Introduction
Modern communication systems require the capability of managing a great amount of data, and with very low bit error rates. The power level involved in the communication links is a key parameter to satisfy the demanded quality [Reference Pozar1, Reference Sorrentino and Bianchi2], and, thus, the development of single-device amplifier technology is continuously evolving. In fact, at the present time, high-power amplifier modules are available at many frequency bands, which must be exploited with suitable power combining techniques. Power combination/division is a classic area within microwave and millimeter-wave systems [Reference Russell3–Reference Epp, Hoppe, Khan and Stride7], which had to keep pace [Reference Xue, Song and Chan8, Reference Komiak9] to enable the realization of very high-power solid-state sources needed for systems such as radar transmitters.
At the same time, frequency discrimination is a fundamental function in any high-frequency front end [Reference Pozar1, Reference Sorrentino and Bianchi2, Reference Matthaei, Young and Jones10, Reference Cameron, Kudsia and Mansour11]. Typically, when both power combination and filtering is needed, the classic approach is to address each functionality independently, leading to separate building blocks, which later are cascaded together [Reference Sorrentino and Bianchi2, Reference Uher, Bornemann and Rosenberg12]. This is a very classical approach which may not lead to optimum designs, especially in an actual context lead by the principles of reducing Size, Weight and Power (SWaP), as well as cost. Thus, a more demanding approach to system design simplification is the integration of more than one function into single modules. Therefore, in this paper, we will focus on networks having both combining and filtering properties integrated within the same architecture, whose development has seen a very significant surge in recent years [Reference Uchida, Yoneda, Konishi and Makino13–Reference Fahmi, Ruiz-Cruz and Mansour26]. The advances in filtering couplers include dielectric resonator technology [Reference Uchida, Yoneda, Konishi and Makino13, Reference Zhang and Xu23], substrate integrated waveguide (SIW) [Reference Rosenberg, Salehi, Bornemann and Mehrshahi15, Reference Feng, Shi, Zhou, Shen and Che22], low temperature cofired ceramics (LTCC) [Reference Shen, Huang, Chen and Wu14], rectangular waveguide [Reference Di Crestvolant, Iglesias and Lancaster16], ridge waveguide [Reference Fahmi, Ruiz-Cruz and Mansour26], surface acoustic wave [Reference Fall, Domingue and Reinhardt18], and planar realizations [Reference Chen, Wu, Qiu and Mao17, Reference Zhang, Lin, Tang, Jiang and Fan19–Reference Gómez-García, Yang, Muñoz-Ferreras and Psychogiou21, Reference Wang, Wang, Guo and Zhang25].
Within the available power combination topologies, the Gysel-type combiners [Reference Gysel27] used in this work are very good candidates for in-phase high-power combiners. Compared to the well-known Wilkinson design [Reference Wilkinson28], the Gysel design has two isolation terminations that are grounded as shown in Fig. 1(a). This increases the power handling capacity due to the more efficient heat sinking of the terminations compared to the floating isolation resistor in the three-port Wilkinson design, at the expense of using five ports. This topology has been also extensively exploited in diverse technologies (planar, waveguide, etc.) and with diverse functionalities [Reference Wu, Guo and Mao29–Reference Fahmi, Ruiz-Cruz and Mansour36]. Designs of Gysel combiners with filtering characteristics were reported in papers [Reference Wu, Guo and Mao29, Reference Karimi, Siahkamari and Khamin-Hamedani31], where band-pass [Reference Wu, Guo and Mao29] and low-pass [Reference Karimi, Siahkamari and Khamin-Hamedani31] filtering characteristics were realized. Dual-band operation was obtained in paper [Reference Moradi, Moznebi, Afrooz and Movahhedi33]. Arbitrary division ratio was implemented in paper [Reference Wang, Zhang and Hu30]. Planar or quasi planar technology is one of the preferred realizations for these networks, as for instance half-mode SIW in paper [Reference Song, Kong, Zhu, Xu, Jiang and Fan32], microstrip in paper [Reference Moradi, Moznebi, Afrooz and Movahhedi33], or suspended stripline in paper [Reference Guo, Song and Fan35]. In waveguide technologies [Reference Fahmi, Ruiz-Cruz and Mansour34], Gysel combiners are usually simpler when compared to more elaborate designs of the classic magic-T designs.
(a) Regular Gysel combiner. (b) Conceptual band-pass filtering Gysel combiner.
