Ferrite-Based Multiport Circulators With RF Co-Designed Bandpass Filtering Capabilities

This article reports on the RF design and practical development of multiport circulators with RF co-designed bandpass filtering functionality. The proposed bandpass filter/circulator (BPFC) concept is based on a hybrid implementation approach, where dual-mode non-reciprocal ferrite-based resonators (FBRs) are cascaded with microwave resonators and mixed-electromagnetic (EM) couplings. In this manner, highly selective bandpass filtering transfer functions are created in the direction of propagation, and high RF signal cancellation is obtained in the reverse direction. A design methodology using coupled-resonator-based synthesis is proposed to facilitate the design of these components using well-known filter design techniques. Various electromagnetically simulated and synthesized examples are presented to demonstrate the operating principles of the BPFC approach alongside its applicability to high-order filtering responses. The BPFC concept is further expanded to the realization of multiport non-reciprocal components. For proof-of-concept demonstration, four multiport prototypes were designed, manufactured, and measured at $S$ -band.

Taking into consideration the aforementioned limitations, this article reports on a new class of multiport BPFCs with highly selective transfer functions. The proposed BPFCs are based on a unique hybrid integration concept, where capacitively loaded dual-mode ferrite-based resonator (FBR) are co-integrated with passive microwave resonators and/or mixedelectromagnetic (EM) couplings to facilitate high-order quasielliptic transfer functions in the direction of propagation and high RF signal suppression in the reverse direction. Scalability to multiport non-reciprocal frequency-selective networks is also discussed and validated with a four-port network. A new design methodology based on coupled-resonator filter synthesis approaches is proposed in this work for the first time to facilitate their design using well-known filter synthesis methods as well as their co-design with advanced filtering and multiplexer topologies. The operating principles of the FBR are presented through coupled-resonator synthesis and EM design examples and are expanded to high-order transfer functions and multiport networks.
The content of this article is organized as follows. In Section II, the theoretical foundations of the BPFC concept are presented through EM simulations and coupled-resonatorbased synthesis. Various examples demonstrating scalability in terms of resonator type, transfer function, and port number are presented. To verify the BPFC concept, four prototypes were designed, manufactured, and tested and are presented in Section III alongside with a comparison with state of the art. Finally, the main contributions of this article are summarized in Section IV.

II. THEORETICAL FOUNDATIONS
This section discusses the theoretical foundations and operating principles of the RF co-designed BPFC concept. It starts by introducing the general design characteristics of the capacitively loaded FBR and its corresponding coupling routing diagram (CRD) representation. Afterwards, the use of the proposed CRD in the realization of higher order transfer functions materialized by a combination of FBRs, reciprocal resonators, and mixed-EM couplings is demonstrated through a wide range of synthesized examples. The applicability of the proposed concept to multiport networks is also discussed.

A. Capacitively Loaded FBR Design
The geometry of the capacitively loaded dual-mode FBR is provided in Fig. 1 alongside its EM simulated response. It aims to reduce the size of a conventional ferrite-based circulator by symmetrically loading the ferrite cavity along its periphery with a capacitive load that is shaped by a discrete capacitor C R and an insert having a width, N W . The FBR design is based on the method in [29] and [55]. When using a TransTech TT1-105 (magnetization saturation M S = 0.175 T, permittivity ε r = 12.2, dielectric loss tangent tanδ D = 0.00025, and linewidth of the ferromagnetic resonance H < 270 Oe) ferrite disk with radius R = 4.97 mm and thickness h f = 1.524 mm and embedding it in a Rogers 4350B substrate (permittivity ε r = 3.48, tanδ D = 0.003, height h = 1.524 mm, and 1-oz copper cladding), the operating frequency of a conventional (i.e., unloaded) circulator is 3.9 GHz [see Fig. 1(b)]. However, when a capacitive load is applied (through C R = 1.25 pF and N W = 1 mm), the operating frequency is lowered to 2.4 GHz. Thus, its effective size is reduced. A comparison between the S-parameters of the unloaded and the capacitively loaded dual-mode FBR is provided in Fig. 1(b) for a ferrite cavity having a height h f = h, i.e., fill factor h f /h = 1. As it can be seen, the capacitive load splits the first two modes of the ferrite cavity (i.e., creating two poles in the passband, P 1 and P 2 ). Furthermore, a higher order mode (P 3 ) and two transmission zeros (TZs) ( f TZ1 and f TZ2 ) in the forward direction and three TZs ( f TZ1 , f TZ2 , and f TZC ) and one passband at a frequency P 3 in the reverse direction are created. The TZs appear at frequencies, where the RF signals arriving at the output from the different transversal resonant paths within the FBR are mutually canceled. The electric field distribution of the first three modes of the FBR under magnetic biasing is provided in Fig. 2. Specifically, Fig. 2(a) and (b) illustrates the first splitted modes that form the BPFC passband after the capacitive loading is applied.

