Inline cross-coupled coaxial cavity filter

An inline microwave bandpass filter where cross coupling between non-adjacent resonators is realized by changing the orientation of selected resonators. The microwave bandpass filter includes a cavity and three or more resonators arranged in a row (or inline) in the cavity. At least one resonator has a different spatial orientation from at least one other resonator. For example, one or more of the resonators may be rotated 90 or 180 degrees with respect to one of the other resonators. This arrangement of resonators facilitates sequential coupling between pairs of adjacent resonators and cross coupling between at least one pair of non-adjacent resonators without the use of additional cross coupling structures such as dedicated coupling probes or extra cavities. One or more plates may be introduced between adjacent resonators to independently control the sequential and cross coupling.

FIELD

The described embodiments relate to microwave bandpass filters. More particularly, the described embodiments relate to inline cross-coupled microwave bandpass filters.

BACKGROUND

In microwave bandpass filter design, transmission zeros (TZs) on one or both sides of the passband are frequently required in order to meet rejection requirements. Transmission zeros are often realized by couplings between non-adjacent resonators, often referred to as cross couplings.

Folded structures are often used to realize couplings between non-adjacent resonators. However, folded structures may not be suitable where there are structural constraints that require an inline configuration and/or input and output connectors on opposite sides of the two end resonators.

One technique used to realize transmission zeros for an inline configuration is to use a coupling probe embedded in the housing of the filter. Reference is now made toFIG. 1Ain which an inline cross-coupled microwave bandpass filter100in accordance with the prior art is illustrated. The filter100includes a housing102, six cavities104ato104f, six resonators106ato106fsituated in the cavities104ato104f, an input port108extending into the first cavity104a, and an output port110extending into to the sixth cavity104f. The filter100also includes a coupling probe112extending into the first and third cavities104aand104cto realize coupling between the first and third resonators106aand106c. However, such a long coupling probe112generates unwanted resonances.

Reference is now made toFIG. 1Bin which the frequency response of the bandpass filter100ofFIG. 1Acentered at 1.54 GHz is illustrated. It can be seen fromFIG. 1Bthat in addition to generating a transmission zero130in the upper stop band, the coupling probe112resonates and generates a spike132in the lower stop band. Other disadvantages for such filters include the difficulty of tuning the cross-coupling.

Other techniques used to realize transmission zeros for an inline configuration include: (1) the extracted pole technique described in J. R. Rhodes and R. J. Cameron, “General extracted pole synthesis technique with application to low-loss TE011-mode filters,”IEEE Trans. Microwave Theory and Tech., vol. 28, pp. 1018-1028, September 1980; and (2) the application of non-resonating nodes described in S. Mari and G. Macchiarella, “Synthesis of inline filters with arbitrarily placed attenuation poles by using non-resonating nodes,”IEEE Trans. Microwave Theory and Tech., vol. 53, pp. 3075-3081, October 2005. However, both techniques require additional resonating or non-resonating structures.

SUMMARY

Embodiments described herein relate to inline microwave bandpass filters where cross couplings between non-adjacent resonators is realized by changing the orientation of selected resonators.

In one broad aspect there is provided a microwave bandpass filter comprising: (a) a cavity defined by a tubular structure and two opposing end walls, the tubular structure having a first end and a second end, one of the opposing end walls being attached to the first end and the other of the opposing end walls being attached to the second end; (b) at least three resonators arranged in a row in the cavity, connected by apertures, wherein at least one resonator has a different spatial orientation from at least one other resonator; (c) an input connector coupled to a first resonator of the at least three resonators; and (d) an output connector coupled to a second resonator of the at least three resonators.

Such a microwave bandpass filter facilitates sequential coupling between pairs of adjacent resonators and cross coupling between at least one pair of non-adjacent resonators without the use of additional cross coupling structures such as dedicated coupling probes or extra cavities.

DETAILED DESCRIPTION

Embodiments described herein relate to inline bandpass filters where cross couplings between non-adjacent resonators is realized by changing the orientation of selected resonators. For example, one or more of the resonators may be rotated 90 degrees or 180 degrees with respect to one or more of the resonators. In some embodiments, plates are introduced between adjacent resonators to control the sequential couplings between the adjacent resonators.

Reference is now made toFIGS. 2A to 2C, in which a microwave bandpass filter200in accordance with an embodiment is illustrated.FIG. 2Ais a perspective view of the bandpass filter200,FIG. 2Bis a side view of the bandpass filter200, andFIG. 2Cis a top view of the bandpass filter200.

