APERIODIC TAPERED CORRUGATED WAVEGUIDE FILTER
United States Patent 3597710
A waveguide band-pass filter utilizes a sequence of capacitive irises to form corrugations within the rectangular waveguide. The capacitive irises are aperiodically spaced along the guide and the capacitance of consecutive irises in the sequence are of different values. The waveguide has its height tapering in steps and each capacitive iris in the sequence is situated between waveguide sections of different heights.
US Patent References:
Microwave filter
Mumford - February 1951 - 2540488
Wave filter
Lewis et al. - February 1952 - 2585563
Broad-band waveguide filter
Cohn - July 1962 - 3046503
Waveguide structure for linear particle accelerators having an undulating configuration
Azam et al. - July 1966 - 3263116
Aperiodic low-pass filter
Hansen - April 1968 - 3380004
Microwave filter
Mumford - February 1951 - 2540488
Wave filter
Lewis et al. - February 1952 - 2585563
Broad-band waveguide filter
Cohn - July 1962 - 3046503
Waveguide structure for linear particle accelerators having an undulating configuration
Azam et al. - July 1966 - 3263116
Aperiodic low-pass filter
Hansen - April 1968 - 3380004
Application Number:
04/880556
Publication Date:
08/03/1971
Filing Date:
11/28/1969
View Patent Images:
Export Citation:
Assignee:
Microwave Development Laboratories, Inc. (Needham Heights, MA)
Primary Class:
International Classes:
H01P1/211; H01P1/20; H03H7/10
Field of Search:
333/73,73W,79,76
Primary Examiner:
Saalbach, Herman Karl
Assistant Examiner:
Chatmon Jr., Saxfield
Claims:
I claim
1. A waveguide filter comprising a rectangular waveguide having a first sequence of capacitive irises forming corrugations within the guide, the capacitive irises in the first sequence being aperiodically spaced along the guide, each iris in the first sequence being of different capacitance, and the height of the waveguide containing the first sequence of irises being tapered whereby each capacitive iris in the first sequence is situated between waveguide sections of different heights.
2. The waveguide filter according to claim 1, wherein the tapered waveguide containing the first sequence of irises has its greatest height at the input end of the filter.
3. The waveguide filter according to claim 1, wherein the capacitance of consecutive irises in the first sequence changes monotonically.
4. The waveguide filter according to claim 3, further including a second sequence of capacitive irises disposed in the rectangular waveguide and forming corrugations therein, the second sequence of capacitive irises being a mirror image of the first sequence, and the height of the waveguide containing the second sequence of irises being tapered oppositely to the taper of the waveguide containing the first sequence whereby the tapered waveguide of the second sequence of irises has its greatest height at the output of the filter.
1. A waveguide filter comprising a rectangular waveguide having a first sequence of capacitive irises forming corrugations within the guide, the capacitive irises in the first sequence being aperiodically spaced along the guide, each iris in the first sequence being of different capacitance, and the height of the waveguide containing the first sequence of irises being tapered whereby each capacitive iris in the first sequence is situated between waveguide sections of different heights.
2. The waveguide filter according to claim 1, wherein the tapered waveguide containing the first sequence of irises has its greatest height at the input end of the filter.
3. The waveguide filter according to claim 1, wherein the capacitance of consecutive irises in the first sequence changes monotonically.
4. The waveguide filter according to claim 3, further including a second sequence of capacitive irises disposed in the rectangular waveguide and forming corrugations therein, the second sequence of capacitive irises being a mirror image of the first sequence, and the height of the waveguide containing the second sequence of irises being tapered oppositely to the taper of the waveguide containing the first sequence whereby the tapered waveguide of the second sequence of irises has its greatest height at the output of the filter.
Description:
FIELD OF THE INVENTION
This invention relates to frequency selective passive apparatus for filtering signals which are in the microwave portion of the electromagnetic frequency spectrum. More particularly the invention relates to waveguide filters of the corrugated and waffle-iron types.
