I. INTRODUCTION
The evanescent-mode technology is one of the most effective solutions for the design of wide spurious free stopband filters with relatively low insertion loss and high-power handling capability [Reference Snyder1, Reference Craven and Skedd2]. An evanescent-mode filter consists of a cascade of capacitive elements which resonates the shunt distributed inductance of an evanescent-mode waveguide. At the higher portion of the spectrum, where the amount of required capacitive loading is commonly modest, partial height pins or ridged waveguide sections are commonly employed to implement the resonators. The typical Q factor achievable with these resonators is high enough to design wide or moderate bandwidth filters suitable for low loss waveguide assemblies.
To maximize the filter insertion loss while providing the highest possible close-in rejection, elliptic, and quasi-elliptic filtering functions with finite frequency transmission zeros are usually recommended. To this purpose, several solutions, such as cross-coupled [Reference Ruiz-Cruz, Zhang, Fahmi and Zaki3] and extracted-pole topologies [Reference Fahmi, Ruiz-Cruz, Mansour and Zaki4], have been reported in the literature of waveguide evanescent-mode filters. Other approaches exploiting mixed lumped/distributed frequency-selective coupling [Reference Bastioli and Snyder5] or non-resonating modes have also been proposed for the generation of transmission zeros in evanescent-mode filters with in-line structure [Reference Wang and Yu6, Reference Bastioli and Snyder7]. However, most of the reported results comprise relatively narrowband filters (less than 5% fractional bandwidth) and/or having transmission zeros not very close with respect to the passband edges.
A rather challenging scenario arises indeed when the transmission zeros must be located extremely close to the passband edges of a wide or moderate bandwidth filter (larger than 8%). Besides the fact that the coupling coefficients required to synthesize the filtering functions might be unpractical to be implemented with conventional techniques, the main issue is that the insertion loss at the passband edges rapidly decreases as the transmission zeros get closer, thus compromising the passband insertion loss flatness. In other words, the Q factor of the evanescent-mode resonators, that is perfectly fine for most of the conventional applications, results not to be high enough in these extreme cases.
An original solution to overcome the above limitations consists of using H-plane TE201 mode cavities embedded within the structure of an evanescent-mode filter [Reference Bastioli and Snyder8]. Such a combination of cavities and resonators results is particularly suitable to practically realize the coupling coefficients that are necessary for the implementation of challenging filtering functions with extremely close transmission zeros and relatively wide bandwidth. A key feature of the proposed technique is that the insertion loss degradation at the filter cut-off frequencies is minimized thanks to the high Q factor of the waveguide cavities, whose corresponding poles are located right at the edges of the passband.
This paper extends the work presented in [Reference Bastioli and Snyder8] and generalizes this technique to the use of both H-plane and E-plane cavities, thus defining a new class of evanescent-mode filters using embedded non-resonating mode waveguide cavities. Several examples of filters using TE201 mode cavities (H-plane) or TM110 mode cavities (E-plane) for the generation of transmission zero below and/or above the passband are presented to show the high design flexibility of the proposed filter class.
II. H-PLANE CONFIGURATION
The TE201 mode cavity has been introduced in [Reference Amari and Rosenberg9] for the design of rectangular waveguide narrowband filters. Such a structure represents one of the earliest contributions regarding the class of non-resonating mode waveguide filters using propagating modes to generate bypass coupling capability [Reference Bastioli10–Reference Tomassoni and Sorrentino14]. The basic idea of this cavity is to exploit the TE10 mode (that is not resonating at the operative frequency) so as to bypass the TE201 mode, the latter being the cavity mode resonating at the operative frequency. By properly controlling the interference between the non-resonating and the resonant paths, a transmission zero can be generated.
To realize waveguide filters with relatively wide passband and stopband while having extremely close transmission zeros, the TE201 mode cavity can be efficiently embedded within an evanescent-mode filter. The basic structure of the proposed solution is shown in Fig. 1, where two evanescent-mode resonators are coupled to a TE201 mode cavity. The evanescent-mode resonators can be realized by means of partial height rods (as in Fig. 1) or using ridged waveguide sections. Although the structure in Fig. 1 includes coaxial connectors, waveguide sections can also be used as input and output interfaces to excite the evanescent-mode resonators.
Fig. 1. Basic structure of a TE201 mode cavity embedded between evanescent-mode resonators: (a) perspective view; (b) side view.
