Corrugated ridge waveguide phase shifting structure

A differential phase shifting structure is disclosed, employing corrugated ridges in square or round waveguides or in coaxial lines operating in the TE.sub.11 mode. The structure provides a substantially constant differential phase shift between two waves polarized orthoganally to each other. The corrugations in the ridge provide a series inductance which can be optimized with the shunt capacitance of the ridge to provide a characteristic impedance matching that of the unloaded structure. The corrugated ridges provide increased differential phase shift per unit length. The differential phase shifting structure is particularly well suited to such applications as circular polarizers, quarter wave plates or polarization rotating half-wave plates.

BACKGROUND OF THE INVENTION 
The invention relates to microwave phase shifting structures, and more 
particularly to wave transmission structures providing differential phase 
shift between two waves polarized orthoganally to each other. 
Structures providing differential phase shift between two orthogonal linear 
polarizations have a variety of applications. The most common application 
is for circular polarizers in which the differential phase shift is 
90.degree. (quarter-wave plate). A differential phase shift of 180.degree. 
(half-wave plate) is used as a polarization rotator for linear 
polarization and as a phase shifter for circular polarization, e.g., Fox, 
A. G., "An Adjustable Waveguide Phase Changer," PROC. IRE, Vol. 35, No. 
12, pp. 1489-1498, December 1947. In conjunction with orthopolarization 
mode transducers they can be used as power dividers. These structures may 
also be used for a single polarization as fixed phase shifters. 
Conventional differential phase shift structures are understood to employ 
periodic lumped or distributed shunt capacitive or periodic lumped or 
distributed shunt inductive loading in the differential phase shift region 
which is inherently mismatched with the unloaded waveguide; hence an 
impedance matching section is required at each end of the phase shift 
section. One conventional design is illustrated in the paper "Phase Shift 
by Periodic Loading of Waveguide and Its Application to Broad-Band 
Circular Polarization," by A. J. Simmons, IRE Transactions, Microwave 
Theory and Techniques, December, 1955, pages 18-21. Other designs are 
illustrated in "Microwave Transmission Circuits," edited by George L. 
Ragan, MIT Rad. Lab Series Volume 9. FIGS. 6.59-6.63 illustrate various 
configurations employing shunt capacitive fin loading for a quarter-wave 
plate circular polarizer, shunt inductive loading in a quarter-wave plate 
circular polarizer, and an array of shunt capacitive posts in a 
differential phase shift section. FIG. 6.69 illustrates two designs 
employing capacitive dielectric slabs. 
However, none of these prior methods use shunt capacitive and series 
inductive loading in the same structure and in the proper ratio to achieve 
impedance matching to the unloaded waveguide and at the same time achieve 
greater differential phase shift per unit length, thus obviating the need 
for impedance transformers at each phase shift section. 
It would therefore be advantageous to provide a structure for achieving a 
differential phase shift between two waves polarized orthogonally to each 
other, and which is impedance matched between the unloaded waveguide and 
the phase shifting section for both components of polarization. Such a 
structure would not require impedance transformer sections at each end of 
the phase shift section, thereby reducing the overall length and 
complexity of the structure. 
It would further represent an advance in the art to provide an easily 
fabricated, differential phase shift per unit length structure which 
provides a relatively large differential phase shift per unit length, with 
low insertion loss over a relatively large bandwidth. 
SUMMARY OF THE INVENTION 
A wave transmission structure is disclosed which provides a relatively 
large differential phase shift per unit length between two electromagnetic 
waves polarized orthogonally to each other. In accordance with the 
invention, two elongated conductive ridge members are oppositely disposed 
along at least a portion of the wave transmission structure, with a series 
of lateral corrugations defined along the extent of the ridge members. The 
corrugations have a depth of less than one quarter of the wavelength of 
interest and provide a means of loading the wave transmission structure 
with a series susceptance. The magnitude of the series susceptance is 
dependent on the depth and spacing of the corrugations in the ridge 
members. The ridge members also provide a shunt susceptance whose 
magnitude per unit length is dependent on the height and width of the 
ridge members. The respective series and shunt susceptance are adjusted by 
appropriate selection of the ridge and corrugation parameters so that the 
characteristic impedance of the loaded section of the wave transmission 
structure matches that of the unloaded section. With the series and shunt 
susceptive loading, the structure provides a relatively large differential 
phase shift per unit length.