The bandpass filter200includes a cavity202, three resonators204a,204b, and204carranged in a row in the cavity202, an input connector206connected to the first resonator204a, and an output connector208connected to the third resonator204c. Although the input and output connectors206and208are shown inFIGS. 2A to 2Cas being connected to the first and third resonators204aand204c, the input and output connectors206and208may be connected to any of the resonators.

The cavity202is defined by a tubular structure211and two opposing end walls214aand214battached to either end of the tubular structure211. In some embodiments, as shown inFIGS. 2A to 2C, the tubular structure211has a rectangular shape, and is defined by a top wall or lid210(which may be removable), a bottom wall212, and two opposing side walls216aand216bthat extend between the top wall210and the bottom wall212. In these embodiments, the cavity202has a width a and a height b (FIG. 2A). In other embodiments, the tubular structure has a cylindrical shape and is defined by a single continuous wall (not shown).

The cavity walls210,212,214a,214b,216aand216bare typically made of a suitable metal such as aluminum or copper. However, the cavity walls210,212,214a,214b,216aand216bmay be made of other suitable metals. Although the cavity walls210,212,214a,214b,216aand216bare typically translucent, for ease of explanation, the cavity walls210,212,214a,214b,216aand216bare shown inFIGS. 2A to 2Cas being transparent.

The three resonators204a,204band204care arranged in a row or “inline” in the cavity. In inline filters, the centers of the resonators are aligned along the same longitudinal axis as opposed to, for example, filters with resonators arranged in two or more rows. Although the filter200is shown as having three resonators204a,204b, and204c, filters in accordance with embodiments described herein may have three or more resonators. The number of resonators is typically selected based on the filter requirements. Preferably, the resonators204a,204band204care coaxial resonators with square or rectangular cavity cross-sections. However, the resonators204a,204b, and204cmay be any type of suitable coaxial resonator.

The first and second resonators204aand204bare separated by a distance d1, and the second and third resonators204band204care separated by a distance d2(FIG. 2C). The distance d1between the first and second resonators204aand204bmay by the same as, or different than, the distance d2between the second and third resonators204band204c. The distances d1d2between resonators are typically measured from the centre points of the resonators204a,204band204c.

At least one of the resonators204a,204b, and204chas a different spatial orientation from at least one other resonator. For example, one or more of the resonators204a,204b, or204cmay be rotated between 1 degree and 360 degrees with respect to one of the other resonators204a,204b, or204c. In a preferred embodiment, one or more resonators204a,204band204cis rotated 90 degrees or 180 degrees from one of the other resonators.

In some embodiments, such as the embodiment shown inFIGS. 2A to 2C, the second resonator204bis rotated with respect to the first and third resonators204aand204cso that the second resonator204bhas a different orientation from the first and third resonators204aand204c. For example, as shown inFIGS. 2A to 2C, the second resonator204bmay be rotated 90 degrees with respect to the first and third resonators204aand204cso that the first and third resonators204aand204care substantially vertical and the second resonator204bis substantially horizontal.

In other embodiments, such as the embodiment shown inFIGS. 13A to 13C, the third resonator is also rotated with respect to the first resonator so that both the second and third resonators have different orientations from the first resonator. For example, as shown inFIGS. 13A to 13C, the third resonator may be rotated 180 degrees with respect to the first resonator so that it can be said to be is upside down with respect to the first resonator.

By having at least one resonator204a,204b, and204cwith a different orientation, the filter200ofFIGS. 2A to 2Cnot only realizes sequential coupling between adjacent resonators (e.g. between first and second resonators204aand204b, and second and third resonators204band204c), but it also realizes cross coupling between at least one pair of non-adjacent resonators (e.g. between first and third resonators204aand204c). Unlike the prior art filters, the cross coupling is achieved without the use of additional cross coupling structures such as dedicated coupling probes or extra cavities.

Each cross coupling (coupling between non-adjacent resonators) creates a transmission zero in the upper or lower stop band, or both. Where the second resonator204bis rotated 90 degrees with respect to the first and third resonators204aand204c, as shown inFIGS. 2A to 2C, the cross coupling between the first and third resonators204aand204cproduces a transmission zero in the upper stop band. Where, however, the second resonator204bis rotated 90 degrees with respect to the first resonator204a, and the third resonator204cis rotated 180 degrees with respect to the first resonator204a, as shown inFIGS. 13A to 13C, the cross coupling between the first and third resonators204aand204cproduces a transmission zero in the lower stop band.