The coupling mechanisms occurring between the various modes are illustrated in Fig. 2 by means of the H-field components. Although evanescent-mode resonators are used at the cavity interfaces, the basic coupling mechanisms are analogous to those described in [Reference Amari and Rosenberg9] for inductive iris-coupled cavities. As is evident, the evanescent-mode resonators excite both the non-resonating TE10 mode and the resonant TE201 mode. To this purpose, the evanescent-mode sections must be offset with respect to the cavity center. The TE201 mode represents an additional resonator, while the non-resonating TE10 mode provides a direct coupling between the two evanescent-mode resonators. The resulting topology is shown in Fig. 3. As is well known, such a topology (commonly referred to as triplet) is capable of generating a transmission zero below or above three resonant poles.
Fig. 2. Coupling mechanisms: (a) resonators offset toward the same direction; (b) resonators offset toward opposite directions.
Fig. 3. Equivalent topology: resonators 1 and 3 represent the evanescent-mode resonators, while resonator 2 represents the resonant TE201 mode.
The waveguide discontinuity between the evanescent mode and the cavity cross-sections, as well as the distance between the resonators and the cavity, can determine the strength of all the coupling coefficients M 12, M 23, and M 13. Irises or waveguide matching sections can be introduced at the cavity interfaces to limit or enhance the strength of the coupling, respectively. Since we are interested in the realization of relatively wide bandwidths, where the coupling coefficients have to be relatively strong, waveguide matching sections are used in the proposed structures. As an example, in Fig. 1 the narrow evanescent-mode section is interfaced with the wide cavity cross-section by means of a short section of enlarged waveguide.
The offset of the evanescent-mode resonators with respect to the cavity center is the most important parameter as it controls the ratio between the sequential coupling and the bypass coupling. As the position of the evanescent-mode resonators tends to the cavity center, the coupling to the resonant TE201 mode (M 12 and M 23) vanishes, while the coupling to the non-resonating TE10 mode (M 13) is maximized. Since we are interested in the realization of extremely close transmission zeros, where the bypass coupling coefficient has to be significantly strong, the proposed structures present rather small offsets.
The relative position of the evanescent-mode resonators with respect to each other determines the sign of the sequential coupling M 23 with respect to M 12. When both evanescent-mode resonators are offset toward the same direction as in Fig. 2(a), the transmission zero is located below the passband. This is equivalent of having a negative bypass coupling M 13, while having positive sequential coupling coefficients M 12 and M 23. On the other hand, with reference to Fig. 2(b), when the resonators are offset toward opposite directions the sign of the sequential coupling M 23 is inverted with respect to the other sequential coupling M 12 (M 23 = −M 12) due to the 180° degree phase shift provided by the resonant TE201 mode. Such a sign inversion is evident by observing that the field lines of one of the two resonators are out-of-phase with the field lines of the resonant TE201 mode. With reference to Fig. 2(b), the green solid lines of one of the resonators are oriented along opposite direction with respect to the closest red dashed lines of the TE201 mode, while at the other resonator they are oriented along the same direction. Thanks to this sign inversion (M 23 = −M 12), the resulting transmission zero is located above the passband. Observe finally that the negative sign of the bypass coupling M 13 comes from the fact that the spurious resonance of the bypassing mode (which is the TE101 mode) is located below the passband. The latter statement has been demonstrated in [Reference Amari and Rosenberg9] for a general topology where the non-resonating mode is modeled as a detuned resonator.
For the application proposed in this paper, the cavity can be conveniently sized, so that the resonant frequency of the TE201 mode is located at the passband edge at which the transmission zero is generated.
Figure 4(a) shows the Ansys HFSS simulation (lossless) of the structure in Fig. 2(a). The structure has been optimized according to the following coupling matrix (f 0 = 10 GHz, fractional bandwidth FBW = 4.2%):
$$M = \left[ {\matrix{ 0 & {0.97} & 0 & 0 & 0 \cr {0.97} & { - 0.14} & {0.4} & { - 0.99} & 0 \cr 0 & {0.4} & {0.95} & {0.4} & 0 \cr 0 & { - 0.99} & {0.4} & { - 0.14} & {0.97} \cr 0 & 0 & 0 & {0.97} & 0 \cr}} \right].$$
Fig. 4. Ansys HFSS simulations of the structures in Fig. 2: (a) resonators offset toward the same direction; (b) resonators offset toward opposite directions.
