Conversely, no condenser is efficient in blocking a.c. energy
at extremely high a.c. frequencies because it behaves like a virtual
short-circuit or conducting path at microwave frequencies. This
is true even though d.c. or low radio frequencies are effectively
blocked or isolated by the same condenser. The reactance or a.c.
impedance across a condenser decreases with increase of frequency.
Specifically, capacitive reactance in ohms must decrease since it
is always equal to: 1/6.2832 x frequency in cycles x capacitance
The fact that inductance behaves like an insulator
instead of a conductor, and capacitance behaves like a short circuit
or conducting path instead of an r.f. block, requires that energy
be propagated rather than conducted from point to point even in
the case of very short distances within an equipment.
concept now is that d.c. is really a.c. at zero cycles or infinite
wavelength. As the a.c. frequency increases from zero, a conductor
steadily decreases in its ability to conduct a.c. while a condenser
increases. The result is a reversal in radio concepts as the frequencies
reach into the microwave region.
While propagation of microwave
energy in free space is quite conventional for direct paths, it
is only during the past few years, even experimentally, that it
has been utilized within the equipment itself or for the antenna
transmission line system. This propagation technique is achieved
by the use of wave guides. Wave guides are simple pipes, usually
rectangular, in which one wall simulates the ionosphere and the
other wall simulates the earth. The concept is comparable to sky
wave propagation on low frequencies in free space. A quarter-wave
dipole (miniature at microwaves) at the points of introducing and
of extracting the energy may be compared with the transmitting and
receiving antennas for lower frequency radio operations in free
Fig. 2. - Physical evolution of a rectangular
Fig. 2 shows the physical evolution of a wave guide. Fig.
2A shows two wires of any length. It may correspond to the open
line shown in Fig. 5. Fig. 2B shows a quarter wavelength shorted
line corresponding to the first 90 degrees for the shorted line
in Fig. 5. Fig. 2C shows the quarter-wave short of Fig. 2B attached
to the open line of Fig. 2A. Note that the point of attachment is
the point of maximum impedance for a shorted line a quarter wavelength
removed from the short. The current will be zero while the voltage
will be maximum at that point. Remember that there is only a.c.
sine wave behavior to consider and dimensions are being held correct
for the frequency and the wavelength. Fig. 2D shows the same type
of quarter-wave short on the opposite side of the parallel wires.
Fig. 2E shows the closed loop formed by Figs. 2C and 2D combined.
Although it is a d.c, short, it is an open circuit for a.c. because
it offers maximum impedance at the point of attachment by virtue
of the fact that each shorting section is a quarter wavelength long.
A sine energy wave that is maximum at one point will be minimum
a quarter wavelength removed. These shorts are really "metallic
insulators" much more nearly a perfect insulator than any conventional
ceramic insulator could ever be with respect to either d.c. or a.c.
Fig. 2F shows a number of loops like that depicted in Fig. 2E. Fig.
2G shows the end result when there are an infinite number of loops
so closely spaced that they become a solid pipe.
3 shows the energy distribution in a wave guide or rectangular pipe.
It is necessary to forget the usual conduction principle where a
wire carrying a.c. has an associated varying magnetic field encompassing
it; or where a varying magnetic field cutting the wire, induces
a voltage across the terminals of such a wire. Instead, it is necessary
to think of the displacement current principle which requires no
wire to carry the energy. It operates on exactly the same principle
that electromagnetic waves propagate in free space from a transmitting
antenna to a receiving antenna without a physical link between them.
The displacement technique operates on the principle that a dielectric
or empty space can be substituted for a wire or coil. If the width
of the wave guide exceeds a half wavelength and does not exceed
a full wavelength in diameter, the wave guide operates on its dominant
mode (known as TE0,1)
and there will be an energy distribution as shown in Fig. 3. The
dominant mode indicates the lowest frequency possible to develop
in a wave guide. When the dominant mode is known as TE0,1
(the most common type encountered in practice), it means transverse
electric type with the electric field component in the wave guide
perpendicular to the axis of the guide. It has no electric component
along the length or long axis of the wave guide. 0,1 or 1,0 means
that there is one half-wave pattern of electric lines across the
cross section of a wave guide along one dimension while there is
zero half-wave patterns of electric lines across a dimension at
right angles to the first, or vice versa. Note particularly, the
following details in Fig. 3:
1. The voltage cancels out
at the side walls to equal a total of zero shown by plus and minus
meeting at the boundary.