Additional resonators may be added to the filter200to increase the number of cross couplings or the number of transmission zeros, or both. For example, a filter having four resonators where the second and third resonators are rotated 90 degrees with respect to the first resonator (i.e. the first resonator is substantially vertical and the second and third resonators are substantially horizontal), and the fourth resonator is rotated 180 degrees with respect to the first resonator (i.e. the fourth resonator is upside down), will realize cross coupling between the first and fourth resonators that produces a pair of transmission zeros, one in the lower stop band and one in the upper stop band.

In addition, because the sequential coupling between adjacent resonators (e.g. first and second resonators204aand204b) in this configuration is dominantly magnetic coupling, rotation of the second resonator204bby 90 degrees makes the inter-resonator coupling less effective compared to known combline configurations, which allows for a more compact design. Specifically, the resonators204a,204b, and204ccan be placed closer together.

The bandpass filter200may also include one or more plates218aand218bsituated between adjacent resonators (e.g. first and second resonators204aand204b, or second and third resonators204band204c) to allow independent control of the sequential and cross coupling. Specifically, by proper arrangement of the location and size of the plates218aand218band the distance between resonators, the desired sequential and cross coupling coefficients can be realized. Although bandpass filter200is shown with only a single plate218aand218bbetween any pair of adjacent resonators, in other embodiments, there may be more than one plate between a pair of adjacent resonators.

In one embodiment, the plates218aand218bare rectangular metal walls with a height H and length L. In some cases, the height H and the length L of the plates218aand218bare the same so that the plates are square. However, the plates218aand218bmay have other suitable shapes and sizes. Preferably the plates218aand218bare made of the same materials as the cavity walls210,212,214a,214b,216aand216b(i.e. aluminum or copper). However, the plates218aand218bmay be made of other suitable materials. In some embodiments, the plates218aand218bare machined as part of the cavity walls212,214a,214b,216a,216band210.

Each plate218aand218bis typically situated within a plane220aor220bthat is substantially parallel to the end walls214aand214bso that each plate218aand218bis substantially parallel to the end walls214aand214b. Each plane220aand220bis defined by an upper left-corner222a,222b, an upper right-corner224a,224b, a lower left corner226a,226band a lower right corner228a,228b. The upper left-corner222a,222bis the corner of the plane220a,220bformed by the first side wall216aand the lid210, the upper right-corner224a,224bis the corner of the plane220a,220bformed by the second side wall216band the lid210, the lower left corner226a,226bis the corner of the plane220a,220bformed by the first side wall216aand the bottom wall212, and the lower right corner228a,228bis the corner of the plane220a,220bformed by the second side wall216band the bottom wall212. Each plate218aand218bis typically situated in one corner222a,224a,226aand228aor222b,224b,226b, and228bof a plane220aor220b.

Reference is now made toFIGS. 3A and 3B, which illustrate a plate218in the lower-left corner226and the lower right corner228of a plane220respectively.

Increasing the size of the plate when it is positioned in some of the corners will increase the sequential coupling coefficient, and increasing the plate size when it is positioned in other corners will decrease the sequential coupling coefficient. The corners which result in an increase in the sequential coupling coefficient will be referred to as increase positions, and the corners which result in a decrease in the sequential coupling coefficient will be referred to as decrease positions. The determination of which corners act as increase positions and which corners act as decrease positions depends on (1) the orientation of the resonators on either side of the plate, and (2) the size of the plate. This means that a corner may change from being a decrease position to an increase position as the size of the plate changes. For example, some corners may be decrease positions when the plate size is less than a threshold value, and increase positions when the plate size is greater than the threshold value.

Each plane220aand220b(and incidentally each plate218aand218b) is typically situated at the mid-point between adjacent resonators (e.g. at the mid-point between the first and second resonators204aand204b, or at the mid-point between the second and third resonators204band204c). However, the planes220aand220bmay be situated at any point between adjacent resonators.

The filter200may also include sequential coupling and/or cross coupling tuning elements (not shown). For example, filter200may include tuning screws situated on one or more cavity walls210,212,214a,214b,216aand216b. The position of the tuning screws on the cavity walls is typically based on the orientation of the resonators within the cavity202. For example, in the filter200shown inFIGS. 2A to 2C, tuning screws may be placed on the lid210or the bottom wall212between cross coupled resonators (e.g. between first and third resonators204aand204c) to facilitate tuning of the cross coupling. Filter200may also include tuning screws placed on one of the side walls216aor216bbetween adjacent resonators (e.g. between first and second resonators204aand204band between second and third resonators204band204c) for adjusting the sequential coupling. Accordingly, all sequential and cross couplings can be effectively adjusted.