Figure 4(b) shows the Ansys HFSS simulation (lossless) of the structure in Fig. 2(b). The structure has been optimized according to the following coupling matrix (f 0 = 10 GHz, fractional bandwidth FBW = 4.2%):
$$M = \left[ {\matrix{ 0 & {0.97} & 0 & 0 & 0 \cr {0.97} & {0.14} & {0.4} & { - 0.99} & 0 \cr 0 & {0.4} & { - 0.95} & { - 0.4} & 0 \cr 0 & { - 0.99} & { - 0.4} & {0.14} & {0.97} \cr 0 & 0 & 0 & {0.97} & 0 \cr}} \right].$$
As expected, the transmission zeros can be located extremely close to the lower or upper passband edges. Observe that the pole located at the passband edge next to the transmission zero corresponds to the TE201 mode resonating into the cavity (while the other two poles correspond to the evanescent-mode resonators). As is evident, such a pole is significantly narrower with respect to the other poles, and that is the reason why the high Q factor of the TE201 mode strongly benefits the resulting insertion loss at the passband edges.
To show the design flexibility of the proposed approach, three filters having same bandwidth but different transmission zero locations have been designed. The basic structure of the filters is shown in Fig. 5. In this example, the evanescent-mode waveguide sections are directly interfaced to the cavity without using any matching sections, and the main parameters to control the filtering function properties are the offset p and the distance d. The Ansys HFSS simulations of the filters are reported in Fig. 6. This example clearly shows that as p and d are properly increased, the transmission zero moves farther away from the passband.
Fig. 5. Basic structure of the three filter examples having same bandwidth but different transmission zero locations.
Fig. 6. Ansys HFSS simulations of the three filter examples: (a) close tranmission zero; (b) medium distance transmission zero; (c) far transmission zero.
III. E-PLANE CONFIGURATION
The concept of using TE201 mode cavities between evanescent-mode resonators can be extended to other types of non-resonating mode waveguide cavities. For those applications requiring E-plane architectures, a convenient solution is the use of TM110 mode cavities [Reference Rosenberg, Amari and Bornemann15]. The basic idea of these cavities is to exploit the TE10 mode (that is not resonating at the operative frequency) so as to bypass the TM110 mode, the latter being the cavity mode resonating at the operative frequency. Figure 7 shows the structure of a TM110 mode cavity embedded between a pair of evanescent-mode resonators. In this case, the evanescent-mode resonators have been realized by means of ridged waveguide sections, while propagating waveguide sections are used as input and output interfaces to excite the evanescent-mode resonators. Observe that partial-height posts and coaxial interfaces (as done in the previous H-plane structures) can also be used in this E-plane configuration.
Fig. 7. Basic structure of a TM110 mode cavity embedded between evanescent-mode resonators: (a) perspective view; (b) side view.
The coupling mechanisms occurring between the various modes are illustrated in Fig. 8 by means of the H-field components. The evanescent-mode resonators excite both the non-resonating TE10 mode and the resonant TM110 mode. To this purpose, the evanescent-mode sections must be offset with respect to the cavity center. The TM110 mode represents an additional resonator, while the non-resonating TE10 mode provides a direct coupling between the two evanescent-mode resonators. The resulting topology is shown in Fig. 9.
Fig. 8. Coupling mechanisms: (a) resonators offset toward the same direction; (b) resonators offset toward opposite directions.
Fig. 9. Equivalent topology: resonators 1 and 3 represent the evanescent-mode resonators, while resonator 2 represents the resonant TM110 mode.
Although different modes are employed, the E-plane configuration with TM110 mode cavities is capable of generating the same pseudoelliptic filtering functions as the H-plane configuration employing TE201 mode cavities. The main difference between the two is that the E-plane configuration leads to more compact solutions (the TM110 mode cavity is half the size of the TE201 mode cavity), while the H-plane configuration yields a better insertion loss (the TE201 mode cavity has roughly 30% higher Q factor than the TM110 mode cavity).
As far as the control of the coupling coefficients is concerned, the same considerations described for the H-plane configuration hold true for an E-plane configuration. The overall strength of the coupling coefficients M 12, M 23, and M 13 depends on the waveguide discontinuity between the evanescent mode and the cavity cross-sections, as well as the distance between the resonators and the cavity. Waveguide matching sections can be introduced at the cavity interfaces to enhance the strength of the coupling.
The ratio between the sequential and the bypass coupling is controlled by the offset of the evanescent-mode sections with respect to the cavity center. In contrast with the TE201 mode cavity, for a TM110 mode cavity the evanescent-mode sections are offset along the E-plane. As the position of the evanescent-mode resonators tends to the cavity center, the coupling to the resonant TM110 mode (M 12 and M 23) vanishes, while the coupling to the non-resonating TE10 mode (M 13) is maximized.