In this paper, a novel detailed systematic methodology to design Gysel combiners design with high-selectivity band-pass filtering characteristics is proposed based on a high order coupled resonator network. The theoretical foundation of the methodology, as well as design examples for higher order filtering functions are provided in detail. Preliminary results, with the lowest possible order filtering function, were presented at the 53rd European Microwave Conference and was published in its Proceedings [Reference Fahmi, Ruiz-Cruz and Mansour36].
The basic proposed concept can be easily explained using the network in Fig. 1(b). The ring has five filtering sections, to be realized using coupled resonators, with five external ports. It was designed in paper [Reference Fahmi, Ruiz-Cruz and Mansour36] with a twofold objective. Inside the predefined operational bandwidth (BW), it acts as a classical Gysel combiner design. At the same time, outside the operational band, it provides the selectivity of a regular band-pass filter in the two input–output paths. In contrast to the classic Gysel design, shown in Fig. 1(a), where the operational BW is pre-determined by the transmission line (TL) characteristics, the coupled resonator design gives the designer the ability to tailor the design to specific BW of interest.
When cross-coupled resonators are used to synthesize the Gysel combiner, a six-pole filtering function can be initially obtained [Reference Fahmi, Ruiz-Cruz and Mansour36]. Now, in this expanded paper, the extension to an arbitrary order will be outlined, introducing the novel methodology and the equations driving the designs. The filtering combiners presented in this work will start from a generalized form of the Gysel combiner. Using odd multiples of the quarter wavelength TL allows for increasing the order and thus the filtering selectivity. The TLs are mapped to resonators, where coupling matrix formulation can be used [Reference Cameron, Kudsia and Mansour11]. Then, the network can be realized in either of the available microwave/millimeter-wave technologies as any other high-frequency filter, whether planar or nonplanar [Reference Matthaei, Young and Jones10, Reference Cameron, Kudsia and Mansour11]. In the proposed filtering combiners, the input/output couplings and the inter resonator couplings are implemented following the design rules of the corresponding technology.
Realization of in-phase combiners using coupled resonator networks
The design of combiner networks with filtering properties must combine two disciplines. On one hand, the essence of realizing band-pass filtering components, in general, is the introduction of frequency selective blocks in different signal paths [Reference Cameron, Kudsia and Mansour11]. More precisely, resonators must be incorporated in the input/output paths of any band-pass filtering component. On the other hand, the design of non-filtering in-phase combiners is based primarily on TL networks [Reference Matthaei, Young and Jones10]. These networks usually employ TL sections whose electrical length is multiples of λ/4 at the center frequency of the design. These TL sections are interconnected in a meaningful arrangement to realize a predetermined input/output transfer function.
Following these two basic premises, a logical approach to the design of band-pass filtering in-phase combiners is to establish a methodology by which the vast wealth of TL component design methodologies is paired with the equally vast wealth of filter design methodologies.
Basis concept
As a starting point, it is worth noting that, in a coupled resonator filter network, the coupling between any two synchronously tuned resonators can be represented as an impedance inverter. At the resonant frequency, an impedance inverter can be realized by a λ/4 section of TL. The characteristic impedance of this TL section is dependent on the targeted coupling between the two resonators [Reference Matthaei, Young and Jones10, Reference Cameron, Kudsia and Mansour11]. A mapping between the TL network parameters and the parameters of the coupled resonator network is the key to a seamless design of band-pass filtering in-phase combiners.
Figure 2(a) shows a λ/4 section of TL of characteristic impedance Zc connected between two ports with normalized reference impedance, that is Zo =1 Ω. Figure 2(b) shows a network with two coupled resonators, 1 and 2, that are also connected between two ports with the same reference impedance Zo =1 Ω. The coupled resonator network can be represented by a 2 × 2 coupling matrix given by (1).
\begin{equation}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{M_n} = \left( {\begin{array}{*{20}{c}}
{\begin{array}{*{20}{c}}
0 \\
{{M_{12}}}
\end{array}}&{\begin{array}{*{20}{c}}
{{M_{12}}} \\
0
\end{array}}
\end{array}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{equation}(a) Regular quarter wavelength transmission line (TL) between two ports with normalized reference impedance. (b) Equivalent based on two coupled resonators.