To illustrate how the sequential coupling coefficient is affected by (i) the location of a plate; (ii) the size of a plate; and (iii) the distance between resonators, reference is made toFIG. 4, which illustrates a two-coupled resonator structure400for eigenmode calculation. The two-coupled resonator structure400has the same configuration as the bandpass filter200ofFIGS. 2A to 2Cexcept it comprises only two resonators404aand404band it does not include input and output connectors. Elements of the two-coupled resonator structure400that correspond to microwave bandpass filter200will be identified by similar reference numerals. Generally, corresponding elements will share the same last two digits. For example, the cavity202of the filter200ofFIGS. 2A to 2Ccorresponds to the cavity402of the resonator structure400ofFIG. 4.

Similar to bandpass filter200, the first resonator404aof resonator structure400has a substantially vertical orientation, and the second resonator404bof resonator structure400has a substantially horizontal orientation. Accordingly, it can be said that the second resonator404bis rotated 90 degrees with respect to the first resonator404a.

When two resonators have the same resonant frequency, equation (1) can be used to calculate the coupling coefficient k where f1and f2are the two eigenmodes of the resonator structure400ofFIG. 4. The two eigenmodes (f1and f2) can be calculated using the eigenmode solver of an electromagnetic (EM) field simulator, such as Ansoft Corporation's HFSS™.

Reference is now made toFIGS. 5A to 5C, which illustrate the sequential coupling coefficient for the resonator structure400ofFIG. 4as a function of the length (or height) of the square plate418when the cavity402width and height are both 1.5 inches, both resonators404aand404bhave a diameter of 0.4 inches and a height of 1.3 inches, the distance between the first resonator404aand the first end wall414ais 0.75 inches and the distance between the second resonator404band the second end wall414bis 0.75 inches. Each ofFIGS. 5A to 5Cillustrates the sequential coupling coefficient for the resonant structure400ofFIG. 4when the plate418is in a different corner422,424,426or428of the plane420. Specifically,FIG. 5Aillustrates the sequential coupling coefficient for the resonator structure400ofFIG. 4when the plate418is positioned in the bottom-left corner426of the plane420,FIG. 5Billustrates the sequential coupling coefficient for the resonant structure400ofFIG. 4when the plate418is positioned in the bottom-right corner428of the plane420, andFIG. 5Cillustrates the sequential coupling coefficient for the resonator structure400ofFIG. 4when the plate418is positioned in the upper-right corner424of the plane420.

FIG. 5Aincludes three coupling coefficient curves502,504, and506illustrating the sequential coupling coefficient when the plate418is positioned in the bottom left corner426of the plane420and the resonators404aand404bare separated by distances of 1.3 inches, 1.2 inches, and 1.1 inches respectively. It is clear from the three coupling coefficient curves502,504and506that, regardless of the distance between the resonators404aand404b, when the plate418is positioned in the bottom left corner426of the plane420the sequential coupling coefficient decreases as the length (or height) of the square plate418increases. Accordingly, when the resonators are oriented in the manner shown in FIG.4—specifically the first resonator404ais substantially vertical and the second resonator404bis substantially horizontal—the bottom-left corner426is a decrease position as that term was defined above. In this position, the plate418reduces the magnetic coupling between the resonators404aand404band thus reduces the total coupling. It can be seen fromFIG. 5A, that the sequential coupling coefficient reduces to zero when the length of the plate418is about half of the resonator height (e.g. ˜0.65 inches when the resonator height is 1.3 inches). After this point, the coupling changes from magnetic coupling to electric coupling and the total coupling begins to increase.

FIG. 5Bincludes three coupling coefficient curves508,510, and512illustrating the sequential coupling coefficient when the plate418is positioned in the bottom right corner428of the plane420and the resonators404aand404bare separated by distances of 1.3 inches, 1.2 inches, and 1.1 inches respectively. It is clear from the three coupling coefficient curves508,510and512ofFIG. 5Bthat, regardless of the distance between the resonators404aand404b, when the plate418is positioned in the bottom right corner428of the plane420, the sequential coupling coefficient increases as the length of the plate418increases. Accordingly, when the resonators are oriented in the manner shown in FIG.4—specifically, the first resonator404ais substantially vertical and the second resonator404bis substantially horizontal—the bottom right corner428is an increase position as that term was defined above. In this configuration, the plate418reduces the electric coupling between the resonators404aand404band thus increases the total coupling. A plate418positioned in the upper-left corner422has the same effect on the sequential coupling coefficient as a plate positioned in the bottom right corner428.