BACKGROUND OF THE INVENTION
In waveguide filters of the type here considered, the low and high impedance sections of the filter are realized by raising and lowering the height of the waveguide which results in corrugation of the waveguide. A waffle-iron filter is basically a corrugated filter except that the waffle-iron filter is slotted in the longitudinal direction to reduce spurious responses in the stop band caused by higher order modes. Corrugated and waffle-iron waveguide filters are usually low-pass in operation, but because waveguide has a cutoff frequency, those filters cannot operate to DC as do most low-pass filters. Because of the corrugations in the waveguide, modes having variations in the direction of the waveguide height are cutoff up to very high frequencies. Corrugated waveguide filters, therefore, have good stop band characteristics.
In the corrugated and waffle-iron low-pass waveguide filters here considered, the corrugations are small compared to a quarter wavelength at the pass band frequencies. Such filters are the waveguide equivalent of the common series-inductive, shunt-capacitance, ladder-type, low-pass filter. The waveguide nature of the corrugated and waffle-iron filters, however, makes it difficult to design them as a direct approximation of the lumped-element, low-pass filter.
The conventional corrugated or waffle-iron filter is a uniform structure in which the low and high impedance sections alternate and recur periodically. When such a filter is designed by the image parameter method the upper cutoff frequency is not accurately predictable and large VSWR (voltage standing wave ratio) ripples are encountered when approaching the upper cutoff. Further, an impedance transformer is required to match the filter to standard waveguide. The impedance transformers at the input and output of the conventional corrugated or waffle-iron filter materially increases the length of the transmission line. A considerable reduction in length can be achieved where the filter can be connected directly to the waveguide without requiring an intervening impedance transformer.
OBJECT OF THE INVENTION
The primary object of the invention is to provide a corrugated or waffle-iron waveguide filter that can be connected to the transmission waveguide without requiring intervening impedance matching devices. A further objective of the invention is to provide a waveguide filter of the corrugated or waffle-iron type which is characterized by substantially equiripple performance across the pass band.
THE INVENTION
The invention resides in a waveguide filter of the corrugated or waffle-iron type in which the height of the waveguide is tapered and in which the filter sections of high and low impedance are aperiodic.
THE DRAWINGS
The invention can be better understood from the exposition which follows when it is considered in conjunction with the drawings in which:
FIG. 1 depicts, in cross section, a conventional corrugated filter employing transformers to match the filter to standard waveguide;
FIG. 2 is a cross-sectional view of a waveguide filter formed by a sequence of thick capacitive irises spaced along a hollow waveguide;
FIG. 3 symbolizes a generalized distributed low-pass prototype filter in impedance inverter form with unity line impedances;
FIG. 4 symbolizes the generalized distributed low-pass prototype filter with line impedances of generalized values;
FIG. 5 depicts an embodiment of the invention in which the height of the waveguide tapers from the meddle toward the ends;
FIG. 6 depicts the preferred embodiment of the invention in which the height of the waveguide tapers from the ends toward the middle;
FIG. 6A depicts a stepped structure employed in the preferred embodiment;
FIG. 7 symbolizes an impedance inverter disposed between lines of different impedances;
FIG. 8 depicts a physical structure realizing the arrangement symbolized in FIG. 7;
FIG. 9A is a front elevational view of a capacitive iris in a rectangular waveguide;
FIG. 9B is a sectional view taken along the parting plane 9B-9B in FIG. 9A;
FIG. 9C symbolizes the equivalent circuit of the FIG. 9B structure; and
FIG. 10 is a front elevational view of a waffle iron filter embodying the invention.