B. BW and Out-of-Band Is Design
As seen in the response of the dual-mode FBR in Fig. 1(b), the poles in the passband are formed by the first two modes and create a wide passband with a fractional BW (FBW) of 17.4%. If narrower FBWs are desired, two design methods can be considered. At first, the BW can be altered by varying N W [29], with wider N W resulting in narrower BW, as shown in Fig. 3(a). In particular, the passband BW is increased by altering the separation between the frequencies of the first two modes [i.e., altering the interresonator coupling M 23 in Fig. 5(a)], as defined by (1). Fig. 3(b) illustrates how N W alters the interresonator coupling. In yet another approach, the BW can be reconfigured by altering the fill factor (h f /h) [20] with smaller fill factors resulting in narrower FBWs. Another performance aspect of the fill factor is that smaller h f /h results in wider spurious-free out-of-band responses; this is plotted in Fig. 4. Thus, smaller fill factors are desirable, and as such, the remaining design examples will be using a fill factor of 0.5 (1)

C. Dual-Mode FBR Modeling Using CRDs
Due to the resonant behavior of the capacitively loaded FBR, coupled resonator-based synthesis techniques-typically used in coupled-resonator filter designs-can be applied to model its RF signal propagation characteristics between two ports at a time and facilitate its use in advanced RF filtering transfer functions as it will be discussed in Section II-D. The FBR's response between two ports (e.g., RF signal propagation from port 1 to port 2 and port 2 to port 3) can be modeled using the CRD in Fig. 5 that comprises three transversal resonating nodes (2-4), two nonresonating nodes (NRNs) (1 and 5), and ten coupling elements (black solid and dashed lines). In particular, the resonating nodes (black circles) are arranged in parallel and nodes 2 and 3 represent the first two modes of the ferrite cavity, whereas node 4 represents the first higher order mode. The resonant frequency of these modes is captured in Table I by the self-coupling coefficients M 22 , M 33 , and M 44 . Furthermore, the coupling element between nodes 2 and 3 represents the coupling between the first two modes, M 23 . The coupling between the two NRNs (nodes 1 and 5) represents the direct RF signal propagation between ports 1 and 2. If desired, the CRD can be converted to a two-port  circuit equivalent for each direction of propagation using conventional filter design techniques (e.g., the ones described in [56]), where each resonating node (black circle) can be represented by a parallel LC tank and each coupling element by its first-order low-pass or high-pass π-type and T-type circuit equivalent. In this case, positive coupling elements can be represented by their low-pass equivalent and negative couplings with their high-pass equivalent.
The lossless normalized frequency response of the CRD is provided in Fig. 5(b). It has been obtained using the normalized coupling coefficients in Table I (obtained  through optimization). Furthermore, the denormalized frequency response of the CRD is illustrated in Fig. 5(c) alongside the EM-simulated response of the capacitively loaded non-reciprocal FBR that has a fill factor of 0.5 (dimensions listed in the caption of Fig. 1) designed to operate at 2.5 GHz. In order to make a direct comparison, loss is accounted in the denormalized frequency response, where an effective quality  Fig. 1 having a fill factor of 0.5. (c) Comparison of the two-port CRDsynthesized response with the EM-simulated response of the dual-mode FBR in Fig. 1 for a fill factor of 0.5. The two-port CRD-synthesized responses have been obtained using the coupling coefficients in Table I and Qs of 100, 100, and 31 for resonators 2, 3, and 4, respectively. factor (Q) of 100 has been considered for the first two modes and 31 for the third mode. While the same CRD model can be used for both the forward (i.e., the RF signal is injected at port 1 and received at port 2) and reverse direction (i.e., the RF signal is injected at port 1 and received at port 3), the values of the couplings related to the first two modes and the higher order mode will be different due to the non-reciprocal behavior of the FBR.
To further validate the CRD in Fig. 5(a), a different example is considered in Fig. 6. In particular, the CRD is applied to a dual-mode FBR using a fill factor equal to 1 and C R = 4.4 pF; the comparison of the CRD-synthesized response using the values in Table II and EM-simulated response is provided in Fig. 6. As it can be seen, a good agreement is observed between these two, thus successfully validating the CRD model.

