July 1951 Electronics
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from Electronics,
published 1930  1988. All copyrights hereby acknowledged.

Maybe in 1951 when this "CorrugatedWaveguide
BandPass Filters" article appeared in Electronics magazine, placing a
special resonating form inside a section of waveguide was a reasonable option for
creating a bandpass filter response, but it sure seems like a hard way of accomplishing
the task. As shown in the photo and illustrations, a tapered metallic block with
machined fins spaced to resonate at a predetermined frequency created a high frequency
cutoff to work in conjunction with the natural low frequency cutoff frequency to
create a bandpass combination. A quick search did not turn up any references to
such structures being used in modern waveguide bandpass filters, although they might
exist. It appears iris coupling of resonating cavities is the method du jour. I
admit to not being a waveguide expert, so do your own research on this one. If nothing
else, this is a good historical reference.
Highpass properties of a waveguide are combined with lowpass
properties of a corrugated surface in a filter designed to give a rapid transition
between pass and attenuation bands. Single corrugated element does work of several
elements in conventional designs
Section of waveguide and corrugated surface which fits into it.
By J. C. Greene, Engineer Airborne Instruments Laboratory
Rapid transition between pass and attenuation bands and a wide frequency range
free of spurious responses are desirable properties of a bandpass filter. Such
a filter can be realized readily by combining the highpass properties of a waveguide
with the lowpass property of a corrugated surface.
In a particular application a filter was designed which had a passband between
2,080 mc and 2,800 me and 70db attenuation, relative to the passband response,
at 2,900 mc. There were no responses which were not attenuated by at least 60 db
from 2,900 me to above 10,000 mc.
Because of the highpass characteristic of a waveguide, a bandpass filter can
be formed readily by incorporating a lowpass structure into the waveguide. One
such lowpass structure is the corrugated surface for which approximate field solutions
have been given in the literature^{16}.
The design considered in this paper for utilizing the corrugated surface structure
is shown in Fig. 1, where one broad face of the waveguide is replaced by a tapered
corrugated surface. Approximate solutions for the attenuation and phase characteristics
of the filter in Fig. 1 are obtained by combining design relations with a loadedline
equivalent circuit representation^{1}.
Fig. 1  Mechanical drawing of tapered corrugated surface which
replaces one face of the waveguide.
Fig. 2  Idealized passband shape. Highfrequency attenuation
at t = ∞ is provided by resonance of the slots in region C of corrugated surface
(see Fig. 1).
Fig. 3  Loaded transmission line representation of one slot
in the corrugated surface.
Fig. 4  Theoretical curves relating attenuation in db per section
and phase shift across one slot for transmission line of length 1' (see Fig. 1)
to the phase shift along the distance between two slots.
Fig. 5  Attenuation curve for actual filter constructed.
An idealized passband shape is illustrated in Fig. 2. The lowfrequency cutoff
f, is provided by the normal cutoff of the waveguide, while the highfrequency cutoff
f ∞, at which there is infinite attenuation, is provided by a resonance of
the slots in region C of the corrugated surface.
The slots in region B of the corrugated surface serve a twofold purpose. They
provide additional resonant elements in the upper rejection band (f > f ∞)
to prevent repetitive pass bands. In addition they serve as a smooth taper which
transforms the characteristic impedance of region C into the characteristic impedance
of the waveguide through the taper in region A.
Filter Characteristics
The loaded transmissionline representation of one slot in the corrugated surface
is shown in Fig. 3. The characteristic equation of the frequency spectrum relating
the phase shift Φ, across one element of the loaded line (including both the
slot and the transmission line of length
l' to the phase shift Θ
along l' between two
adjacent slots is
where a is the broad dimension of the waveguide.
Putting Φ = ß  jα and
neglecting resistive losses one obtains for the pass band (α = 0)
cos (ß + 2 n
π) = cos
θ  (Z/2Z_{0}) sin θ tan (pθ) (3)
where n = 0, ±1, ±2, etc. and in the cutoff band
(ß = 0 or
π) ± cosh
α =
cos θ  (Z/2Z,) sin (θ) tan (pθ)
where α
= attenuation in nepers per section of loaded line, (ß +
2nπ)
= phase shift per section of loaded line.
