Alden Fisher, Michael D. Sinanis, Mohammad Abu Khater, Dimitrios Peroulis
©SHUTTERSTOCK.COM/NICOELNINO
In today’s crowded RF spectrum, receivers must be highly selective to mitigate any interference, whether intentional or from adjacent channels. The upper part of the C band (4–8 GHz) has been designated for space-to-Earth satellite communications and space exploration [1]. This long-range communication demands sensitive, low-loss receivers that can recover weak signals. Customarily, a tradeoff between size and performance presents itself, which poses a challenge to the microwave community as size is often critical in satellite payloads. Therefore, a compact, radiation-impervious filtering solution is needed.
This article describes our work, which received first place for the Packaged C-Band Filter Student Design Competition at the 2022 IEEE International Microwave Symposium (IMS), held in Denver, Colorado. In this article, we describe the design challenges and subsequent implementation of a substrate integrated, evanescent-mode (EVA-mode) cavity resonator bandpass filter (BPF), with dual out-of-band transmission zeros (TZs) for enhanced selectivity.
The Packaged C-Band Filter Student Design Competition challenged teams to create a BPF centered at 7.3 GHz with 8% fractional bandwidth (584 MHz), all while being constrained to an 18.5-mm square package ${(}{342}{mm}^{2}{)}$ [2]. The participating teams received a Kyocera package shown in Figure 1, which fans out to eight pins. Although the total area of the filter was constrained to be within the package, the volume was not, meaning the design could exceed the package height. The challenge with this package was twofold: integration and managing parasitics. The input and output connections of any given filter must occur via two of these eight pins; therefore, the design of this filter is restricted by the pin locations. The package also demonstrated strong parasitics above 10 GHz and poor matching ${(|}{S}_{11}{|}{<}{10}\,{\text{dB}}{)}$ above 4.4 GHz, with a simple thru line between two pins in the package [2]. Furthermore, the provided package needed to be on a carrier RF board with adequately designed transition and end launch connectors.
Figure 1. The package used in this competition has eight pins and a main face area of 342 mm2. All units are in millimeters: a = 2.8, b = 2.29, c = 1.27, d = 0.64, h = 2.87, g = 1.07, s = 0.41, l = 2.4, and w = 18.55 square.
The filter’s transmission response, in decibels, was to be sampled at seven discrete points: three in the passband (7.1, 7.3, and 7.5 GHz) and four in the rejection band (4.6, 6.6, 8, and 10 GHz). Scoring was based on these points alone, which were weighted depending on how close they were to the center frequency [2]. A graphical representation of the scoring for a sample filter response is shown in Figure 2. Care was taken to reduce the loss in the passband and create notches at the 6.6- and 8-GHz points to maximize the score. Note that return loss is not directly accounted for in the scoring but will affect the filter’s insertion loss.
Figure 2. Conceptual plot shows forward response of an ideal third-order Chebyshev filter with competition scoring values overlaid. The multipliers should be taken to the gain value of the filter, in decibels, and summed to give the final score. This lossless filter example would have a score of about 14.
Low-loss resonators generally require a large volume to store electromagnetic energy, thus increasing its unloaded quality factor, given as: \[{Q}_{u}\propto\frac{{E}_{\text{stored}}}{{E}_{\text{lost}}}{.} \tag{1} \]
Conventional planar and lumped-element technologies typically exhibit more loss, particularly at higher frequencies, when compared to cavity resonators. Since cavities take full advantage of the substrate’s volume, this leads to a higher quality factor. The size can be increased by leveraging the lack of a height requirement to further reduce this design’s loss. This enables a small footprint while minimizing loss beyond conventional planar and lumped technologies. Additionally, EVA-mode cavities allow for a more compact design with a reasonable tradeoff of loss [3], [4]. Table 1 briefly summarizes typically achievable quality factors for various technologies. It is clear that given the size and realizable quality factors, EVA-mode cavity resonators are a favorable choice for this design challenge. Furthermore, implementation in substrate-integrated waveguide (SIW) technology allows for simple manufacturing and offers post-fabrication tuning flexibility.
Table 1. Typical quality factors for various, commonly used technologies.