FIG. 5Cincludes three coupling coefficient curves514,516, and518illustrating the sequential coupling coefficient when the plate418is positioned in the upper-right corner424of the plane420and the resonators404aand404bare separated by distances of 1.3 inches, 1.2 inches, and 1.1 inches respectively. It is clear from the three coupling coefficient curves514,516, and518that, regardless of the distance between the resonators404aand404b, when the plate418is positioned in the upper-right corner424of the plane420, the sequential coupling coefficient decreases as the length of the plate418increases until the length of the plate418is roughly equal to half of the resonator height (e.g. ˜0.65 inches when the resonator height is 1.3 inches), then the sequential coupling coefficient increases as the length of the plate increases. This is because when the plate418is positioned in the upper-right corner424increasing the length of the plate418increases the electric coupling. When the length of the plate418is less than half of the resonator height (e.g. ˜0.65 inches when the resonator height is 1.3 inches), the coupling is magnetic coupling therefore as the electric coupling increases, the total coupling decreases. When the plate is greater than half of the resonator height (e.g. ˜0.65 inches when the resonator height is 1.3 inches), however, the coupling changes to electric coupling and thus increasing the electric coupling, increases the total coupling.

Accordingly, when the resonators are oriented in the manner shown in FIG.4—specifically, the first resonator404ais substantially vertical and the second resonator404bis substantially horizontal—the upper-right corner424is a decrease position when the length (or height) of the square plate418is less than half of the resonator height, and an increase position when the length (or height) or the square plate418is greater than half of the resonator height.

FIGS. 5A to 5Calso illustrate that, regardless of the position and the size of the plate, the sequential coupling coefficient decreases as the distance d between resonators404aand404bincreases.

Changing the thickness of the plate418has a similar effect on the sequential coupling as changing the length (or height) of the plate418. For example, when the plate418is positioned in the bottom left corner426of the plane420, the sequential coupling coefficient decreases as the thickness of the plate418increases. In some embodiments, the plate418has a thickness of 0.04 inches. However, the plate418may have any suitable thickness.

Accordingly, the sequential coupling between adjacent resonators (e.g. first and second resonators404aand404b) can be effectively controlled by changing (i) the size of the plate418; (ii) the position of the plate418; and (iii) the distance d between the resonators404aand404b. For example, by moving the same size plate418from the lower-left corner426to the lower-right corner428, the sequential coupling can be significantly increased. Similarly, the same sequential coupling can be realized with different combinations of resonator distance, plate size, and plate location. Each of the combinations will result in different cross couplings.

To illustrate how the cross coupling coefficient is affected by the size of a plate and the distance between resonators, reference is made toFIG. 6, which illustrates the cross coupling coefficient for filter200ofFIGS. 2A to 2Cas a function of the length of the plates218aand218bwhen the plates218aand218bare positioned in the lower-left corner226aand226bof the respective planes220aand220b.FIG. 6includes three cross coupling coefficient curves602,604and606illustrating the cross coupling coefficient when adjacent resonators (i.e. the first and second resonators204aand204b, and second and third resonators204band204c) are separated by a distance of 1.3 inches, 1.2 inches and 1.1 inches respectively. It can be seen from the three curves602,604, and606ofFIG. 6that the cross coupling coefficient reduces monotonically as the size of the plate increases and as the resonator distance increases. If the plates218aand218bare moved to the lower-right corner228aand228bof the respective planes220aand220b, the cross coupling coefficient curves are similar to the three curves602,604and606ofFIG. 6.

Reference is now made toFIG. 7, which illustrates the cross coupling coefficient for filter200ofFIGS. 2A to 2Cas a function of the length of the plates218aand218bwhen the plates218aand218bare positioned in the top-left corner222aand222bof the respective planes220aand220b.FIG. 7includes three cross coupling coefficient curves702,704and706illustrating the cross coupling coefficient when adjacent resonators (i.e. the first and second resonators204aand204b, and second and third resonators204band204c) are separated by a distance of 1.3 inches, 1.2 inches and 1.1 inches respectively. It can be seen from the three curves702,704, and706ofFIG. 7that, similar to the three curves602,604and606ofFIG. 6, the cross coupling coefficient reduces monotonically as the size of the plate increases and as the resonator distance increases. If the plates218aand218bare moved to the top-right corner224aand224bof the respective planes220aand220b, the cross coupling coefficient curves are similar to the three curves702,704and706ofFIG. 7.

The nonadjacent or cross coupling between non adjacent resonators may be calculated by detuning the second resonator204bofFIGS. 2A to 2C, removing the input/output ports, finding the two resonant frequencies using the eigenmode solver of an EM field simulator, such as Ansoft Corporation's HFSS™, and then using equation (1) to calculate the cross coupling coefficient.

Changing the thickness of the plates218aand218bdoes not have significant impact on cross coupling.