The values of n_{0} in Eq. 3 represent space harmonics of the fundamental
(n = 0) component of the wave. The positive values of n represent transmitted waves,
the negative values reflected waves. All of these components are necessary to fully
describe the propagated wave.
To simplify the analysis, the space harmonic components are neglected. This is
a valid assumption in the pass band, since the amplitudes of the space harmonics
are greatly reduced in the pass band. The assumption becomes less valid as the frequency
approaches that at which the slots become resonant.
Design relationships among the dimensions of a slot are^{5}
b'/2 <
l' < (λ_{g1})^{2}/10
(5)
b'/b < 0.1
(6)
where λ_{g1} is the guide wavelength in the unloaded section at the upper
cutoff frequency, f_{1}. It can be demonstrated that the passband resistive
losses due to a finite conductivity in the conducting surfaces vary inversely with
the quantity b'/b. This value was chosen to be as large as possible, namely 0.1.
It may be seen from Eq. 4 that an infinite attenuation occurs when pθ =
π/2. The
frequency at which this infinite attenuation occurs is f∞. However,
Hence at the infinite attenuation frequency (λ_{g}
= λ_{g}∞)
or
Eq. 7 means that at the infinite attenuation frequency, the slot depth,
(b  b') /2, equals one quarter of a guide wavelength.
The values of l
and l' are not critical
and are generally chosen to keep the overall length of the filter as short as possible.
Typical values are
l' = 2l = 0.1_{co}∞.
The value of the ratio Z/Z_{0} is taken to be 2l/b', the ratio of the slot
height to the line height.
Theoretical curves relating 4, and a in db to e are shown in Fig. 4. The curves
have been calculated for p = 2 and Z/Z_{0} = 2. At the point of infinite
attenuation, θ = 45 deg, while at the upper cutoff point θ = 36 deg. Hence
the ratio of the cutoff wavelength, λ_{g1} to the infinite attenuation wavelength,
λ_{g}∞ is λ_{g1}/λ_{g}∞ = 45
deg/36 deg = 1.25. The slot requires the cutoff wavelength to be decreased
by 25 percent before its attenuation becomes infinite.
Referring to Fig. 4, representing the characteristics of the slots in region
C of the filter, it can be seen that repetitive pass bands will occur. The first
repetitive pass band occurs when λ_{g} = λ_{g1}/2. To avoid this
pass band as well as higher ones, it is necessary to include slots in region B of
the filter which will resonate in the vicinity of the higher passbands. In general,
this condition is fulfilled merely by having a reasonable length of taper.
Design Procedure
The filter can be easily incorporated as an inserted section in a waveguide,
with waveguide input and output. It can also be incorporated into a coaxial line
through the use of waveguide to coaxial transformers. The transforming sections
form the input and output of the filter.
The lowfrequency cutoff determines the wide dimension of the waveguide, a, and
is simply related to it by
λ_{c}= 2a
Generally, both the upper cutoff frequency f_{1} and a minimum
attenuation at a point between f_{1} and f∞ are
specified. Once these are known, the slot depth and number of slots in region C
can be determined. First a is calculated from the highfrequency cutoff f,
by Eq. 2. Because λ_{g1}/ λ_{g}∞
= 1.25, λ_{g}∞ may be readily found. The slot depth is then made
equal to λ_{g}∞/4.
The number of slots required is the desired attenuation in db at some frequency
between f_{1} and f∞ divided by the attenuation of one
slot at that frequency as determined from Fig. 4.
The lengths of the tapered sections in regions A and B should be about equal
and as long as possible for the best match. A theoretical curve relating the vswr
introduced by a taper as a function of its length has been given by Frank'. From
this curve and a consideration of the variation in guide wavelength in the pass
band, a value giving small mismatch reflections over the entire pass band is found
to be 1.5 λ_{c} or 3a.