DETAILED DESCRIPTION OF THE DISCLOSURE 
The present invention comprises a novel corrugated ridge waveguide phase 
shifting structure. The following description is presented to enable a 
person skilled in the art to make and use the invention, and is provided 
in the context of a particular application and its requirements. Various 
modifications to the preferred embodiment may be apparent to those skilled 
in the art. Thus, the present invention is not intended to be limited to 
the embodiment shown, but is intended to be accorded the widest scope 
consistent with the principles and novel features disclosed herein. 
To facilitate an understanding of the invention, it is helpful to refer to 
the schematic illustration in FIG. 1, representing the equivalent circuit 
of a waveguiding structure or transmission line. The equivalent circuit 
comprises cascaded series inductances L and shunt capacitances C. The 
characteristic impedance Z.sub.o and the phase velocity v are related to 
the series inductance L per unit length and the shunt capacitance C per 
unit length by the expressions of Equations 1 and 2. 
EQU Z.sub.o .about.(L/C).sup.1/2 (1) 
EQU v.about.(LC).sup.-1/2 (2) 
The phase change per unit length (.beta.) is related to the R.F. frequency 
F and the phase velocity, as well as the series inductance L and shunt 
capacitance C, by the expressions of Equations 3 and 4. 
EQU .beta.=.omega./v (3) 
where .omega.=2.pi.F 
EQU .beta..about..omega.(LC).sup.1/2 (4) 
If the series inductance L and the shunt capacitance C are changed by the 
same ratio, the characteristic impedance Z.sub.o would not change, but the 
phase change per unit length (.beta.) would change in proportion to the 
square root of the product of the series inductance L and the shunt 
capacitance. 
In accordance with the invention, corrugated ridges are employed in the 
phase shift waveguide structure which increase the series inductance L and 
shunt capacitance C over that of the unridged waveguide for waves with the 
electric field polarized parallel to the plane of the ridge. For waves 
with the electric field polarized perpendicular to the ridges, the ridges 
have much less effect on either the characteristic impedance or the phase 
shift per unit length of the unloaded waveguide. 
The net result is a differential phase shift between waves polarized 
parallel to the ridges and waves polarized perpendicular to the ridges. 
The differential phase shift is given by Equation 5. 
EQU .DELTA. phase=(.beta..sub.11 -.beta..sub.1)l, (5) 
where l is the length of the phase shift section, .beta..sub.11 is the 
phase shift per unit length for waves polarized parallel to the ridge, and 
.beta..sub.1 is the phase shift per unit length for waves polarized 
perpendicular to the ridge. 
The characteristic impedance presented by the phase shift section to the 
respective orthogonally polarized waves will be the same, if the ratio L/C 
remains the same. This will be the case if the relationship of Equation 6 
is maintained. 
EQU L.sub.1 /C.sub.1 =L.sub.11 /C.sub.11 =L/C (6) 
where L.sub.1, L.sub.11, C.sub.1, C.sub.11 represent the series inductance 
and shunt capacitance presented to waves having their electric fields 
respectively polarized perpendicular and parallel to the ridges. 
The magnitude of the shunt capacitance is controlled by the height and the 
width of the ridge. The series inductance is controlled by the depth of 
the corrugation (D) and the characteristic impedance of the corrugation 
gap (Z.sub.ogap). If the depth D is less than a quarter wavelength, a 
corrugation provides a series inductance L proportional to the number of 
corrugations per unit length and to (Z.sub.ogap) (tan .beta..sub.gap D), 
where Z.sub.ogap is the characteristic impedance of the gap and 
.beta..sub.gap is the propagation constant of the gap. 
The advantages of corrugated ridge structures employing the invention over 
the conventional designs referred to above result from several factors. 
The corrugated ridge structures allows control of the series inductance 
per unit length as well as the shunt capacitance. The ratio of the series 
inductance and shunt capacitance can be controlled to effect an impedance 
match to the unridged waveguide. The capability to adjust the series 
inductance results in greater versatility in applying the invention to a 
particular application to achieve lower insertion loss, larger phase shift 
per unit length, and broader bandwidth. 
Conventional designs using only shunt susceptances are inherently 
mismatched to the unloaded waveguide, and hence require matching 
transformers at each end. The corrugated ridge design is shorter than the 
convention designs providing the same amount of differential phase shift 
for two reasons. Because the corrugated ridge design allows for 
characteristic impedance matching, smaller impedance matching sections are 
required. Also, the corrugated ridge design provides greater phase change 
per unit length because both the series inductance L and shunt capacitance 
C contribute to the phase shift by the square root of their product. 