When there is more than one plate between a pair of adjacent resonators, the contribution from each plate may add up or cancel depending on the location of this plate. An exemplary filter800with multiple plates between adjacent resonators is shown inFIGS. 8A to 8C.FIG. 8Ais a perspective view of the bandpass filter800,FIG. 8Bis a side view of the bandpass filter800, andFIG. 8Cis a top view of the bandpass filter800. Bandpass filter800has the same configuration as bandpass filter200ofFIGS. 2A to 2Cexcept that it has four rectangular plates818a,818b,818cand818d, two between each pair of adjacent resonators. Elements of microwave bandpass filter800that correspond to microwave bandpass filter200ofFIGS. 2A to 2Cwill be identified by similar reference numerals. Generally, corresponding elements will share the same last two digits. For example, the cavity202of the filter200ofFIGS. 2A to 2Ccorresponds to the cavity802of the filter800ofFIGS. 8A to 8C.

In filter800, two of the rectangular plates818cand818dare positioned at the lower-left corner826aand826bof the corresponding planes820aand820b, and two of the rectangular plates818aand818bare positioned in the lower-right corner828aand828bof the corresponding planes820aand820b. Each of the plates818cand818din the lower-left corner826a,826bhas a length of LAand height of L. Each of the plates818aand818bin the lower-right corner828a,828bhas a length of LBand height of L.

In filter800, the sequential coupling between adjacent resonators (i.e. between the first and second resonators804aand804b, or between the second and third resonators804band804c) and cross coupling between the first and third resonators804aand804cis a function of LBas shown inFIG. 9. Specifically,FIG. 9illustrates the sequential coupling curve902and cross coupling curve904of filter800where the distance between adjacent resonators d is 1.25 inches and the height L of the plates818a,818b,818cand818dis 0.7 inches. It is assumed that LA+LB=L in the example. When LAreduces to 0 inches, the filter800ofFIGS. 8A to 8Cand the filter200ofFIGS. 2A to 2Chave the same configuration. The filter800ofFIGS. 8A to 8Ccan therefore be considered as the result of splitting the plates218aand218binFIGS. 2A to 2Cinto two pieces. As can be seen from curves902and904, the cross coupling remains unchanged and sequential coupling increases when the length LBof the plates818aand818bin the lower-right corner828a,828bincreases. Therefore, by separating the plate into two pieces, the sequential coupling and cross coupling can be controlled independently. In particular, making one piece smaller and the other piece bigger does not change cross coupling, but changes sequential coupling significantly.

Using the configurations described herein, a filter may be designed following these general steps. First, in order to realize the coupling values that can meet the desired filter performance, the initial values for resonator distance, position and sizes of the coupling plate(s) are estimated using the curves shown inFIGS. 5A,5B,5C,6and7through interpolation. Understandably, if the filter center frequency, cavity size, or resonator sizes are different from the examples herein, new curves of sequential and cross coupling values need to be calculated. These initial dimensions are then optimized using conventional methods to meet the desired filter performance.

Alternatively, the size of the plate(s) can be selected to realize the required cross coupling value usingFIG. 6orFIG. 7as if a single plate is to be used. Then, it is decided how the plate can be split to realize the desired sequential coupling through direct calculation of the sequential coupling or data curves similar toFIG. 9. These initial dimensions are then optimized using conventional methods to meet the desired filter performance. Using multiple coupling plates between adjacent resonators offers additional design flexibility.

To more clearly demonstrate how the orientation of the resonators, plate positions, plate sizes, and distance between resonators can be used to achieve filters with desired frequency responses, five exemplary filters designed in accordance with the principles described herein will be discussed. For ease of comparison, each of the four filters described below have been designed to have a center frequency of 1.54 GHz and a bandwidth of 48.8 MHz. In addition, in each of the five exemplary filters described below, the cavity width a is 1.5 inches, the cavity height b is 1.5 inches, the thickness of each plate is 0.04 inches, the diameter of each resonator is 0.4 inches, and the height of each resonator is 1.3 inches.

The first exemplary filter is the filter200ofFIGS. 2A to 2Cwhere the distance between adjacent resonators is 1.3 inches; the length and height of the plates218aand218bis 0.6 inches; the distance between the first resonator204aand the first end wall214ais 0.75 inches; and the distance between the third resonator204cand the second end wall214bis 0.75 inches.

The second exemplary filter is the filter800ofFIGS. 8A to 8Cwhere the distance between adjacent resonators is 1.25 inches, the height of the plates818a,818b,818cand818dis 0.7 inches; the length of the plates818cand818dis 0.15 inches; the length of the plates818aand818bis 0.55 inches; the distance between the first resonator804aand the first end wall814ais 0.75 inches; and the distance between the third resonator804cand the second end wall814bis 0.75 inches.