THE EXPOSITION
FIG. 1 shows a conventional corrugated filter 1 having impedance transformers 2 and 3 connecting the input and output of the filter to standard waveguides 4 and 5. "Standard" waveguide, in the context of this exposition, means the commonly available waveguide whose dimensions have been fixed by the Electronics Industry Association (EIA) and which is designated by a number preceded by WR, as in WR-90. The filter 1 is a periodic waveguide structure having sections of high and low impedance which result from abruptly raising and lowering the height of the waveguide. The high and low impedance sections alternate and thus form corrugations in the waveguide. The corrugations, in the longitudinal direction of the guide, are small compared to a quarter wavelength at the pass band frequencies. The input waveguide 4 is connected to a quarter wave λg(4), ), stepped, impedance transformer 2 which, in the illustration, has five sections of decreasing height, the section of smallest height being joined to the input port 1A of the filter. The output port 1B of the filter is connected to a similar quarter wave, stepped impedance transformer 3 having its section of greatest height connected to the output waveguide 5. The impedance transformers are necessary to permit the corrugated filter to be matched to standard waveguide. The length of the transformer is substantial in comparison to the length of the corrugated waveguide. In situations where compactness is a desirable attribute, elimination of the transformers obviously is conducive to that objective. However the transformers cannot be eliminated from the conventional corrugated filter without seriously degrading the performance of that filter when it is inserted in standard waveguide. Because the conventional corrugated filter is essentially a periodic structure, large ripples are encountered in the pass band as the upper cutoff frequency is approached. Further, the image parameter method of designing the conventional corrugated waffle-iron filter does not permit accurate prediction of the upper cutoff frequency.
FIG. 2 is a cross-sectional view of a waveguide filter formed by a sequence of thick capacitive irises C1, C2...C7 spaced along the interior of a hollow rectangular waveguide W1 in the manner disclosed in my patent application Ser. No. 786,967, filed Dec. 26, 1968. This capacitive iris filter can be matched to standard waveguide without requiring impedance transformers simply by arranging the thick capacitive irises in a length of standard waveguide. The capacitive iris arrangement provides moderate harmonic rejection in a filter of very short length. The thick capacitive iris filter is derived from the generalized distributed low-pass prototype filter shown in impedance inverter form in FIG. 3. In that prototype, the line impedances between the impedance inverters K 1 , K 2 ...K N +1 are all of unity impedance, viz., Z 0 =1., as explained in the above-cited copending application. In that prototype, the impedance inverter is given by
where V i is the junction VSWR (voltage standing wave ratio) as discussed in my monograph "Table Of Element Values For The Distributed Low-Pass Prototype Filter," IEEE Transactions on Microwave Theory and Technique, Vol. MTT-13, No. 5, Sept. 1965.
Consider now a similar generalized distributed low-pass prototype filter, shown in FIG. 4, in which the line impedances between the impedance inverters K 1 , K 2 , etc., instead of all being of unity impedance, take on general values Z i . The impedance inverter between lines Z i -1 and Z i is given by
where v i is the junction VSWR of the ordinary distributed low-pass prototype. Note that when Z i -1 =Z i =1 we have
as in the FIG. 3 prototype.
By choosing suitable values for the main line impedance Z i , we can cause the waveguide heights to taper in any desired manner. Thus, we can produce an aperiodic corrugated filter in which the waveguide height tapers from the center outwardly as in FIG. 5 or an aperiodic corrugated filter in which the waveguide height tapers inwardly toward the center as in FIG. 6. The FIG. 6 embodiment can be constructed by corrugating the interior of a length of standard waveguide. If that is down, the filter can be connected directly to standard waveguide without requiring an intervening impedance transformer.
The realization of an impedance inverter K i disposed between lines whose impedances Z 1 and Z 2 are different is symbolically depicted in FIG. 7. It is always possible to find reference planes P1 and P2 to convert the asymmetric structure depicted in FIG. 8 to the "symmetric" impedance inverter K i indicated in FIG. 7. The plane P1 is located 1/2φ 1 from the forward face of the thick capacitive iris and plane P2 is located 1/2φ 2 from the rear face of the thick capacitive iris. It is necessary to measure the actual electrical length between any pair of adjacent irises in the filter from the reference planes on either side of the irises to account for the phase shift introduced by the irises.