The terminating resistance of the network is given by (2)
\begin{equation}R = {R_n}\frac{{BW}}{{{f_o}}}\end{equation}In order for the two networks to be exactly equivalent, they must exhibit the same performance when terminated in the same impedance. The terminating impedance of the coupling matrix circuit can be transformed to the nominal Zo =1 Ω by means of a transformer with the proper turn ratio as shown in (3):
\begin{equation}NT = \sqrt {{R_n}\frac{{BW}}{{{f_o}}}} \end{equation}Using simple network analysis, it can be shown that, at the center frequency of the networks, for the two networks to have the same response, certain relationships must be maintained between the parameters of the two circuits, namely the coupling between the two resonators i and j:
\begin{equation}\,\,\,\,\,\,{M_n}\left( {i,j} \right) = \frac{{{R_n}}}{{{Z_c}\left( {{\text{between nodes i}},{\text{and j}}} \right){ }}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{equation} In order to demonstrate this equivalence, a simple demonstration is attempted. A λ/4 at 
${f_o}\,$section of TL of characteristic impedance Zc = 0.15Ω is inserted between two port impedances of Zo =1 Ω. The mismatched TL circuit can be mapped to a coupled resonator network with the following normalized coupling matrix:
\begin{equation}{M_n} = \left( {\begin{array}{*{20}{c}}
{\begin{array}{*{20}{c}}
0 \\
{\frac{{{R_n}}}{{0.15}}}
\end{array}}&{\begin{array}{*{20}{c}}
{\frac{{{R_n}}}{{0.15}}} \\
0
\end{array}}
\end{array}} \right),\,\,R = {R_n}\frac{{BW}}{{{f_o}}}\,\,\end{equation} It is worth noting that the coupling matrix circuit has three parameters, 
${R_n}$, 
${f_o}$, and 
$BW$, for simplicity 
${R_n}$ can be set to unity and the parameters 
${f_o}$, and 
$BW$ can be used to obtain the response of the circuit at the center frequency and with a certain BW [Reference Cameron, Kudsia and Mansour11].
Figure 3 shows the scattering parameter response of the two networks with the parameters governed by (4) and (5). The results are shown for different values of the 
$BW$, parameter. It is evident that across a finite BW, the two networks have similar responses and that at the center frequency, they match exactly.
Scattering parameter response of the networks in Figure 2, fulfilling (4) and (5) with fo = 4 GHz, Zc = 0.15 Ω, Rn = 1.
In-phase isolated combiners
In-phase isolated combiners constitute a very useful component in many designs, particularly in high power amplifier designs. Gysel combiners offer an attractive option for the design of such combiners. A generalized network for the Gysel combiner is shown in Fig. 4. The design goal is to have power incident at port P1 equally split between paths P1-P2 and P1-P3, while simultaneously port P1 is isolated from ports P4 and P5, and, most importantly, port P2 is isolated from port P3.
Generic Gysel combiner with N denoting the order of the combiner.
The original design proposed by Gysel [Reference Gysel27] corresponds to the case where N =1 and it will be named the first-order Gysel combiner design accordingly. In this case, paths P1-P2 and P1-P3 are realized by two identical second-order band-pass filters. Paths P2-P4 and P3-P5 are also realized using second-order band-pass filters, while path P4-P5 is realized using a third-order band-pass filter.
The selectivity of the network can be increased, at the expense of BW, by using longer electrically equivalent sections of TL between the central port (port P1 in Fig. 4) and the two input ports (P2 and P3). This corresponds to increasing the order N of the network. The response of the different order networks is shown in Fig. 5. It is clear that, increasing the electrical length of the TL section results in an increase of the selectivity of the input/output out-of-band response.
Scattering parameter response of generic Gysel combiners with N = 1, 2, and 3 in Figure 4.
Filtering Gysel combiners
The next step is to map the TL networks of the Gysel combiners to coupled resonator networks in order to realize band-pass filtering Gysel combiners of different orders. The first-order TL network is mapped into a six-resonator network. The second-order TL network is mapped to a 10-resonator network while the third-order TL network is mapped to a 14-resonator network. The responses of these networks are shown in Fig. 6. Sample network diagrams for the first- and second-order networks are shown in Fig. 7.
Scattering parameter response of filtering Gysel combiners with N= 1, 2, and 3 in Figure 4. (fo = 5 GHz, BW = 0.5 GHz, Rn; = 1).
Network diagrams for filtering Gysel combiners of first order (a), and second order (b).
Experimental verification
As a proof of concept, a compact filtering Gysel combiner realized in combline waveguide technology is presented, using six coaxial resonators. This is not a restriction on the possible implementations. For our proof of concept, the external couplings will be realized by tapping-in the center conductor of standard coaxial connectors, while the inter resonator couplings are realized using ridges connecting the coaxial resonators, from their grounded ends.