Reference is now made toFIG. 10, which illustrates the frequency response of both the first and the second exemplary filters. Specifically,FIG. 10illustrates the simulated S11and S21scattering parameter (“s-parameter”) curves1002and1004for the first exemplary filter, and the simulated S11and S21s-parameter curves1010and1012for the second exemplary filter. It can be seen from the S11and S21curves1002and1004that the first exemplary filter is a three pole filter with a transmission zero1006in the upper stop band. As described above, the transmission zero1006is generated by the cross coupling between the first and third resonators204aand204c. It can be seen from the S11and S21curves1010and1012that the second exemplary filter realizes the same sequential and cross coupling values as the first exemplary filter using multiple plates between adjacent resonators.

The third exemplary filter is filter1100illustrated inFIGS. 11A and 11Bwhere the distance between adjacent resonators is 1.1 inches; the plates1118aand1118bhave a length and height of 0.3 inches; the distance between the first resonator1104aand the first end wall1114ais 0.75 inches; and the distance between the third resonator1104cand the second end wall1114bis 0.75 inches.FIG. 11Ais a perspective view of the bandpass filter1100, andFIG. 11Bis a top view of the bandpass filter1100. Bandpass filter1100has the same configuration as bandpass filter200ofFIGS. 2A to 2Cexcept that the plates1118aand1118bare positioned in different corners of the planes1120aand1120b. Specifically, the first and second plates1118aand1118bare placed in the lower-left corners1126aand1126bof the first and second planes1120aand1120brespectively. Elements of microwave bandpass filter1100that correspond to microwave bandpass filter200ofFIGS. 2A to 2Cwill be identified by similar reference numerals. Generally, corresponding elements will share the same last two digits. For example, the cavity202of the filter200ofFIGS. 2A to 2Ccorresponds to the cavity1102of the filter1100ofFIGS. 11A and 11B.

Reference is now made toFIG. 12, which illustrates the frequency response of the third exemplary filter. Specifically,FIG. 12illustrates the simulated S11and S21scattering parameter (“s-parameter”) curves1202and1204for the third exemplary filter. By decreasing the distance between adjacent resonators from 1.3 inches to 1.1 inches, the cross coupling of the third exemplary filter is increased over the first exemplary filter. However, decreasing the distance between the resonators also increases the sequential coupling. To compensate for the increase in the sequential coupling caused by the reduced distance between the resonators, the plates1118aand1118bare moved from the lower-right corner1128a,1128bto the lower-left corner1126a,1126b. As illustrated inFIGS. 5A and 5B, this has the effect of reducing the sequential coupling while maintaining the same cross coupling. We can see from curves1202and1204ofFIG. 12that the third exemplary filter is also a three-pole filter with a transmission zero1206in the upper stop band. The third exemplary filter, however, achieves the same bandwidth as the first exemplary filter using a different resonator distance, plate size and plate location, resulting in a different out-of-band rejection level. Specifically, as can be seen fromFIG. 12, the transmission zero1206ofFIG. 12is closer to the passband than the transmission zero1006ofFIG. 10.

The fourth exemplary filter is the bandpass filter1300ofFIGS. 13A to 13Cwhere the distance between adjacent resonators is 1.27 inches; the length and height of the plates1318aand1318bis 0.6 inches; the distance between the first resonator1304aand the first end wall1314ais 0.75 inches; and the distance between the third resonator1304cand the second end wall1314bis 0.75 inches.FIG. 13Ais a perspective view of the bandpass filter1300,FIG. 13Bis a side view of the bandpass filter1300, andFIG. 13Cis a top view of the bandpass filter1300. Bandpass filter1300has the same configuration as the bandpass filter200ofFIGS. 2A to 2Cexcept the third resonator1304cis rotated 180 degrees from the first resonator1304a. In addition, the plates1318aand1318bare positioned in different corners of the planes1320aand1320b. Specifically, the first plate1318ais positioned in the lower-right corner1328aof the first plane1320a, and the second plate1318bis positioned in the upper-right corner1324bof the second plane1320b. Elements of microwave bandpass filter1300that correspond to microwave bandpass filter200will be identified by similar reference numerals. Generally, corresponding elements will share the same last two digits. For example, the cavity202of the filter200ofFIGS. 2A to 2Ccorresponds to the cavity1302of the filter1300ofFIGS. 13A to 13C.