EVA-mode cavity resonators can be approximated as a shorted coaxial feed of some electrical length, ${\beta}{l},$ with added parallel capacitance from the center post to the grounded sidewalls. This creates an inductive structure in parallel with an annular ring capacitance, forming a resonator, shown in Figure 3(a) [4]. The capacitance is typically implemented as a bending membrane to achieve wide frequency tunability [4], [13], [15], [16], [17], [18]. This, however, is not of interest in this work since the design requirements are at a fixed frequency. Unlike a traditional cavity, an EVA-mode cavity utilizes a post in the center that disturbs the fundamental mode, lowering its operational frequency [3], [19]. This reduces the total size of the cavity at the cost of loss [3], [4].
Figure 3. An example of (a) an ideal single-mode and (b) dual-mode EVA-mode cavity resonator with equivalent circuit overlaid and explicit circuit representation below.
As the technology is decided, the topology can now be investigated. First, we conducted a tradeoff study to look at the order of the filter to maximize the points for the competition. We started with the assumption that we could fit two to four resonators in the package, attain the correct center frequency, and maintain a ${Q}_{u}$ higher than planar and lumped technologies. The packaging optimization problem can be simplified to packing N congruent circles into a unit square, although the coupled cavity resonators will eventually overlap. For the Kyocera package, the maximum diameter of two and three circles is 10.94 mm and 9.5 mm, respectively [20]. When designing the individual resonators, this maximum size is slightly reduced to account for the vias of the outer sidewall. However, despite the marginally larger resonator and subsequently higher ${Q}_{u},$ the second order does not compete with the third order in terms of selectivity and score. Although the fourth order would keep the size of the resonators comparable to the third order (only 3.4% smaller area) and increase the score marginally, it requires them to be placed in the corners of the package. This would have complicated the external couplings of the pins and was ultimately abandoned. For these reasons, we proceeded with a third-order Chebyshev with 0.2-dB ripple both for its steep roll-off and for the valleys of its in-band ripples occurring at nonsampled points for scoring. The ideal response is shown in Figure 4, with the corresponding coupling matrix in (2) [21], [22]. \begin{align*}\left[{M}_{\text{BPF}}\right] & = \left[{\begin{array}{lllll}{{M}_{SS}}&{{M}_{S1}}&{{M}_{S2}}&{{M}_{S3}}&{{M}_{SL}}\\{{M}_{1S}}&{{M}_{11}}&{{M}_{12}}&{{M}_{13}}&{{M}_{1L}}\\{{M}_{2S}}&{{M}_{21}}&{{M}_{22}}&{{M}_{23}}&{{M}_{2L}}\\{{M}_{3S}}&{{M}_{31}}&{{M}_{32}}&{{M}_{33}}&{{M}_{3L}}\\{{M}_{LS}}&{{M}_{L1}}&{{M}_{L2}}&{{M}_{L3}}&{{M}_{LL}}\end{array}}\right] \\ & = \left[{\begin{array}{ccccc}{0}&{0.903}&{0}&{0}&{0}\\{0.903}&{0}&{0.841}&{0}&{0}\\{0}&{0.841}&{0}&{0.841}&{0}\\{0}&{0}&{0.841}&{0}&{0.903}\\{0}&{0}&{0}&{0.903}&{0}\end{array}}\right] \tag{2} \end{align*}
Figure 4. Illustration of the ideal response of the desired filter implemented using a third-order Chebyshev BPF with 0.2-dB ripple, which would have a competition score of 13.9. The corresponding coupling diagram is also displayed.
To implement this, we decided to use a 125-mil (3.175-mm) TMM3 as our substrate due to its availability in reasonable thicknesses, low loss ${(}{\delta} = {0}{.}{002}{@}{10}{GHz}{),}$ and manufacturing compatibility [13], [23]. As a rule of thumb, to attain the optimal ${Q}_{u}$ for these types of resonators, the center post to outer wall radius ratio is approximately 0.25 to 0.33 [24]. This served as an initial starting point and was later optimized. After getting a single resonator to operate at 7.3 GHz, copper pads were added to give post-fabrication tuning flexibility. The next step is to work on the input coupling. A pad connected to a single via is created on the TMM3 substrate, feeding the electromagnetic energy from the package. The distance between the via and the resonator’s center post was constrained by the package pad but could be varied slightly to achieve the desired coupling. The feed structure was fixed when the reflection group delay at ${f}_{0}$ was at the desired point given in [22] as: \[{\tau}_{11}{(}{\kern0.1emf}_{0}{)} = \frac{2}{{FBW}{\pi}{f}_{0}{M}_{01}^{2}}{.} \tag{3} \]
The interresonator coupling structure is next to determine. To achieve the desired coupling, two resonators are brought together, overlapping while externally weakly coupled to minimize the external loading effects. Fine-tuning of the center frequency is expected as the resonator structure changes due to this coupling. However, the post capacitance can be easily adjusted to return to the desired center frequency. This is done until the coupling equation is satisfied: \[{M}_{12} = \frac{1}{FBW}\frac{{\kern-0.1emf}_{1}^{2}{-}{\kern-0.1emf}_{2}^{2}}{{\kern-0.1emf}_{1}^{2} + {\kern-0.1emf}_{2}^{2}}{.} \tag{4} \]
In this case, ${f}_{1}$ and ${f}_{2}$ are 7.05 GHz and 7.55 GHz, respectively.