Referring now to FIGS. 2-4, an exemplary embodiment of a phase shifting 
structure employing the invention is illustrated. This embodiment is a 
millimeter wave circular polarizer 5 in coaxial waveguide, operating in 
the TE.sub.11 mode. The coaxial waveguide comprises an outer conductor 10 
and an inner conductor 15 concentrically disposed inside the outer 
conductor 10, both of circular cross section. In accordance with the 
invention, corrugated ridge members 20, 30 are formed on and extend 
symmetrically outwardly in opposing directions from the center conductor 
15. The corrugations 25 have a width T, a spacing G and a depth D. Each 
ridge 20 and 30 has a total height H and a width W. In this embodiment, 16 
corrugations per unit wavelength in the coaxial waveguide are formed in 
each ridge (See FIGS. 3 and 4). 
In general, the differential phase shift per unit length is increased as 
the number of corrugations is increased. Thus, while a structure embodying 
the inventions may have some utility when only a few, for example, five 
corrugations per unit length are employed, the advantages of high 
differential phase shift are believed to be provided when many 
corrugations (ten or greater) per unit length are employed. 
For a wave with electric field polarization parallel to the ridged sections 
20 and 30, i.e., E.sub.11 as shown in FIG. 3, the loading provided by the 
ridges 20 and 30 5 is capacitive. If the depth D of the corrugations is 
less than a quarter wavelength, the corrugated ridges 20 and 30 also 
provide a series inductive loading. By proper choice of the ridge 
dimensions, the characteristic impedance in the phase shifting section 40, 
determined by the square root of the ratio of the inductance L per unit 
length and the capacitane C per unit length (L/C), can be made equal to 
the characteristic impedance of the unridged waveguide sections 45, 
thereby achieving a characteristic impedance match between the unridged to 
ridged waveguide sections. For this condition, the phase velocity in the 
ridged section 40 will be reduced in proportion to the square root of the 
product of the shunt capacitance C per unit length and the series 
inductance L per unit length. 
For electric field polarization orthogonal to the ridge, i.e., E.sub.1 as 
shown in FIG. 3, the effect of the corrugated ridges 20, 30 on the phase 
velocity is minimal, and the characteristic impedance is very nearly the 
same as the unridged sections of the waveguide 45 if the ridge is thin, 
i.e., if the ridge width W is relatively small in relation to the width of 
the outer waveguide conductor in the same region. 
As described above, the net result is that the device 5 provides a 
differential phase shift between waves with the electric field polarized 
parallel to the corrugated ridge and waves with the electric field 
polarized orthogonal to the ridge, and also presents an impedance match 
for waves of both polarizations. Thus, impedance matching structures are 
not required when the ridge is relatively thin. Moreover, the device 5 
provides a larger differential phase change per unit length than with 
conventional uncorrugated ridges. 
To provide the circular polarization function, the differential electrical 
length of the differential phase shift section 40 is equal to one quarter 
of the wavelength. The differential phase shift (.DELTA. phase) provided 
by a quarter wavelength differential electrical length is 90.degree.. The 
appropriate length of the phase shift section for a particular frequency 
and a given corrugated ridge design may be determined from Equations 1-5. 
It is to be noted that while the exemplary embodiment depicted in FIGS. 2-4 
illustrates the application of the invention to coaxial waveguides 
operating in the TE.sub.11 mode, the technique can be applied to other 
configurations as well, such as round or square waveguide. This exemplary 
device represents an application which presents difficulties to 
conventional designs, since it is generally more difficult to design a 
polarizer in higher order mode coaxial line than in dominant mode 
waveguide. Moreover, the mechanical tolerances are quite critical for 
millimeter wave applications. 
Measurements on the device 5 illustrated in FIGS. 2-4 and having the 
dimensions indicated in Table 1, indicate that, over about a 10% frequency 
bandwidth, the device 5 exhibits a differential phase shift that deviates 
from the ideal 90.degree. by less than .+-.3.degree. and a power 
reflection of less than 1%. 
TABLE 1 
______________________________________ 
Outer conductor diameter: 
1.12 mm (.439 inches) 
Inner conductor diameter: 
.54 mm (.212 inches) 
Ridge width W: .06 mm (.025 inches) 
Corrugation depth D: 
.11 mm (.045 inches) 
Corrugation spacing G: 
.005 mm (.019 inches) 
Corrugation width T: 
.005 mm (.019 inches) 
Ridge height H: .015 mm (.060 inches) 
Length of corrugated section 40: 
101 mm .399 inches 
______________________________________ 
Useful results are also obtained with devices employing wider ridges, e.g., 
as wide as the center conductor. An exemplary device 5a employing wide 
ridges 20a and corrugation 25a within an outer conductor 10a is shown in 
FIGS. 5 and 6. Exemplary electric field lines are depicted in FIG. 5, 
illustrating the TE.sub.11 mode of operation for this embodiment. In this 
embodiment, the width W of the ridges 20a, 30a is the same as the diameter 
of inner conductor 15a, as shown in FIG. 5. It is simpler to employ this 
ridge width because it is easier to mill flat sides on circular 
corrugations which have been turned on a lathe than to mill a thin 
corrugated ridge on a cylindrical center conductor. 