Prototype design
The initial parameters for the first-order mapped network with six poles is obtained by (4), and they were later further optimized [Reference Garcia-Lamperez, Salazar-Palma and Sarkar37, Reference Garcia-Lamperez, Salazar-Palma, Padilla-Cruz and Carpintero38] using a center frequency of f0 = 5 GHz. Across the BW = 0.5 GHz, it was imposed:
a) Power split condition: S21 = S31 = −3.05 dB.
b) Input reflection coefficients conditions at input and output ports: S11, S22, S33 <−20 dB.
c) Port to port isolation conditions: S14, S15, S32 <−20 dB.
The optimized coupling matrix is given by (6) and its response is compared to the first-order TL network in Fig. 8.
\begin{equation}{M_n} = \left( \begin{matrix}
0.0000 & 1.4413 & 1.4413 & 0.0000 & 0.0000 & 0.6350 \\
1.4413 & 0.0000 & 0.0000 & 1.9283 & 0.0000 & 0.0000 \\
1.4413 & 0.0000 & 0.0000 & 0.0000 & 1.9283 & 0.0000 \\
0.0000 & 1.9283 & 0.0000 & 0.0000 & 0.0000 & 2.1613 \\
0.0000 & 0.0000 & 1.9283 & 1.0000 & 0.0000 & 2.1613 \\
0.0000 & 0.0000 & 0.0000 & 2.1613 & 2.1613 & 0.0000
\end{matrix}\right)\end{equation}
\begin{equation*}{R_{n1}} = 1.6867,\,{R_{n2}} = 2.0154,{R_{n3}} = 1.5904.\end{equation*}Comparison between the response of Gysel combiners: classical design (according to Figure 4 with N = 1) and filtering design (according to (6) with BW = 0.5 GHz).
In our design, for a compact filtering power combining circuit design, we propose the use of the ubiquitous capacitively loaded combline coaxial resonators [Reference Matthaei, Young and Jones10, Reference Cameron, Kudsia and Mansour11]. For moderate fractional BWs (>5%), to be able to achieve relatively large BWs, realization of inter-resonator coupling may prove challenging using the conventional window-type coupling arrangements. For such BWs, stronger inter resonator couplings can be achieved by utilizing ridges that connect the coaxial resonators at their short circuit ends.
Obtaining the initial dimensions of the coupled coaxial resonator filters follows the classical approach of calculating coupling curves to obtain those initial dimensions and then resorting to optimization of critical dimensions to arrive at the final dimensions [Reference Cameron, Kudsia and Mansour11]. The structure has one plane of symmetry and can be conveniently simulated by finite element-based solvers. Figure 9 shows the proposed structure, while Fig. 10 shows the simulated electromagnetic (EM) response of the structure compared to the coupling matrix response.
Compact coaxial resonator filtering Gysel combiner: (a) 3-dimensional model; (b) Top view.
Measured results
The proposed design lends itself to manufacturing using standard, inexpensive, CNC (Computer Numerical Control)milling. The structure can be manufactured of two pieces, a housing with the coaxial resonators inter-connected by ridges and a cover. The inputs are realized by tapping-in the center conductors of standard SMA (SubMiniature version A) coaxial connectors to the coaxial resonators at the appropriate heights to obtain the correct levels of input coupling. The fabricated hardware is shown in Fig. 11.
Manufactured prototype hardware consisting of a housing and a cover before and after assembly and tuning.
To experimentally demonstrate the novel concept, and verify the design, the filtering Gysel combiner was fabricated out of aluminum without any plating. The measured results are shown in Fig. 12 where they are compared to EM simulations. The measured results agree well with the simulations. Minimal amplitude imbalance of ∼0.05 dB and phase imbalance of ∼1° between the two input–output paths are obtained.
The extended wide-band measured results of the prototype hardware are shown in Fig. 13. It is worth noting that traces associated with ports 2 and 3 are almost identical. The out-of-band rejection is clearly superior to that of a classical Gysel combiner based on regular TL sections. If used to combine signals from two solid state sources, good harmonic suppression can be obtained, even in the presence of the higher order resonances. These resonances are located at frequencies that are not harmonics of any signals generated within the pass band. Extending the rejection band can be sought using known techniques such as using stepped impedance resonators or using other transmission media known for superior out-of-band characteristics such as ridge waveguides.
Extended wide-band measured S-parameters of the manufactured prototype shown in Figure 10.
