Chad Bartlett, Michael Höft
©SHUTTERSTOCK.COM/SDECORET
Standard technologies for mid- to high-frequency-range circuits generally come in the form of microstrip and coplanar waveguides. Inherently, these types of circuits provide attractive attributes, such as low cost, simple fabrication, and a high-degree of miniaturization and planarity. However, for high-performance and mission-critical applications, such as satellite constellations, broadcast communications, and remote sensing, these high-end circuits require a much more robust transmission line technology, such as metallic waveguides, which can accommodate higher operational frequencies and wider bandwidths with low signal loss and high-power handling.
In terms of filter design, resonators (or the resonant modes) allow for selective frequencies to propagate throughout the circuit. A properly tuned set of resonators creates the collective passband of a filter. In conjunction, nonresonating modes [1] can be viewed as modes that do not resonate within the vicinity of the selected passband and generally resonate far below or far above the passband. The advantage of the using nonresonating modes lies in the ability to create additional (nonresonating) pathways throughout the circuit. These pathways create a functional bypassing method and allow for instances of destructive interference that will ultimately allow for the generation of transmission zeros in the filter response.
The nonresonating-mode concept [1] has allowed for many advanced topologies and high-performance filter designs to be put forth in the literature. A comprehensive discussion of the history and state of the art of nonresonating modes provided in [2] allows for a dynamic view of the adoption of this technique and its ability to not only improve the characteristic filter response but also facilitate highly compact and lightweight structures with low geometric complexity, ultimately paving the way for future generations of high-performance terrestrial and satellite communications. Furthermore, advancements in this technique, such as [3], have even demonstrated the inclusion of resonant irises in transverse magnetic (TM) dual-mode filters as a means of improving the nonresonating-mode technique described in [4].
In regard to fundamental first-order designs, singlets provide designers with an effective tool for generating one passband pole and one transmission zero though the use of a nonresonating-mode bypass coupling. This method allows for direct control of the transmission zero location and can influence the rejection characteristics above and below the passband and has been applied to many advanced filter topologies, such as [5], [6], [7], [8], and [9]. However, in regard to the use of asymmetric irises with use of evanescent modes as singlets [10], [11], [12], the generation of transmission zeros has been shown to be limited to the upper passband and located far away from the passband. This limitation seems to be caused by the relatively weak evanescent bypass coupling and has yet to be overcome in such designs. In light of the drawbacks of this type of structure, the authors propose an alternative approach and define a special case of the singlet, which is able to not only create the necessary passband pole and functional transmission zero but also integrate an E/H-plane bend and 90° polarization rotation into an ultracompact structure. The introduction of this novel singlet building block has been defined and termed the anglet [13].
The following article is provided to the microwave community as an extended version of an award-winning paper from the 2023 IEEE Radio and Wireless Week Student Paper Contest [13] and expands the concept in order to demonstrate novel topologies for advanced and compact filter design. Specifically, the use of multiple anglets is demonstrated as a unique alternative to typical E-plane cross-coupled filter designs with and without the use of source/load coupling.
The ability to integrate multiple components (e.g., [14] and [15]) into highly compact structures is an invaluable asset and has gained much attention in the literature due to the widespread use of additive manufacturing (e.g., [16], [17], [18], and [19]). However, despite these advancements in manufacturing, one of the most difficult challenges that filter designers face is finding suitable methods or structures that facilitate the generation of transmission zeros for improving the selectivity of the characteristic response, and understandably, this difficulty is further exacerbated—in some cases, leading to infeasibility—when attempting to manufacture these complex components with computer numerical control milling.
In light of these challenges, the versatile and unique physical profile of the anglet allows designers to overcome three fundamental challenges at once, those being a 90° bend, a 90° polarization rotation, and the generation of a pole/transmission zero pair. This structure is a first-order building block, and as demonstrated in [13], it can be readily applied in higher-order filter designs to achieve complex characteristics. Figure 1 depicts the key concept of integrating three components, namely, a twist, bend, and singlet, into one fundamental unit. One of the key aspects of the anglet’s versatility is due to the orthogonal positions of the input and output ports and is shown in the form of a rectangular cavity anglet in Figure 2. Depending on the selection of either port, the resonating mode will be regarded as either a TE101 or TM110 mode, and the evanescent bypass coupling will, in turn, be regarded as either a TE20 or TM12 nonresonating mode, respectively, and in this manner, the selected orientation of the structure will provide either an E- or H-plane bend and the inherent 90° polarization rotation. This unique physical profile distinguishes the anglet from other nonresonating-mode designs, as highlighted in Table 1.