Experimental Results
An experimental curve for the filter based on the previous design considerations
is given in Fig. 5. The corrugated surface was designed to be inserted in standard
1.5 by 3in. waveguide having a cutoff frequency of 2,080 mc. The desired upper
cutoff frequency was 2,800 mc (λ_{g1} = 16.0 cm.) This gives the infinite
attenuation frequency as 3,200 mc (λ_{g}∞ = 12.8 cm). It was also
desired to have at least 70 db of attenuation at 2,900 mc (λ_{g} = 15.0
cm).
Because λ_{g1} corresponds to θ = 36 deg. on the curve of Fig.
4, at λ_{g} = 15.0 cm, θ = 38.4 deg. From Fig. 4, the attenuation in db
per slot at θ = 38.4 deg is 9 db. Hence eight slots in region C should be sufficient
to give the desired attenuation. Actually ten slots were used because the attenuation
of a slot will be slightly less than shown in Fig. 4 due to resistive losses in
the slot. The passband loss, averaging approximately 2.5 db, is a combination of
resistive loss in the slots and mismatch loss in the tapers.
Higher Order Modes
In the above analysis it was assumed that only the dominant mode TE_{1,0}
is propagated. For the usual waveguide dimensions (broad face twice as wide as the
narrow face) higherorder modes may be propagated at frequencies greater than twice
the normal cutoff frequency. If these higherorder modes are propagated, spurious
responses may appear in the rejection band.
Because of the symmetry of the filter, only TE_{1,2n} (n = 0,1,2, ...)
and TM_{1,2n} (n = 1,2,3, ...) modes can be excited within the filter itself^{4}.
The first of these modes, the TE_{1,2} and the TM_{1,2} will not
be propagated for frequencies less than four times the normal cutoff frequency.
In general this is far enough into the rejection band to be of little consequence.
Should higherorder modes, such as the TE_{2,0}, TE_{3,0} be
set up in the input section leading to the filter, they will pass through the filter
and produce narrow spurious pass bands for frequencies in the vicinity of twice
the normal cutoff frequency, three times this frequency, and so on.
At the cutoff frequency for the higher modes, the guide wavelength for these
modes is infinite and rapidly decreases as the frequency is increased. Until the
wavelength decreases to a value such that the slots in region C become resonant,
no attenuation is offered to the modes.
The higher modes can often be eliminated by careful design of the input circuit
to eliminate asymmetrical structures tending to excite the higherorder modes. They
may also be eliminated in the output section when of a special type, such as ridged
waveguide output. In this case, the ridged section is designed so that it passes
the dominant mode, but is cut off for the higherorder modes in the vicinity of
the spurious response pass bands. Compensating sections of different widths, a,
can be included in the filter proper so that they are below cutoff for the higherorder
modes over the frequency range of the spurious responses'.
References
(1) A. W. Lines, G. R. Nicoll and A. M. Woodward, Some Properties of Corrugated
Waveguides, Telecommunications Research Establishment Report No. T2114 ; reprinted
in Proc. IEE, 97, Part III, No. 48, July 1950.
(2) C. C. Cutler, Electromagnetic Waves Guided by Corrugated Conducting Surfaces,
Bell Telephone Laboratories Report No. MM44160218.
(3) H. H. Goldstein, The Theory of Corrugated Transmission Lines and Waveguides,
Rad. Lab. Report No. 494, April 1944.
(4) S. B. Cohn, Analysis of a Wide Band Waveguide Filter, Proc. IRE, 37, p 651,
June 1949.
(5) S. B. Cohn, Design Relations for the WideBand Waveguide Filter, Proc. IRE,
38, p 799, July 1950.
(6) W. Rotman, A Study of Single Surface Corrugated Guides, Air Force Cambridge
Research Laboratory Report No. E5055, Feb. 1950.
(7) N. H. Frank, Dielectric Structures in Waveguides, "Rad. Lab. Handbook," p
30, Feb. 1943.
(8) Radio Research Laboratory Staff, "VeryHighFrequency Techniques," Mc GrawHill
Book Co., New York, Section 2728, 1947.
Posted March 20, 2024 (updated from original post
on 11/18/2022)