FIG. 9A depicts a thick capacitive iris in a rectangular waveguide. FIG. 9B is a sectional view taken along the parting plane 9B-9B in FIG. 9A. In FIG. 9A, the waveguide height is denoted by b in accordance with conventional notation and should not be confused with a normalized susceptance. FIG. 9B is identical to FIG. 8, and shows waveguide heights of b 1 and b 2 on either side of the capacitive iris, where b 1 and b 2 are each less than the main waveguide height b. The equivalent circuit of the thick asymmetrical capacitive iris is symbolized in FIG. 9C. The transfer matrix of the thick iris equivalent circuit of FIG. 9C, including the fringing capacitances, is
The mathematics which follow are a generalization of equations 10 through 13 given in the cited copending application. Because the distances 1/2φ 1 and 1/2φ 2 to the reference planes located on each side of the thick iris (FIG. 8) are, in general, different, equation 11 in the cited copending application becomes two conditions, giving φ 1 and φ 2 . The actual equations are, ##SPC1##
is the insertion loss of the thick iris when terminated in resistive impedances Z 1 and Z 1 .
Note that when Z 1 =Z 2 =1, then φ 1 =φ 2 =φ and equations 11 to 13 of the copending application result from the foregoing equations.
The structure shown in FIG. 6 is the preferred embodiment of the invention because it permits standard waveguide to be employed in its fabrication. If in that embodiment, the thickness t 1 , t 2 ...of the capacitive irises is uniform throughout the filter, and because the capacitance of the capacitive sections increases from the ends of the filter toward the central portion, the iris gaps h 1 , h 2 , h 3 , h 4 become progressively narrower. It is not, however, a necessary condition that the irises all be of the same thickness t. The distances 1 1 , 1 2 ...1 n , measured between the faces of the irises, are in general different so that the irises are aperiodically spaced along the guide. In the preferred embodiment, the lengths 1 1 , 1 2 , 1 3 become progressively shorter as the center of the filter is approached. The waveguide heights b 1 , b 2 , b 3 also become progressively smaller, causing the waveguide height to taper in steps from the ends toward the middle of the filter, In a filter having many sections, the center sections may all be uniform, as in the conventional corrugated filter, with the taper occurring over the first three or four filter sections at each end.
The embodiment of FIG. 6 can be constructed by securing two identical stepped elements 8 and 9 in a length 10 of standard hollow rectangular waveguide. Each stepped element may be of the form depicted in FIG. 6A and can be made from a single slab of metal. The elements 8 and 9 are brazed or otherwise fastened within the waveguide to the top and bottom broad walls in a manner assuring good electrical continuity between the joined parts. The filter embodiment depicted in FIG. 6 is a symmetrical structure which permits either end to serve as the input port with the other end serving as the output port.
In the preferred embodiment of FIG. 6 the sections are tapered to cause the filter to terminate in waveguide having a height b that matches the height of standard waveguide. In the preferred embodiment, the requirement for a transformer to match the standard waveguide to the filter is completely eliminated. The tapered sections in the filter may be viewed as combining the impedance matching function with a filtering function. This is especially so in a filter having a large number of sections in which the impedance matching is performed by three or four tapering sections at each end of the filter with the central portion of the filter being corrugated in the manner of the conventional filter.
In some situations, it may not be feasible or desirable to completely eliminate the conventional impedance matching transformers. In such circumstances, the aperiodic tapered filter can be constructed to terminate in waveguide which is of a different height b from the standard waveguide and a conventional device may be employed to provide the requisite impedance match. That is, referring to FIG. 6, the tapered sections may terminate in a waveguide of height b which is somewhat less than the height of a standard waveguide and a quarter wave stepped transformer may then be employed to connect the terminating waveguide to the standard waveguide in the transmission line. The advantage of such a procedure is that the transformer need not have as many steps as in the conventional arrangement of FIG. 1 and therefore a reduction in length is obtained by employing an aperiodic tapered filter even where that filter does not provide complete matching to standard waveguide.