Figure 1. The fundamental concept of the component integration and topology of the anglet. The resonating node is black, and the source/load nodes are white. Solid lines indicate the direct coupling paths, the dashed line indicates the bypass coupling path, and the half-window frame symbol distinguishes the use of an anglet from a singlet in schematic form.
Figure 2. A rectangular cavity anglet: the (a) front view and (b) perspective view. The electromagnetic field orientation of the resonating and nonresonating modes: the (c) front view and (d) perspective view.
Table 1. A summary of basic rectangular waveguide cavities utilizing nonresonating modes.
As described in [13] and Figure 1, the topology of the anglet includes a half-window symbol in order to communicate the angular (E- or H-plane) change and intrinsic polarization rotation. Figure 2(a) and (b) depicts the rectangular cavity anglet, with the input port orientated toward the front, and the resulting bend-and-twist motion ending in the H-plane direction. Figure 2(c) and (d) is provided as a depiction of the resonant and nonresonant modes’ orientation throughout the structure.
The characteristic response of an anglet can be described by a 3 × 3 coupling matrix, using equations from [7], [13], [20], and [21], as \[{[}{m}{]} = \left[{\begin{array}{ccc}{0}&{{M}_{S1}}&{{M}_{SL}}\\{{M}_{S1}}&{{M}_{11}}&{{M}_{1L}}\\{{M}_{SL}}&{{M}_{1L}}&{0}\end{array}}\right] \tag{1} \] \[{Q}_{{e}_{Sii}} = \frac{{\pi}\cdot{f}_{{\tau}_{Sii}}\cdot{\tau}_{Sii}{(}{f}_{{\tau}_{Sii}}{)}}{2} \tag{2} \] \[{M}_{SL} = \frac{{M}_{S1}{M}_{1L}}{{\Omega}_{Z}} \tag{3} \] where ${\tau}_{Sii}$ is the group delay and ${f}_{{\tau}_{Sii}}$ is its associated center frequency for ${i} = {1},{2},$ and the authors propose (3) as a solution to the source/load coupling, where ${\Omega}_{Z}$ is the normalized transmission zero frequency. A demonstration of the control of the transmission zero location is given in Figure 3. Four test cases are provided, where the transmission zero is moved above and below the 10-GHz center frequency location.
Figure 3. The simulated transmission response of the rectangular cavity anglet described in Figure 2. The transmission zeros (${T}_{Zi}$ for ${i} = {1},{2},{3},{4}$) are varied by adjusting the port position via ${d}_{1}$.
An anglet-based filter was described in [13] as a quasi-triplet design, where the transmission zero was placed below the passband, using two rectangular cavities and one L-shaped anglet cavity. This initial study demonstrated that 1) the transmission zero can be placed in the lower passband and 2) the transmission zero location can be placed close to or far away from the passband. This demonstration is contrary to previous evanescent-mode designs that utilized asymmetric irises [10], [11], [12]. To demonstrate the use of anglets in higher-order designs, as well as illustrate the advanced use of the transmission zeros, we demonstrate three different multi-anglet filter designs with various characteristic responses and fractional bandwidths (FBWs) by simulation. In this manner, strong region characteristics can be demonstrated at different locations in the frequency band. The proposed topology is provided in Figure 4 and demonstrates the use of two anglets to create a fifth-order filter with two transmission zeros. This can be realized with the use of three resonator cavities and two rectangular anglet cavities. Furthermore, it can be noted that the use of two anglets in this manner allows for the combination of two 90° polarization rotations (i.e., 0 or 180° rotation), ultimately resulting in the output port of the filter having the same polarization orientation as the input port (i.e., the twist is effectively eliminated). Three different examples of simulated S-parameters of this fifth-order concept are displayed in Figure 5(a)–(c) for operation at 10 GHz, with FBWs of approximately 4%, 2.1%, and 4.1%, respectively. The transmission zeros that are portrayed are located in different positions and demonstrate strong rejection characteristics in the selected regions. For instance, in Figure 5(b), the transmission zero closest to the passband reaches $\approx$60 dB at 9.68 GHz, while the transmission zero farthest from the passband reaches $\approx$130 dB at 8.4 GHz.
Figure 4. The topology of the fifth-order filter utilizing two anglets without the use of source/load coupling. Resonating nodes are black, and source/load nodes are white. Solid lines indicate direct coupling paths, and dashed lines indicate bypass coupling paths.
Figure 5. Lossless simulated S-parameter results of three sample variations of a fifth-order filter utilizing two anglets without the use of source/load coupling, as proposed in Figure 4. Characteristics with (a) 4% FBW, (b) 2.1% FBW, and (c) 4.1% FBW.
