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
|September 1948 Radio & TV News
of Contents]These articles are scanned and OCRed from old editions of the Radio & Television
News magazine. Here is a list of the
Radio & Television News articles
I have already posted. All copyrights are hereby acknowledged.
rectangular waveguide cutoff frequency
Thanks to Terry W. for
providing this article.
available vintage Radio
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!
To anyone 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
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
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 in farads.
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.
The 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 space.
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.
Fig. 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 characteristic.
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 guide.
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 power 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 instrument.
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 diameter.
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
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 adjustment.
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.
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