The embodiment of the invention depicted in FIG. 5 has sections arranged to cause the filter to taper from the middle toward the ends. Thus in the FIG. 5 embodiment, the waveguide height b 1 , b 2 , b 3 becomes progressively smaller in proceeding away from the center of the filter while the distances 1 1 , 1 2 , 1 3 become progressively larger due to the increase in reference plane spacing which accompanies the decrease in gap susceptance. Assuming the standard waveguide height must be equal to or larger than the height of the largest section, the FIG. 5 filter, because of the direction of its taper, terminates in a waveguide of height b t which is substantially smaller than the standard waveguide height and therefore transformers are required to match the terminal waveguide to standard waveguide.
A waffle-iron filter can be obtained by modifying the aperiodic tapered corrugated filter here described to have slots, as indicated in FIG. 10, which extend in the longitudinal direction through the high and low impedance sections of the waveguide. The longitudinal slots, as is known, reduce the spurious response in the stop band caused by TE on type higher order modes. The provision of longitudinal slots makes the waffle-iron filter more difficult and costly to build than the related corrugated type, but the improved stop band characteristic of the waffle-iron filter, in many instances, make the waffle-iron filter the preferred type. The reduction in capacity of the irises caused by the longitudinal slots can be compensated by narrowing the gap heights h 1 , h 2 ...or by employing other techniques known to the filter art.
Because the invention may be embodied in varied forms, it is not intended that this patent be limited to the precise structures here illustrated or described. Rather it is intended that the patent be construed to embrace those filter structures which, in essence, utilize the invention defined in the appended claims.
This invention relates to frequency selective passive apparatus for filtering signals which are in the microwave portion of the electromagnetic frequency spectrum. More particularly the invention relates to waveguide filters of the corrugated and waffle-iron types.
BACKGROUND OF THE INVENTION
In waveguide filters of the type here considered, the low and high impedance sections of the filter are realized by raising and lowering the height of the waveguide which results in corrugation of the waveguide. A waffle-iron filter is basically a corrugated filter except that the waffle-iron filter is slotted in the longitudinal direction to reduce spurious responses in the stop band caused by higher order modes. Corrugated and waffle-iron waveguide filters are usually low-pass in operation, but because waveguide has a cutoff frequency, those filters cannot operate to DC as do most low-pass filters. Because of the corrugations in the waveguide, modes having variations in the direction of the waveguide height are cutoff up to very high frequencies. Corrugated waveguide filters, therefore, have good stop band characteristics.
In the corrugated and waffle-iron low-pass waveguide filters here considered, the corrugations are small compared to a quarter wavelength at the pass band frequencies. Such filters are the waveguide equivalent of the common series-inductive, shunt-capacitance, ladder-type, low-pass filter. The waveguide nature of the corrugated and waffle-iron filters, however, makes it difficult to design them as a direct approximation of the lumped-element, low-pass filter.
The conventional corrugated or waffle-iron filter is a uniform structure in which the low and high impedance sections alternate and recur periodically. When such a filter is designed by the image parameter method the upper cutoff frequency is not accurately predictable and large VSWR (voltage standing wave ratio) ripples are encountered when approaching the upper cutoff. Further, an impedance transformer is required to match the filter to standard waveguide. The impedance transformers at the input and output of the conventional corrugated or waffle-iron filter materially increases the length of the transmission line. A considerable reduction in length can be achieved where the filter can be connected directly to the waveguide without requiring an intervening impedance transformer.