Conclusion
A novel systematic methodology for the design of band-pass filtering in-phase, isolated Gysel combiners with high selectivity was proposed. The design relies on the mapping between TL network parameters and coupled resonator network parameters. The proposed methodology was used to demonstrate Gysel combiners of various orders.
To show the validity and practicality of the proposed design methodology, a novel realization for filtering Gysel combiners was presented. Design examples with varying levels of selectivity were given. The designs use coupled resonators arranged in a ring to simultaneously realize a two-way in-phase combiner function as well as a filtering function. Coupling matrix formulation of the networks is used along with circuit level optimization to synthesize the element values of a coupled resonator network that satisfies the intended performance. Classical filter design methodologies are then used to realize the filtering Gysel combiner network. In the presented experimental prototype, the realization was chosen to be in coaxial resonators that are intercoupled by ridges.
The proof-of-concept experimental prototype was fabricated, assembled, and tested. The measured response of the fabricated design agreed well with simulations. The measured results demonstrate good performance with minimal amplitude and phase imbalance across the passband. If used as an in-phase combiner, the combined output will have a very wide stopband.
Acknowledgements
The authors wish to acknowledge Ms. Gada Saad from Scientific Microwave Inc. for help with manufacturing the prototype hardware.
Funding statement
This work was partially supported by the Agencia Estatal de Investigacion of the Spanish Government (MCIN/AEI/10.13039/501100011033) and UE (European Union) “NextGenerationEU”/PRTR (J.A.R-C, grant numbers PID2020-116968RB-C32 DEWICOM, TED2021-130650B-C21 ANT4CLIM).
Competing interests
The authors report no conflict of interest.
Mohamed M. Fahmi received B.Sc. (with Honors) in Electronics Engineering from Mansoura University, Egypt, in 1999. The MS degree in Electrical Engineering from Howard University, Washington DC, USA in 2003, and the Ph.D. degree in Electrical Engineering from the University of Maryland, College Park, USA, in 2007. He worked as a postdoctoral researcher at the department of Electrical and Computer Engineering at the University of Maryland from January to July 2008, and as a postdoctoral fellow at the department of Electrical and Computer Engineering at the University of Waterloo, Canada, from September 2008 to January 2012. He worked as a microwave engineer, senior microwave engineer and as a manager of Passive Component Engineering at Nanowave Technologies Inc. in Etobicoke, Canada, from February 2012 to February 2017. He worked as a senior system engineer, Radar Specialist at General Dynamics Mission Systems Canada, in Ottawa, Canada, from February 2017 to February 2018. In February 2018, he joined Defence Research and Development Canada as a Group Leader, Radar Technology and Engineering. Dr. Fahmi is an adjunct associate professor at department of Electrical and Computer Engineering at the University of Waterloo, Canada. His current research interests include CAD of microwave devices and systems.
Jorge A. Ruiz-Cruz received the Ingeniero de Telecomunicacion and Ph.D. degrees from the Universidad Politecnica de Madrid (UPM), Madrid, Spain, in 1999 and 2005, respectively. Before starting the Ph.D. program, he was with the company RYMSA (2000). After finishing his Ph.D., he worked as Research Associate in the University of Maryland. Then, he joined Universidad Autonoma de Madrid in 2006, where he became Associate Professor in 2009 and Full Professor in 2021. In 2023, he joined the UPM, as a full professor in the Department of Signals, Systems and Radio communications. His current research interests include the computer-aided design of microwave passive devices and systems (filters, multiplexers, orthomodes, etc.).
Raafat R. Mansour received the B.Sc. degree (Hons.) and the M.Sc. degree both in electrical engineering from Ain Shams University, Cairo, Egypt, in 1977 and 1981, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, Ontario, Canada, in 1986.
He is a professor of Electrical and Computer Engineering Department at the University of Waterloo, and holds Tier 1-Canada Research Chair (CRC) in Micro-Nano Integrated RF Systems since 2010. He also held an NSERC Industrial Research Chair (IRC) for two terms (2001−2005) and (2006−2010). He is the Founding Director of the Center for Integrated RF Engineering (CIRFE) facility at the University of Waterloo. Prior to joining the University of Waterloo in January 2000, Dr. Mansour was with COM DEV Cambridge, Ontario, over the period 1986−1999, where he held various technical and management positions in COM DEV’s Corporate R&D Department. Dr. Mansour holds 45 US and Canadian patents (41 awarded, 4 pending) and more than 420 IEEE refereed publications. He is a coauthor of a comprehensive.
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