In filter1300ofFIGS. 13A to 13C, both the second and third resonators1304band1304chave a different spatial orientation than the first resonator1304a. Similar to the filter200ofFIGS. 2A to 2C, the second resonator1304bis rotated 90 degrees with respect to the first resonator1304aso that the first resonator1304ais substantially vertical and the second resonator1304bis substantially vertical. However, unlike the filter200ofFIGS. 2A to 2C, the third resonator1304cis also rotated with respect to the first resonator1304a. Specifically, the third resonator1304cis rotated 180 degrees with respect to the first resonator1304aso that the third resonator1304cis upside down with respect to the first resonator1304a. As described above, this results in cross coupling between the first and third resonators1304aand1304cthat produces a transmission zero in the lower stop band of the frequency response of the filter.

Similar to filter200, the first plate1318aof filter1300is positioned in the lower-right corner1328aof the first plane1320a. However, unlike filter200, the second plate1318bof filter1300is positioned in the upper-right corner1324bof the second plane1320b. It should be noted that because of the orientation of the second and third resonators1304band1304cthe second plate1318bof filter1300(although situated in a different corner) will have the same effect on the second and third resonators1304band1304cof filter1300as the second plate218bwill have on the second and third resonators204band204cof filter200. This is because both the second plate1318bof filter1300and the second plate218bof filter200are situated in the corner that is closest to the top of the corresponding second resonator204b,1304band the bottom of the corresponding third resonator204c,1304c.

Reference is now made toFIG. 14, which illustrates the frequency response of the fourth exemplary filter. Specifically,FIG. 14illustrates the simulated S11and S21scattering parameter (“s-parameter”) curves1402and1404for the fourth exemplary filter. It can be seen from the s-parameter curves1402and1404that the fourth exemplary filter is a three-pole filter with a transmission zero1406below its passband.

The fifth exemplary filter is the bandpass filter1500ofFIG. 15where the distance between resonators is 1.12 inches between the first and second resonators1504aand1504b,1.1 inches between the second and third resonators1504band1504c,1.5 inches between the third and fourth resonators1504cand1504d,1.35 inches between the fourth and fifth resonators1504dand1504e,1.2 inches between the fifth and sixth resonators1504eand1504f; and the first plate1518ahas a length and height of 0.48 inches, the second plate1518bhas a length and height of 0.38 inches, and the third plate1518chas a length and height of 0.475 inches. The distance between the first resonator1504aand the first end wall1514ais 0.75 inches. The distance between the sixth resonator1504fand the second end wall1514bis 0.75 inches.

Bandpass filter1500has the same configuration as the bandpass filter200ofFIGS. 2A to 2Cexcept it includes three additional resonators1504d,1504eand1504f. The fourth and sixth resonators1504dand1504f, similar to the first and third resonators1504aand1504c, have a substantially vertical orientation, and the fifth resonator1504e, similar to the second resonator1504b, has a substantially horizontal orientation. Accordingly, filter1500will have two transmission zeros in the upper stop band. The first transmission zero is produced by the cross coupling between the first and third resonators1504aand1504c, and the second transmission zero is produced by the cross coupling between the fourth and sixth resonators1504dand1504f.

In addition, bandpass filter1500has a different configuration of plates over filter200. Specifically, bandpass filter1500has three plates1518a,1518b, and1518c. The first plate1518ais situated between the second and third resonators1504band1504cin the lower-left corner of the first plane1520a. The second plate1518bis situated between the fourth and fifth resonators1504dand1504ein the lower-right corner of the second plane1520b. The third plate1518cis situated between the fifth and sixth resonators1504eand1504fin the lower-right corner of the third plane1520c. Bandpass filter1500also has a metal wall1550between the third and fourth resonators1504cand1504d. Such wall is a well-known conventional way of controlling the sequential coupling between the third and the fourth resonators1504cand1504d. In the fifth exemplary filter the wall1550has a height of 0.815 inches.

Elements of microwave bandpass filter1500that correspond to microwave bandpass filter200are identified by similar reference numerals. Generally, corresponding elements will share the same last two digits. For example, the cavity202of the filter200ofFIGS. 2A to 2Ccorresponds to the cavity1502of the filter1500ofFIG. 15.

Reference is now made toFIG. 16, which illustrates the frequency response of the fifth exemplary filter. Specifically,FIG. 16illustrates the measured S11and S21scattering parameter (“s-parameter”) curves1602and1604and the simulated S11and S21curves1610and1612for the fifth exemplary filter. It can be seen from the s-parameter curves1602,1604,1610and1612that the fifth exemplary filter is a six-pole filter with two transmission zeros1606and1608in the upper stop band.