D. BPFCs Exhibiting High-Order RF Filtering Transfer Functions and High IS
Having modeled the capacitively loaded dual-mode FBR with its CRD equivalent, as shown in Fig. 5, it can be combined with other types of reciprocal and non-reciprocal microwave resonators [e.g., resonator types are presented in Fig. 7(a)] to create advanced RF filtering responses with high selectivity, improved out-of-band response, and high IS. Specifically, in the forward direction, the selectivity and outof-band response can be improved by adding reciprocal resonators (e.g., distributed resonant elements, lumped-elements) Proposed BPFC concept using the dual-mode FBR in Fig. 1. (a) Incorporated resonator types: passive microwave resonator (left, solid circle) that creates a pole in the forward and reverse direction, mixed-EM coupling (middle, line with an arrow) that creates a TZ in the forward and reverse direction, and the non-reciprocal FBR (right, circle with arrow) that is modeled using the CRD in and mixed-EM couplings. The poles in the passband can be increased by increasing the number of the reciprocal resonators and the out-of-band response can be improved by adding TZs through mixed-EM couplings as well as by increasing the number of resonators in each RF signal path. The IS and out-of-band response in the reverse direction can be improved by adding FBRs, which also improve the passband selectivity in the forward direction. To illustrate the capabilities of the concept, various design examples are considered for two generalized BPFC topologies, namely, the Y-junction BPFC and the -junction BPFC that are shown in Fig. 7(b) and (c), respectively, and are discussed in the next sections. In order to model the BPFCs, two separate CRDs (i.e., one for the forward direction and one for the reverse direction) need to be used.  Table I. The passive resonators are implemented with a Q = 100.  Table I. The passive resonators are implemented with a Q = 100.

E. Y-Junction BPFCs
The Y-junction BPFC [see Fig. 7(b)] is the simplest form of a high-order BPFC comprising of one dual-mode FBR, Fig. 10. Comparison of the CRD-synthesized responses for the four-pole/ two-TZ BPFC in Fig. 8 and the six-pole/two-TZ BPFC in Fig. 9. N-number of passive reciprocal resonators, and M-number of mixed-EM couplings that are added in each RF path (boxed in green in Fig. 7). In particular, a Y-junction only adding passive reciprocal resonators to the dual-mode FBR is shown on the left and a Y-junction BPFC using both passive resonators and mixed-EM couplings is shown on the right. Thus, in the forward direction of propagation, a transfer function shaped by N + 2 poles (N from the reciprocal resonators in each RF path and two from the dual-mode FBR, where the number of poles refers to the poles in the passband) and up to M + 2 TZs (for M mixed EM couplings in each RF path) can be created. Furthermore, a transfer function shaped M + 3 TZs can be obtained in the reverse direction. The out-of-band IS of the Y-junction BPFC is controlled by the number of poles and TZs. Higher out-of-band IS can be obtained by increasing the number of passive resonators or by adding mixed EM couplings that increase the number of TZs.   Table I. To increase the passband selectivity without increasing the number of the dual-mode FBRs, two reciprocal resonators could be added in each RF path (N = 4). In this manner, a transfer function shaped by six poles and two TZs in the forward direction and three TZs in the reverse direction can be obtained, as seen in Fig. 9. In both examples, the passive resonators exhibit a quality factor (Q) equal to 100. When comparing the two BPFCs in Figs. 8 and 9 [see Fig. 10], the IS remains the same. The only difference is the selectivity of the response due to increasing the number of poles in the passband (4 versus 6).