The sign of the sequential coupling M 23 with respect to M 12 depends on the relative position of the evanescent-mode resonators with respect to each other. For similar considerations to those discussed for the H-plane configuration, the structure in Fig. 8(a) (offset toward the same direction) generates a transmission zero below the passband, while the structure in Fig. 8(b) (offset toward opposite directions) generates a transmission zero above the passband.
As far as the cavity dimensions are concerned, the cavity can be conveniently sized, so that the resonant frequency of the TM110 mode is located at the passband edge at which the transmission zero is generated.
As an example, Fig. 10 shows the Ansys HFSS simulation of the structure in Fig. 8(a). As is for the previous H-plane structures, this simulation confirms that also E-plane structures using TM110 mode cavities are suitable to realize filtering functions with extreme close-in rejection.
Fig. 10. Ansys HFSS simulations of the structure in Fig. 8(a).
Finally, as far as the practical manufacturing of these E-plane configurations is concerned, the structure can be manufactured from two halves, while the evanescent-mode resonators could be realized by means of metallic rods inserted between them.
IV. RESULTS
An 11th-order evanescent-mode filter employing two TE201 mode cavities has been designed and manufactured. The filter passband ranges from 9.950 to 11.000 GHz, where the required insertion loss must be larger than 1.5 dB with no more than 1 dB variation across the whole bandwidth. The required VSWR in the passband is 1.5:1. An extreme close-in rejection of 45 dB is required between 11.040 and 11.050 GHz, while 60 dB attenuation must be guaranteed from 11.5 to 20 GHz as well as below 9.4 GHz.
The filter structure and its equivalent topology are shown in Figs 11 and 12, respectively. The two TE201 mode cavities are embedded as fifth and seventh resonators. Each cavity is responsible for the generation of a transmission zero at 11.036 and 11.048 GHz, respectively. The evanescent-mode sections are sized to provide a spurious free stopband up to 20 GHz. Based on the authors’ experience, the expected Q factors are 1600 for the evanescent-mode resonators (40% of the theoretical value) and 6000 for the TE201 mode cavities (60% of the theoretical value). The filter has been designed according to the following coupling matrix (f 0 = 10.443 GHz, fractional bandwidth FBW = 10.4%): M S1 = M 11 L = 0.963, M 12 = M 1011 = 0.801, M 23 = M 910 = 0.584, M 34 = M 89 = 0.547, M 45 = 0.352, M 56 = −0.34, M 67 = 0.31, M 78 = −0.322, M 46 = −0.403, M 68 = −0.427, M SS = M LL = 0, M 11 = M 22 = M 33 = 0, M 44 = 0.007, M 55 = −0.788, M 66 = 0.014, M 77 = −0.833, M 88 = 0.007, M 99 = M 1010 = M 1111 = 0.
Fig. 11. Evanescent-mode waveguide filter using two TE201 mode cavities and nine evanescent-mode resonators.
Fig. 12. Equivalent topology of the filter in Fig. 11.
The manufactured prototype is shown in Fig. 13. To maintain temperature stability, the filter is made out of silver plated INVAR. Observe that a realization in aluminum would imply a frequency drift of about 30 MHz (±15 MHz) over temperature (from −55 to 80 °C). Such a frequency drift would be unacceptable, as it is comparable with the extent of the upper transition band (the distance between the passband edge and the first transmission zero is 36 MHz).
Fig. 13. Manufactured filter.
The measured S parameters are shown in Fig. 14 along with the corresponding Ansys HFSS simulation (lossless). Observe the extreme close-in rejection provided by the two transmission zeros. The measured insertion loss is 0.45 dB at the filter center frequency and 1.2 dB at the highest frequency of the passband. These data are in agreement with the expectations regarding the Q factors of the resonators (1600) and the cavities (6000).
Fig. 14. Experimental results and Ansys HFSS simulation (lossless) of the filter.
To demonstrate the benefit provided by the cavities on the passband edge insertion loss, Fig. 15 shows the upper cut-off frequency of the proposed filter (continuous lines) and the comparison with the simulation of an equivalent hypothetical filter involving only evanescent-mode resonators (dashed lines). The latter simulation has been derived by setting the Q factor of the fifth and seventh resonators at 1600 (as is for the other resonators). The two simulations have been derived from the equivalent lumped element circuits of the two filters using Genesys circuit simulator. As is evident, for the proposed filter having 6000 Q factor for the fifth and seventh resonators the insertion loss at the highest passband frequency is considerably lower (1.2 versus 2.2 dB), while at the same time the attenuation at the two transmission zeros is higher. The insertion loss at the filter center frequency (not shown) is around 0.45 dB in both cases. This comparison demonstrates that besides making it possible to generate extremely close transmission zeros, the proposed structure including non-resonating mode waveguide cavities allows us to alleviate the insertion loss degradation occurring at the passband edges, thus improving the amplitude flatness of the whole passband.