OBJECT OF THE INVENTION
The primary object of the invention is to provide a corrugated or waffle-iron waveguide filter that can be connected to the transmission waveguide without requiring intervening impedance matching devices. A further objective of the invention is to provide a waveguide filter of the corrugated or waffle-iron type which is characterized by substantially equiripple performance across the pass band.
THE INVENTION
The invention resides in a waveguide filter of the corrugated or waffle-iron type in which the height of the waveguide is tapered and in which the filter sections of high and low impedance are aperiodic.
THE DRAWINGS
The invention can be better understood from the exposition which follows when it is considered in conjunction with the drawings in which:
FIG. 1 depicts, in cross section, a conventional corrugated filter employing transformers to match the filter to standard waveguide;
FIG. 2 is a cross-sectional view of a waveguide filter formed by a sequence of thick capacitive irises spaced along a hollow waveguide;
FIG. 3 symbolizes a generalized distributed low-pass prototype filter in impedance inverter form with unity line impedances;
FIG. 4 symbolizes the generalized distributed low-pass prototype filter with line impedances of generalized values;
FIG. 5 depicts an embodiment of the invention in which the height of the waveguide tapers from the meddle toward the ends;
FIG. 6 depicts the preferred embodiment of the invention in which the height of the waveguide tapers from the ends toward the middle;
FIG. 6A depicts a stepped structure employed in the preferred embodiment;
FIG. 7 symbolizes an impedance inverter disposed between lines of different impedances;
FIG. 8 depicts a physical structure realizing the arrangement symbolized in FIG. 7;
FIG. 9A is a front elevational view of a capacitive iris in a rectangular waveguide;
FIG. 9B is a sectional view taken along the parting plane 9B-9B in FIG. 9A;
FIG. 9C symbolizes the equivalent circuit of the FIG. 9B structure; and
FIG. 10 is a front elevational view of a waffle iron filter embodying the invention.
THE EXPOSITION
FIG. 1 shows a conventional corrugated filter 1 having impedance transformers 2 and 3 connecting the input and output of the filter to standard waveguides 4 and 5. "Standard" waveguide, in the context of this exposition, means the commonly available waveguide whose dimensions have been fixed by the Electronics Industry Association (EIA) and which is designated by a number preceded by WR, as in WR-90. The filter 1 is a periodic waveguide structure having sections of high and low impedance which result from abruptly raising and lowering the height of the waveguide. The high and low impedance sections alternate and thus form corrugations in the waveguide. The corrugations, in the longitudinal direction of the guide, are small compared to a quarter wavelength at the pass band frequencies. The input waveguide 4 is connected to a quarter wave λg(4), ), stepped, impedance transformer 2 which, in the illustration, has five sections of decreasing height, the section of smallest height being joined to the input port 1A of the filter. The output port 1B of the filter is connected to a similar quarter wave, stepped impedance transformer 3 having its section of greatest height connected to the output waveguide 5. The impedance transformers are necessary to permit the corrugated filter to be matched to standard waveguide. The length of the transformer is substantial in comparison to the length of the corrugated waveguide. In situations where compactness is a desirable attribute, elimination of the transformers obviously is conducive to that objective. However the transformers cannot be eliminated from the conventional corrugated filter without seriously degrading the performance of that filter when it is inserted in standard waveguide. Because the conventional corrugated filter is essentially a periodic structure, large ripples are encountered in the pass band as the upper cutoff frequency is approached. Further, the image parameter method of designing the conventional corrugated waffle-iron filter does not permit accurate prediction of the upper cutoff frequency.