With the wide ridge embodiment of FIGS. 5 and 6, the impedance matching is 
degraded from the structure employing thin ridges, and it may be useful to 
employ short impedance transformers. Because a quarter wavelength in the 
corrugated media is shorter than that of the unloaded waveguide, these 
transformers are quite short. This composite length of the phase shifter 
employing wide ridges with the impedance transformer is still shorter than 
the conventional phase shifter structure employing solid ridges. Due to 
packaging constraints in some applications, the length of the structure is 
an important characteristic. 
Another embodiment of the invention is illustrated in FIGS. 7 and 8. In 
this structure 60, the corrugated ridge members 70, 75 are disposed in a 
circular waveguide 65 in a diametrically opposed relationship to define a 
differential phase shifting section 76. Exemplary field lines depicting 
the TE.sub.11 mode of operation for this embodiment are shown in FIG. 7. 
FIGS. 9 and 10 depict another embodiment of the invention which is suitable 
for dual frequency operation. The dual frequency structure 80, is suitable 
for use in a dual frequency RF system. The structure 80 comprises a hollow 
outer conductor 81 and a hollow inner conductor 82 disposed concentrically 
within the outer conductor 81. Corrugated ridges 83 and 84 are disposed in 
a diametrically opposed relationship on the inside surface of the outer 
conductor 81 to form a first differential phase shifting section 87. 
Similarly, the corrugated ridges 85 and 86 are disposed in a diametrically 
opposed relationship on the inner surface of the inner conductor 82 to 
form a second differential phase shifting section 88. Exemplary electric 
field lines are shown in FIG. 9, depicting the TE.sub.11 mode of operation 
for this embodiment. 
The annular region between the conductors 81 and 82 may be used to conduct 
a signal whose frequency is within a first frequency band and provide a 
differential phase shift to the first signal. The cylindrical region 
within the inner conductor 82 may be used to conduct a second signal whose 
frequency is within a second frequency band which is higher than the first 
bandwidth. Thus, the structure 80 is a dual frequency, differential phase 
shifting structure. The dimensions of the respective corrugated ridge 
pairs 81-82 and 83-84 are selected to provide the desired respective first 
and second differential phase shifts. With the inner conductor 82 carrying 
a high frequency wave than the outer conductor 81, the relative dimensions 
of the corrugated ridges 85, 86 are scaled down from the dimensions of the 
corrugated ridges 83, 84, as will be apparent to those skilled in the art. 
FIGS. 11-12 depict another embodiment of the invention. This embodiment is 
similar to the dual frequency, differential phase shift structure shown in 
FIGS. 9-10, except that no corrugated ridges are disposed within the 
hollow inner conductor. Thus, the structure 90 comprises a hollow 
cylindrical outer conductor 91 and a hollow cylindrical inner conductor 
92. Corrugated ridges 93 and 94 are disposed on the inner surface of the 
outer conductor 91 in a diametrically opposed relationship to define a 
differential phase shift section 95 (FIG. 12) in the annular region 96 
between the inner and outer conductors 91 and 92. As with the embodiments 
depicted in FIGS. 2-10, this coaxial wave transmission structure operates 
in the TE.sub.11 mode, illustrated by the electric field line depicted in 
FIG. 11, as opposed to the usual TEM mode for cylindrical waveguides. The 
annular region 96 carries a first signal in a lower frequency band and 
provides a differential phase shift, while a second signal in a higher 
frequency band is carried inside the hollow inner conductor region 97. The 
structure 90 does not provide a differential phase shift to the second 
signal. 
FIGS. 13-14 depict an embodiment of the invention in square waveguide. The 
structure 100 comprises a square waveguide 101 and a pair of corrugated 
ridges 102 and 103 which form a differential phase shifting section 104. 
This embodiment operates in the TE.sub.10 mode. 
A differential phase shift structure has been described, which provides 
shunt and series susceptance loading to provide impedance matching and 
increased differential phase shift per unit length. It is understood that 
the above-described embodiments are merely illustrative of the possible 
specific embodiments which can represent principles of the present 
invention. Other arrangements may be devised in accordance with these 
principles by those skilled in the art without departing from the scope of 
the invention.