2. The electric field at the center
of the wave guide diameter (equidistant from the boundary walls)
adds rather than cancels out (plus and plus or minus and minus meet)
to result in a sine wave energy distribution as illustrated. This
is a simplified form of "Poynting's Vector" to facilitate a graphic
portrayal of how the electric component must be zero at the boundaries
and maximum between the boundaries but varying in a sinusoidal manner.
If the wave guide diameter is doubled for a given wavelength, or
if the wavelength is halved for a given diameter wave guide, then
in this example, there would be a TE2,0
or TE0,2 mode in which
two parallel sets of the pattern illustrated in Fig. 3 would exist.
TE3,0 would mean that
the wave guide diameter exceeds a wavelength and a half, etc. To
avoid multimoding with the energy divided between these different
modes or energy patterns, the wave guide diameter must be less than
a wavelength. Multimoding may be used where it is not feasible to
shrink the wave guide size or lower the frequency. In such event,
care must be taken not to couple at a zero energy point.
3. A magnetic field (shown by dotted circular lines) corresponds
to the field which would exist around a wire if an electric current
were flowing in same. It is distorted to square circles because
the wave guide is rectangular in shape. The field alternates in
direction each half wavelength in accordance with the sinusoidal
4. Energy may be introduced or extracted
most efficiently if a quarter-wave dipole protrudes into the wave
guide at any point where the electric field is maximum plus or minus
in the illustration.
5. Energy may also be introduced or
extracted, alternately or optionally, if a small loop is provided
in the center of the narrow side of the wave guide pipe so that
it couples to the magnetic field. It is immaterial whether a. dipole
is used with the optimum position of the electric field or if a
loop is used with the optimum position of the magnetic field.
Fig. 3. - Energy distribution in a rectangular wave guide operated
at the dominant or TE0,1
Fig. 4 compares propagation in a wave guide pipe on microwaves
with that of the ionosphere and the earth from a lower frequency
transmitting station. There is little difference between a low frequency
radio station propagating long waves in the many miles separation
between the earth and .the ionosphere, and a microwave transmitter
propagating miniature waves between the two walls of a small pipe.
The wave guide pipe will be more efficient and stable since its
walls, of good electrical conductivity, facilitate reflection and
it is free of changes in dimension due to night and day, seasons
or sunspot cycles. The pipe dimensions should be 3" x 1 1/2" at
3000 megacycles, dropping to 1/2" 1/4" at 30,000 megacycles.
To propagate energy in a wave guide, it must be below cut-off
dimension in wavelength or above cut-off dimension in frequency.
If the wave guide dimension in Fig. 4A is less than a half wavelength,
energy cannot enter or be accommodated. If it is at "cut-off" or
exactly a half wavelength the energy can be accommodated as illustrated
in Fig. 4A but it will not make propagational progress down the
wave guide's longitudinal axis. Attenuation will be total as the
energy will bounce back and forth at one spot, undergoing a loss
each time it reflects at a wall. If the wave guide is more than
a half wavelength in width, as in the case of Fig. 4B, the energy
will make progress at some angle, as shown. The attenuation will
go down since there will be less points of contact for reflection
to the opposite wall or boundary. If the wave guide width is further
increased, the reflecting angle will increase so there will be still
less points of contact, further reduction in attenuation losses
and greater efficiency in propagation of energy down the wave guide.
Fig. 4. - Free space propagation versus propagation in a wave
Fig. 4B might be compared with sky wave propagation at medium
frequency while Fig. 4C might be compared with sky wave propagation
at high frequency as commonly known for standard and shortwave broadcasting
or for amateur radio communication. The principle is similar. The
velocity of energy in a wave guide is less than it is in free space
for direct path communication. It cannot be 186,000 miles-per-second
because the energy takes a zigzag path. Its velocity would only
be comparable if it did not have to reflect from wall to wall. It
is zero at cut-off (Fig. 4A) and increases as the angle widens out
in Fig. 4C. Think of it as 186,000 miles-per-second along the zigzag
route illustrated with actual velocity from one end to the other
end of the wave guide being its resultant straight line distance.
It is comparable to a caterpillar whose wiggles appear to move faster
than the progress it is making over the ground.
handling capacity of a wave guide is much greater than is possible
with any practical size conductor. At 3000 megacycles, the 3" x
1 1/2" wave guide can handle over 3,000,000 watts of energy without
arc-over between the narrow wall dimensions. Only two opposite surfaces
of the wave guide are required. The other two are merely for keeping
the parallel surfaces properly spaced. The ionosphere and the earth
may be considered as "Nature's wave guide" while the pipes may be
called "fabricated wave guide."