Further advancements of the multi-anglet filter designs that are proposed in the previous section can include the canonical effects provided by the use of source/load coupling. In this manner, a fifth-order filter response can take advantage of five transmission zeros. The proposed topology appears in Figure 6, while the vacuum shell of the filter model is in Figure 7, where the source/load coupling can be seen clearly as a thick iris. The simulated S-parameters of this design are shown in Figure 8 for operation at 10 GHz, with a 4% FBW. Three transmission zeros are placed below the passband, and two transmission zeros are placed above the passband. Reviewing the model in Figure 7, it can be noted that this design is suitable for either additive or subtractive manufacturing, does not require any overly complex geometries, and can act as an alternative approach to classical [22] E-plane folded and cross-coupled designs.
Figure 6. The topology of the fifth-order filter utilizing two anglets and source/load coupling. Resonating nodes are black, and source/load nodes are white. Solid lines indicate direct coupling paths, and dashed lines indicate bypass coupling paths.
Figure 7. The vacuum shell of the proposed 4% FBW filter utilizing two anglets with source/load coupling. The structure is formed from three regular rectangular cavities and two rectangular-shaped anglets as the interconnects.
Figure 8. Lossless simulated S-parameter results of the fifth-order 4% FBW filter utilizing two anglets with source/load coupling, as proposed in Figure 6 and modeled in Figure 7.
To verify the proposed design methodology, the canonical design from Figures 6 and 7 is manufactured for X-band operation in an aluminum alloy. The basic dimensions are provided in Figure 9 and Table 2. The filter is milled with two main sections that house the four (upper and lower) resonator cavities and input/output transitions, while three thinner sections are designed for the fifth resonator and the corresponding transition irises. Figure 10 depicts each of the milled components and the fully assembled filter. Once assembled, the filter was tested using a Rohde & Schwarz ZVA67 network analyzer. Figure 11 compares the simulated and measured results from 8 to 12 GHz. This direct comparison demonstrates very accurate measured results: the measured return loss is better than 20 dB throughout the passband, and the measured insertion loss is in the range of 0.31 to 0.46 dB. A close-up view of the passband insertion loss is available in Figure 12 over the range of 9.5 to 10.5 GHz. Analyzing the filter’s response, the unloaded quality factor is estimated to be approximately ${Q}_{u}\approx$ 2,400. In addition to the results discussed, the simulated-versus-measured group delay response is provided in Figure 13 and exhibits a very accurate measured profile compared to the simulation.
Figure 9. The dimensional layout of the fabricated filter utilizing two anglets with source/load coupling. (a) Top view. (b) Side view. To simplify the drawings, the structure is dimensioned with regard to the top filter section with the label abbreviation (T), and its synonymous dimension in the bottom filter section is of dimension (B); I is the source/load iris, R is the middle resonator cavity, and S is an offset. Input/output waveguides are standard WR90. See Table 2 for dimensional values.
Figure 10. The fabricated X-band prototype of the fifth-order filter utilizing two anglets with source/load coupling from Figures 7 and 9. The (a) disassembled internal filter cavities and iris coupling foils and (b) fully assembled filter.
Figure 11. Simulated-versus-measured S-parameter results of the fifth-order 4% FBW filter with source/load coupling. Effective conductivity is taken as 5.6 MS/m.
Figure 12. A close-up view of the simulated-versus-measured insertion loss of the fifth-order 4% FBW filter with source/load coupling. Effective conductivity is taken as 5.6 MS/m.
Figure 13. The simulated-versus-measured group delay response of the fifth-order 4% FBW filter utilizing two anglets with source/load coupling. Effective conductivity is taken as 5.6 MS/m.
Table 2. The filter dimensions.
This article has provided an extended view of the anglet concept. Novel filters have been proposed by utilizing multiple anglets for demonstration of various filter characteristics with multiple transmission zeros. The versatility and control over the anglet’s transmission zeros allow for an alternative approach to typical E-plane folded designs and ultimately provide engineers with a new first-order building block for filter design. A design utilizing two anglets to create an E-plane folded structure with source/load coupling was selected for fabrication and demonstration of a canonical response with five passband poles and five transmission zeros. Highly accurate measurements were achieved in the frequency band of interest. As exemplified in this work, RF filter designers can readily apply this new building block concept to achieve higher-order designs and complex filter characteristics.
This project has received funding from the European Union’s Horizon 2020 research and innovation program, under Marie Skłodowska-Curie Grant 811232-H2020-MSCA-ITN-2018. This article is an expanded version from the 2023 IEEE Radio and Wireless Symposium, in Las Vegas, NV, USA, on 22–25 January 2023 (DOI: 10.1109/RWS55624.2023.10046313). Chad Bartlett is the corresponding author.
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Digital Object Identifier 10.1109/MMM.2023.3314323