F. -Junction BPFCs
The -junction BPFC details are provided in Fig. 7(c). It comprises three dual-mode FBRs based on the CRD in Fig. 5, N-  out-of-band can be created. Furthermore, a transfer function shaped by M + 6 TZs can be obtained in the reverse direction. The out-of-band IS of the -junction BPFC is controlled by the number of poles and TZs. Higher out-of-band IS can be obtained by increasing the number of passive resonators or by adding mixed EM couplings that increase the number of the TZs.
To demonstrate the operating characteristics of the -junction BPFC, a synthesized example case comprising three dual-mode FBRs is shown in Fig. 11. The transfer function in the forward direction is shaped by four poles at the center passband and four TZs in the out-of-band. In the reverse direction, the transfer function is shaped by six TZs. This topology uses multiple dual-mode FBRs; therefore, the IS in the reverse direction is increased when compared to the Y-junction topologies. To enhance the out-of-band rejection at frequencies lower than the passband, one mixed-EM coupling is added to each RF branch (i.e., M = 2, two in each RF path). It introduces TZs, as shown in Fig. 12. The frequency locations of the TZs are obtained using (2), where M 0 is the coupling strength for the TZ and M 1 is the coupling slope with respect to the normalized frequency. The TZ is created at a frequency TZ , where M TZi ( TZ ) is equal to zero. As seen in the synthesized response in Fig. 12, the IS level and frequency selectivity is equivalent to the ones obtained by the CRD in  (2)

G. Multiport BPFCs
The ferrite-based BPFC concept can be expanded to the realization of multiport circulator devices with bandpass filtering capabilities. A conceptual block diagram of a K -port BPFC is shown in Fig. 13(a), where K -number of dual-mode FBRs are incorporated to achieve a transfer function shaped by 2K poles and 2K TZs in the forward direction and 3K TZs in the reverse direction for each direction of propagation. To increase the selectivity for a fixed number of ports, N-number of passive reciprocal resonators can be added in each RF path; this is seen in Fig. 13(b) for the case of a four-port BPFC. The forward direction exhibits a transfer function shaped by 2K + N poles and 2K TZs, and the reverse direction exhibits a transfer function shaped by 3K TZs. Finally, to improve the out-of-band IS, M-number of mixed-EM couplings can be added at the input of the RF ports; this is provided in Fig. 13(c).
To demonstrate the operating principles of the multiport BPFC concept, a four-port BPFC example using four dual-mode FBRs and four mixed-EM couplings is considered in Fig. 14. In this configuration, the forward direction is shaped by four poles at the passband and six TZs in the out-of-band response and its reverse direction is shaped by eight TZs. It is worth noting that the mixed-EM coupling element in port 1 is the same as in port 3; similarly, the mixed-EM coupling in port 2 is the same as in port 4. As a result, when looking at the transmission from port 1 to port 3 (or from port 2 to port 4), the TZs are merged at a single frequency.
To demonstrate the design versatility, a four-port BPFC using two dual-mode FBRs, two passive reciprocal resonators, and two mixed-EM couplings in each path of propagation (i.e., port 1-port 2, port 2-port 3, etc.) are considered to create a high-order multiport BPFC with improved out-of-band IS; this is presented in Fig. 15.

III. EXPERIMENTAL RESULTS
In order to experimentally validate the ferrite-based BPFC concept, four prototypes were designed, manufactured, and measured at S-band. These include: 1) two four-pole/two-TZ three-port BPFCs using a single dual-mode FBR and three passive resonators; 2) one four-pole/six-TZ three-port BPFC  using three dual-mode FBRs and three mixed-EM couplings (two dual-mode FBRs and one mixed-EM coupling in each branch); and 3) one four-pole/six-TZ four-port BPFC that comprises four FBRs and four mixed-EM couplings. The FBR is designed using a TransTech TT1-105 material and following the design process in Section II-A for h/ h f = 0.5 and R = 4.97 mm. Afterward, it is combined with other resonators or dual-mode FBRs through impedance inverters to create higher order transfer functions. The coupling elements represented by straight black lines are implemented with quarter wavelength long TLs either as distributed microstrip TLs or by  III   COMPARISON WITH THE STATE-OF-THE-ART CIRCULATORS AND NON-RECIPROCAL FILTERS their first-order lumped element pi-equivalent. The mixed-EM couplings are materialized through parallel LC resonators. Finally, the passive microwave resonators are implemented with capacitively loaded shorted TLs. The EM design and analysis of the circuits were completed in the software package ANSYS HFSS. The RF characterization of each prototype was performed by means of S-parameter measurements using a Keysight 8917A PNA.