At this point, the external feed structure, the distance between each resonator, and the iris slit complete the physical coupling structures. It should be noted here that the filter is symmetric, resulting in similar coupling dimensions between resonators “1â€/â€3†and “2â€. The remaining challenge is ensuring the filter feeds are fixed to one of the package pads. This was made easy by employing the optimization mentioned previously. Figure 5(a) shows the final filter and its dimensions.
Figure 5. (a) The dimensions of the BPF, (b) the exploded view of the total assembly, (c) the filter with TZs, and (d) how the filter sits in the package, making contacts to the package pins. All units are in millimeters: a1–3 = 4.7, b1–3 = 1.18, c1,3 = 1.84, c2 = 1.5, g1,3 = 0.25, g2 = 0.3, rc = 6.8, a = 3.75, c = 2.1, g = 0.35, s = 0.7, and d = 6.28.
There are typically three mechanisms for loss in these cavity resonators: dielectric, ohmic, and radiation [9]. The low-loss TMM3 helps to mitigate the dielectric loss, and the resistivity and thickness of copper dictate ohmic losses. On the other hand, the annular capacitive gap is a significant source for energy to radiate, thus reducing the quality factor. If the gap cannot be made smaller, another way to reduce the leakage is by adding a grounded cap over the resonator [25]. This adds to the post capacitance and detunes the resonator. However, the resonator can easily be retuned by either adjusting the static annular capacitor in simulation or physically trimming one of the tuning copper pads postfabrication. Simulations showed ${Q}_{u}$ improvement up to 34%, from 230 to 308. For this reason, we included the grounded cap in the final design, displayed in Figure 5(b).
The carrier printed circuit board (PCB) is designed to hold the Kyocera package and provide a connectorized interface. For this we chose a grounded coplanar waveguide (GCPW) structure on a 20-mil 4003 substrate. The GCPW launches are created only for the two pins actually utilized in the design (i.e., input and output of filter). For the GCPW technology, the center feed width and gap are 0.9 mm and 0.25 mm, respectively. The feed line was optimized to help improve the matching to the package. Figure 5 shows the final layout.
As can be seen in the lower left portion of Figure 5(a), space is still available that could be used to add the TZs out of band. This area would allow a slightly smaller single resonator than the other three. We decided to implement a dual-mode resonator coupled to the filter to provide better isolation at the adjacent sampled rejection frequencies, 6.6 GHz and 8 GHz.
An EVA dual-mode cavity resonator is similar to the single resonator discussed above and shown in Figure 3(a), but has two posts capacitively coupled, shown in Figure 3(b) [26]. This setup takes advantage of the even and odd modes, whereby two TZs are made possible [27], [28], [29]. The summed outer capacitance, ${C}_{2},$ comprises the even mode, and in conjunction, the internal capacitance, ${C}_{1},$ between the two posts comprises the odd mode, creating two TZs [28], [29]. The higher frequency is associated with the odd mode, whose fields exist in line with the two posts [28]. For this reason, the dual-mode resonator is placed accordingly to couple into both modes. To minimize any additional parasitics, the dual-mode resonator is coupled directly to resonator “1â€, creating a hybrid BPF and bandstop filter (BSF) design.
We created a resonator size that could fit entirely in the unused area, occupying approximately 25.5% less area than the other three resonators. Increasing the coupling does not detune the filter much but does improve the rejection, similar to a standard BSF behavior [30]. The final structure that works for the size and provides sufficient rejection is shown in Figure 5(c). Figure 6 shows that the notch at 8 GHz, the higher frequency TZ, is weaker since that corresponds to the odd mode, which implies weaker coupling. Adding these notches improves the score by approximately 31%, from 10.9 to 14.3, which exceeds the lossless score of the regular BPF (i.e., 13.9). Figure 6(a) shows the comparison in simulated results for both the regular BPF and the one with added TZs. Note that the unloaded quality factor is similar between the two topologies, indicating that the increase in score is exclusively due to adding the two TZs.