FIG. 2 is a cross-sectional view of a waveguide filter formed by a sequence of thick capacitive irises C1, C2...C7 spaced along the interior of a hollow rectangular waveguide W1 in the manner disclosed in my patent application Ser. No. 786,967, filed Dec. 26, 1968. This capacitive iris filter can be matched to standard waveguide without requiring impedance transformers simply by arranging the thick capacitive irises in a length of standard waveguide. The capacitive iris arrangement provides moderate harmonic rejection in a filter of very short length. The thick capacitive iris filter is derived from the generalized distributed low-pass prototype filter shown in impedance inverter form in FIG. 3. In that prototype, the line impedances between the impedance inverters K 1 , K 2 ...K N +1 are all of unity impedance, viz., Z 0 =1., as explained in the above-cited copending application. In that prototype, the impedance inverter is given by
where V i is the junction VSWR (voltage standing wave ratio) as discussed in my monograph "Table Of Element Values For The Distributed Low-Pass Prototype Filter," IEEE Transactions on Microwave Theory and Technique, Vol. MTT-13, No. 5, Sept. 1965.
Consider now a similar generalized distributed low-pass prototype filter, shown in FIG. 4, in which the line impedances between the impedance inverters K 1 , K 2 , etc., instead of all being of unity impedance, take on general values Z i . The impedance inverter between lines Z i -1 and Z i is given by
where v i is the junction VSWR of the ordinary distributed low-pass prototype. Note that when Z i -1 =Z i =1 we have
as in the FIG. 3 prototype.
By choosing suitable values for the main line impedance Z i , we can cause the waveguide heights to taper in any desired manner. Thus, we can produce an aperiodic corrugated filter in which the waveguide height tapers from the center outwardly as in FIG. 5 or an aperiodic corrugated filter in which the waveguide height tapers inwardly toward the center as in FIG. 6. The FIG. 6 embodiment can be constructed by corrugating the interior of a length of standard waveguide. If that is down, the filter can be connected directly to standard waveguide without requiring an intervening impedance transformer.
The realization of an impedance inverter K i disposed between lines whose impedances Z 1 and Z 2 are different is symbolically depicted in FIG. 7. It is always possible to find reference planes P1 and P2 to convert the asymmetric structure depicted in FIG. 8 to the "symmetric" impedance inverter K i indicated in FIG. 7. The plane P1 is located 1/2φ 1 from the forward face of the thick capacitive iris and plane P2 is located 1/2φ 2 from the rear face of the thick capacitive iris. It is necessary to measure the actual electrical length between any pair of adjacent irises in the filter from the reference planes on either side of the irises to account for the phase shift introduced by the irises.
FIG. 9A depicts a thick capacitive iris in a rectangular waveguide. FIG. 9B is a sectional view taken along the parting plane 9B-9B in FIG. 9A. In FIG. 9A, the waveguide height is denoted by b in accordance with conventional notation and should not be confused with a normalized susceptance. FIG. 9B is identical to FIG. 8, and shows waveguide heights of b 1 and b 2 on either side of the capacitive iris, where b 1 and b 2 are each less than the main waveguide height b. The equivalent circuit of the thick asymmetrical capacitive iris is symbolized in FIG. 9C. The transfer matrix of the thick iris equivalent circuit of FIG. 9C, including the fringing capacitances, is
The mathematics which follow are a generalization of equations 10 through 13 given in the cited copending application. Because the distances 1/2φ 1 and 1/2φ 2 to the reference planes located on each side of the thick iris (FIG. 8) are, in general, different, equation 11 in the cited copending application becomes two conditions, giving φ 1 and φ 2 . The actual equations are, ##SPC1##
is the insertion loss of the thick iris when terminated in resistive impedances Z 1 and Z 1 .
Note that when Z 1 =Z 2 =1, then φ 1 =φ 2 =φ and equations 11 to 13 of the copending application result from the foregoing equations.