Fig. 15. Comparison between the proposed filter with 6000 Q factor for the fifth and seventh resonators (continous line) and an equivalent filter with 1600 Q factor for all the resonators (dashed line).
As far as temperature stability is concerned, thanks to the INVAR manufacturing the overall frequency shift from −40 to +85 C is less than 4 MHz (Fig. 16).
Fig. 16. Temperature tests.
Finally, Fig. 17 shows a broadband measurement of the manufactured prototype. As expected, the upper stopband extends up to the required 20 GHz. Observe that all the spurious responses coming from the lower (such as the TE101 mode) and higher-order modes of the cavities are efficiently suppressed below −60 dB by the evanescent-mode resonators.
Fig. 17. Broadband measurment.
V. CONCLUSIONS
An original solution for the design of waveguide evanescent-mode filters with extreme close-in rejection has been proposed in this paper. The novel solution combines evanescent-mode resonators with non-resonating mode waveguide cavities, thus allowing the realization of filters with relatively wide passband and stopband while having transmission zeros extremely close to the passband edges. Both H-plane and E-plane non-resonating mode waveguide cavities have been presented and verified through accurate full-wave simulations. The experimental results (including temperature tests) of an X-band filter validate the proposed solution. To the authors’ best knowledge the manufactured filter attains unique electrical performances which are otherwise not achievable with conventional techniques.
Simone Bastioli (S′10, M′11) received the Master's and Ph.D. degrees in Electronic Engineering from the University of Perugia, Italy, in 2006 and 2010, respectively.
In 2005, he was an intern at Ericsson AB, Mölndal, Sweden, working on waveguide filters and transitions for radiofrequency applications. In 2006, he was admitted as Ph.D. student at University of Perugia with a scholarship funded by the Italian Space Agency (ASI). In 2009, he was with RF Microtech Srl, Perugia, Italy, where he was responsible for the design of advanced microwave filters for private and European Space Agency (ESA) funded projects. In 2010, he joined RS Microwave Company Inc., New Jersey, USA, where he is currently employed as a senior microwave research engineer, working on reduced size multimode cavity filters, advanced high-power evanescent-mode filters, dielectric resonator, and lumped element filters.
Dr. Bastioli is a member of MTT-8 Filters and Passive Components Technical Committee. He was the recipient of the 2012 IEEE Microwave Prize. In 2008, he was awarded with the Best Student Paper Award (First Place) at the IEEE MTT-S International Microwave Symposium (IMS) held in Atlanta, GA, USA, and with the Young Engineers Prize at the European Microwave Conference held in Amsterdam, The Netherlands. In 2009, he was the recipient of the Hal Sobol Travel Grant presented at the IEEE MTT-S IMS held in Boston, MA, USA. His research activities resulted in more than 20 publications in international journals and conferences, as well as four patent applications.
Richard V. Snyder is the President of RS Microwave (Butler, NJ, USA), author of 84 papers, three book chapters and holds 19 patents. His interests include E–M simulation, network synthesis, dielectric and suspended resonators, high power notch and bandpass filters, and active filters. He received his BS, MS, and Ph.D. degrees from Loyola-Marymount, USC and PINY.
Dr. Snyder served the IEEE North Jersey Section as Chairman and 14 year Chair of the MTT-AP chapter. He chaired the IEEE North Jersey EDS and CAS chapters for 10 years. He received twice the Region 1 award. In January 1997 he was named a Fellow of the IEEE and is now a Life Fellow. In January 2000, he received the IEEE Millennium Medal. Dr. Snyder served as General Chairman for IMS2003, in Philadelphia. He was elected to ADCOM in 2004. Within the ADCOM, he served as Chair of the TCC and Liaison to the EuMA. He served as an MTT-S Distinguished Lecturer, from 2007 to 2010, as well as continuing as a member of the Speakers Bureau. He was an Associate Editor for the IEEE Transactions on Microwave Theory and Techniques, responsible for most of the filter papers submitted. He is a member of the American Physical Society, the AAAS, and the New York Academy of Science. He was the MTT-S President for 2011. Also a reviewer for IEEE-MTT publications and the MWJ, Dr. Snyder teaches and advises at the New Jersey Institute of Technology. He is a visiting professor at the University of Leeds, in the UK. He served 7 years as Chair of MTT-8 and continues in MTT-8/TPC work. He was previously the Chief Engineer for Premier Microwave.