Figure 6. (a) Simulated results of both the regular third-order bandpass overlaid with the added TZs filter, denoted as “1†and “2â€, respectively. (b) Synthesized, ideal BPF with TZs, based on coupling matrix, performance of the final filter design that won first place. The coupling diagram is overlaid on the plot.
We can now generate the coupling matrix of the enhanced filter with TZs. Appending the two additional resonators to the matrix from (2), we arrive at (5): \begin{align*}\left[{M}_{{\text{BPF}}\_{\text{TZ}}}\right] = \left[{\begin{array}{lllllll}{0}&{0.903}&{0}&{0}&{0}&{0}&{0}\\{0.903}&{0.285}&{0.841}&{0}&{0.9}&{0.2}&{0}\\{0}&{0.841}&{{-}{0}{.}{08}}&{0.841}&{0}&{0}&{0}\\{0}&{0}&{0.841}&{{-}{0}{.}{1}}&{0}&{0}&{0.903}\\{0}&{0.9}&{0}&{0}&{2.244}&{0}&{0}\\{0}&{0.2}&{0}&{0}&{0}&{{-}{2}{.}{6}}&{0}\\{0}&{0}&{0}&{0.903}&{0}&{0}&{0}\end{array}}\right] \tag{5} \end{align*}
In (5), the added resonators (indicated in red) are shifted to the appropriate rejection frequency as outlined in [31], and the notch couplings to resonator “1†(indicated in blue) are obtained numerically. The three primary resonators in (5) (indicated in green) are slightly tuned to regain a proper BPF performance in the passband. Figure 6(b) shows the synthesized lossless response for this filter.
The exploded view of the entire filter is shown in Figure 5(b), where, from bottom to top, we see the carrier PCB, Kyocera package, filter PCB, and radiation cap. Figure 7 shows the final, assembled filters. The filter was placed in the package and soldered using low-temperature solder paste. The tight fabrication tolerances eliminated the need for precise placement, so the filter PCB is aligned properly by fitting it in the package, as highlighted in Figure 5(d). The cap was placed on top of the filter, guided only by the alignment pins. The cap is made from (CNC)-machined copper, and alignment holes are added to the filter PCB and cap. Minor tuning of the post capacitances, through trimming the copper pads, compensates for fabrication tolerances.
Figure 7. (a) The final filter we competed with, which includes the two TZs from the dual-band resonator and (b) the regular third-order BPF used for comparison. (c) The completely assembled filter with radiation cap.
Figure 8 shows the measured performance of both the regular BPF and with added TZs (used in the competition) for comparison. Both filters have similar performance in the passband with a slight frequency offset. Using the method outlined in [22] and confirming in simulation, ${Q}_{u}$ for the resonators in the simple BPF and BPF with TZs are 180 and 166, respectively. The behavior above 9.25 GHz is not captured in simulation and is believed to be caused by the package parasitics being loaded by the filter. Only the mechanical drawings for the package were provided, from which we created the simulation model.
Figure 8. Measured performance of the two types of filters, standard BPF and with TZs. The competition score is displayed.
From Figure 8, the BPF with dual TZs increased the score by 43% when compared to the regular BPF, from 8.1 to 11.6. As the loss is approximately similar (8% difference in ${Q}_{u}),$ the increase in score is due exclusively to the notches presented at 6.6 GHz and 8 GHz. The BPF with dual TZs is the filter that won first place in the competition.
This work placed first in the IMS 2022 Student Design Competition for a packaged BPF centered at 7.3 GHz with 8% fractional bandwidth. By employing EVA-mode cavity resonators, excellent performance has been achieved with approximately 1-dB insertion loss and an out-of-band rejection in the 6.6- and 8-GHz notches greater than 30 dB, resulting in a score of 11.6 in the competition. This article has explored the reduction in loss and the hybridization of a BPF and BSF in this design. The addition of a radiation cap improved the ${Q}_{u}$ in simulation by as much as 34%. Finally, filter performance can effectively use most of the available surface area by adding an additional resonator coupled to the primary filter with minimal disturbance. Essentially, this creates a hybrid and modular approach to filter design with EVA-mode cavity filters [32]. Although this work implemented a static filter, the location of precisely placed rejection notches can be made reconfigurable by tuning the capacitance in situ, utilizing a tunable membrane, for example, [26].
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Digital Object Identifier 10.1109/MMM.2023.3265466