Fig. 5. - Inductive and capacitive effects in a two-wire line
or wave guide. (sorry for the lousy image)
Fig. 5 shows how wave guide pipe replaces inductance, capacitance,
parallel resonant LC or series resonant LC circuits. By moving a
dipole probe back and forth through a slit in the wave guide wall,
it behaves like a tunable or variable inductance or capacitance.
The behavior of an open-ended and shorted line is identical except
that they duplicate their phenomena a quarter-wave length or 90
electrical degrees removed from each other.
The net result
is that the basic microwave transmitter, in its simplest form, need
be no more than a vacuum tube and a piece of microwave plumbing
or pipe as illustrated in Figs. 1 and 6. This is the same technique
developed by Fonda and Freedman which was discussed in the article
"Generating Microwaves" in the March, 1947 issue of RADIO NEWS.
This particular unit uses a Type 6V6 operating at a choice of frequencies
in the vicinity of 2860 megacycles. In this illustration energy
coupled by a loop through the wave guide cavity hole shown in Fig.
6 is fed through a calibrated wave guide attenuator to an indicating
The same phenomena and results possible at microwave
frequencies may also be realized at any frequency or wavelength
as long as the physical requirements prove feasible, and can be
utilized. For example, a complete set of events (half wavelength)
involves dimension of .2 inch at 30,000 megacycles (1 centimeter
wavelength.) The dimension would have to be 20 inches at 300 megacycles
(1 meter wavelength). In the broadcast band, at 1000 kilocycles,
the dimension would be 500 feet. This statement can be readily appreciated
by anyone using an automobile radio on the highway. When the vehicle
goes into a tunnel or underpass (even for a few feet), the signal
goes dead on the broadcast band while working normally on very high
frequencies (such as two-way mobile radio) and still better on microwaves.
Microwaves are incomparable for operation in subways or tunnels.
Every tunnel, underpass, sides of steel bridges, walls between two
sides of a street, two sides of a gorge or canyon etc., forms a
wave guide. Energy propagates best there, if at all, when it can
accommodate more than a half wavelength for the equivalent of its
Table 1. - Data shown indicates various
conditions for shorted and open lines. Reference should be made
to Fig. 5 for details on points "a", "c", "e", "g" and "i".
The phenomena possible to develop
with simple plumbing or mere pipe on microwaves, therefore, make
possible results that on lower radio frequencies always require
coils, condensers, transformers, resistors, and insulators. These
can be eliminated on microwaves by utilizing the inversion, capacitive,
inductive, and transformation effects existing along some quarter
wavelength of any overall half wavelength for either an open or
a shorted line. The impedance in a wave guide may be anything from
virtual zero to virtual infinity somewhere along its length. For
example, in Fig. 5, there are spotted the conditions and behaviors
of Table 1. Any values between those indicated can be developed
at intermediate distances.
The possibilities for using wave
guides are as numerous as applications for the vacuum tube. Both
are limited only by human imagination and ingenuity. It only requires
that dimensional relationships be correct for the frequency or wavelength
employed and the electric and magnetic fields be coupled at the
correct point or points for energy introduction or extraction.
The applications tor microwaves today are:
Fig. 6. - Dismantled view of equipment in Fig. 1. showing a
conventional receiving tube used to generate microwaves. The
fundamental and harmonic frequencies are masked out because
the wave guide dimension is below cut-off for frequencies below
about 2800 megacycles. The tube operates at transit time equal
to seven periods of oscillation for generating 2860 megacycles
in this case. It may be varied by electrode voltages or physical
11. Radar where
distant objects much larger than the wavelength effectively reflect
sufficient energy back to the transmitting source to give indications
of distance and direction on a calibrated cathode-ray tube substituted
for a loudspeaker.
2. Communications and Relay systems where
directivity, channel availability, exceptional bandwidth or privacy
are desired. It is particularly valuable tor channels of exceptional
bandwidth as required for broadband FM, pulsed or contrast (television)
forms of modulation.
3. Microwave Spectroscopy for absorption
studies of gases and liquids too rarefied for analysis by the x-ray
or the electron microscope. The individual molecules of gases or
liquids are sufficiently large in size with respect to the small
wavelengths on microwaves to affect the latter ropagational characteristics
in a wave guide. This can be translated into useful scientific
or technical information in medical and industrial research.
At the present time, communications and relay systems utilize
the lower microwave frequencies while radar utilize the medium microwave
frequencies and microwave spectroscopy utilizes the highest microwave