The structure shown in FIG. 6 is the preferred embodiment of the invention because it permits standard waveguide to be employed in its fabrication. If in that embodiment, the thickness t 1 , t 2 ...of the capacitive irises is uniform throughout the filter, and because the capacitance of the capacitive sections increases from the ends of the filter toward the central portion, the iris gaps h 1 , h 2 , h 3 , h 4 become progressively narrower. It is not, however, a necessary condition that the irises all be of the same thickness t. The distances 1 1 , 1 2 ...1 n , measured between the faces of the irises, are in general different so that the irises are aperiodically spaced along the guide. In the preferred embodiment, the lengths 1 1 , 1 2 , 1 3 become progressively shorter as the center of the filter is approached. The waveguide heights b 1 , b 2 , b 3 also become progressively smaller, causing the waveguide height to taper in steps from the ends toward the middle of the filter, In a filter having many sections, the center sections may all be uniform, as in the conventional corrugated filter, with the taper occurring over the first three or four filter sections at each end.
The embodiment of FIG. 6 can be constructed by securing two identical stepped elements 8 and 9 in a length 10 of standard hollow rectangular waveguide. Each stepped element may be of the form depicted in FIG. 6A and can be made from a single slab of metal. The elements 8 and 9 are brazed or otherwise fastened within the waveguide to the top and bottom broad walls in a manner assuring good electrical continuity between the joined parts. The filter embodiment depicted in FIG. 6 is a symmetrical structure which permits either end to serve as the input port with the other end serving as the output port.
In the preferred embodiment of FIG. 6 the sections are tapered to cause the filter to terminate in waveguide having a height b that matches the height of standard waveguide. In the preferred embodiment, the requirement for a transformer to match the standard waveguide to the filter is completely eliminated. The tapered sections in the filter may be viewed as combining the impedance matching function with a filtering function. This is especially so in a filter having a large number of sections in which the impedance matching is performed by three or four tapering sections at each end of the filter with the central portion of the filter being corrugated in the manner of the conventional filter.
In some situations, it may not be feasible or desirable to completely eliminate the conventional impedance matching transformers. In such circumstances, the aperiodic tapered filter can be constructed to terminate in waveguide which is of a different height b from the standard waveguide and a conventional device may be employed to provide the requisite impedance match. That is, referring to FIG. 6, the tapered sections may terminate in a waveguide of height b which is somewhat less than the height of a standard waveguide and a quarter wave stepped transformer may then be employed to connect the terminating waveguide to the standard waveguide in the transmission line. The advantage of such a procedure is that the transformer need not have as many steps as in the conventional arrangement of FIG. 1 and therefore a reduction in length is obtained by employing an aperiodic tapered filter even where that filter does not provide complete matching to standard waveguide.
The embodiment of the invention depicted in FIG. 5 has sections arranged to cause the filter to taper from the middle toward the ends. Thus in the FIG. 5 embodiment, the waveguide height b 1 , b 2 , b 3 becomes progressively smaller in proceeding away from the center of the filter while the distances 1 1 , 1 2 , 1 3 become progressively larger due to the increase in reference plane spacing which accompanies the decrease in gap susceptance. Assuming the standard waveguide height must be equal to or larger than the height of the largest section, the FIG. 5 filter, because of the direction of its taper, terminates in a waveguide of height b t which is substantially smaller than the standard waveguide height and therefore transformers are required to match the terminal waveguide to standard waveguide.
A waffle-iron filter can be obtained by modifying the aperiodic tapered corrugated filter here described to have slots, as indicated in FIG. 10, which extend in the longitudinal direction through the high and low impedance sections of the waveguide. The longitudinal slots, as is known, reduce the spurious response in the stop band caused by TE on type higher order modes. The provision of longitudinal slots makes the waffle-iron filter more difficult and costly to build than the related corrugated type, but the improved stop band characteristic of the waffle-iron filter, in many instances, make the waffle-iron filter the preferred type. The reduction in capacity of the irises caused by the longitudinal slots can be compensated by narrowing the gap heights h 1 , h 2 ...or by employing other techniques known to the filter art.
Because the invention may be embodied in varied forms, it is not intended that this patent be limited to the precise structures here illustrated or described. Rather it is intended that the patent be construed to embrace those filter structures which, in essence, utilize the invention defined in the appended claims.