A. Four-Pole/Two-TZ BPFC Using a Single Dual-Mode FBR
To validate the four-pole/two-TZ BPFC using a single dual-mode FBR, two prototypes were designed for a center frequency of 2.2 GHz and FBW of 9.3% using as a basis the CRD in Fig. 8. The photographs of the manufactured prototypes are provided in Fig. 16. Furthermore, a photograph of the fully assembled prototype in Fig. 16(a) is provided in Fig. 17. The prototypes were manufactured on a RO4350B substrate with the following characteristics: relative dielectric permittivity ε = 3.48, tanδ D = 0.003, h = 1.524 mm, and 1-oz copper cladding. The difference between these two prototypes is in the implementation of the inverters; the first prototype uses quarter wavelength-long TLs, while the second prototype uses first-order lumped element TLs implemented in highpass and low-pass pi-networks (circled in blue and white) to suppress spurious modes above and below the passband.
The comparison between the EM-simulated and RFmeasured S-parameters for both prototypes is provided in Fig. 18 and is in good agreement, thus validating the BPFC concept. The RF performance [see Fig. 18(a)] of the first prototype is summarized as follows: center frequency ( f cen ) = 2.2 GHz, FBW = 8.2%, IL = 2.0 dB, f cen IS = 27.8 dB, maximum in-band IS = 27.8 dB, and minimum 3-dB BW Fig. 18. EM-simulated and RF-measured S-parameters for the four-pole/two-TZ prototype in (a) Fig. 16(a) and (b) Fig. 16(b). IS = 6.9 dB. The RF performance of the second prototype [see Fig. 18

B. Four-Pole/Six-TZ BPFC Using Three Dual-Mode FBRs
A four-pole/six-TZ BPFC was designed and measured to validate the concept in Fig. 12. The photograph of the manufactured prototype is shown in Fig. 19(a). Each RF path consists of two dual-mode FBRs and two frequencydependent couplings. The inverters were implemented with quarter wavelength-long TLs, and the frequency-dependent couplings were realized through parallel LC resonators. The prototype was designed on an RO4350B substrate to operate at 2.5 GHz with FBW of 6.5%. The RF measured and EMsimulated results are provided in Fig. 19(b) and demonstrate a good agreement. The RF performance is summarized as follows: f cen = 2.5 GHz, FBW = 4.9%, IL = 4.3 dB, f cen IS = 29.3 dB, and minimum 3-dB BW IS = 8.7 dB.

C. Multiport BPFC
A four-pole/six-TZ multiport BPFC was designed, built, and measured to experimentally validate the topology in Fig. 14. A photograph of the prototype with and without the magnet assembly is shown in Fig. 20. The inverters are made up  of quarter-wavelength long TLs and the frequency-dependent couplings were made up of parallel LC resonators. As seen in Fig. 20(b), multiple magnets were required to properly bias the BPFC. The prototype was designed for a center frequency of 2.5 GHz with FBW of 8.4%. Its corresponding EM-simulated and RF measured S-parameters are shown in Fig. 21. The measured RF performance is summarized as follows: f cen = 2.5 GHz, FBW = 6.4%, IL = 2.5 dB, f cen IS = 29.4 dB, and minimum 3-dB BW IS = 8.6 dB.

D. Comparison With the State of the Art
A comparison of the proposed BPFCs with current stateof-the-art ferrite-based circulators and non-reciprocal BPFs is provided in Table III. As it can be seen, the proposed BPFC concept is the only one applied to multiport networks with up to four ports, whereas all the rest are limited to two-and threeport networks. Furthermore, the proposed devices exhibit the highest number of poles and TZs and can be arbitrarily scaled to higher order transfer functions and number of poles. The non-reciprocal filters using STM topologies (see [42], [43], [45]) are only demonstrated for low frequencies (<1.2 GHz), and they exhibit higher IL (3.7-5.5 dB), lower order transfer functions (≤3 poles), and very low IS (6.2 dB in [43]). While the non-reciprocal BPF in [52] exhibits a seventh-order transfer function and gain, it requires dc power to operate. In addition, the size of the transistor-based design in [52] is larger than the proposed BPFCs. The co-designed BPF and quasi-circulator in [54] exhibit similar performance with regard to IS; however, it consumes dc power and has only been demonstrated for a lower order transfer functions with up to two poles. When compared to ferrite-based circulators without filtering capabilities (see [9], [18], [22], [25], [27]), the proposed concept exhibits similar size and comparable IS. When doing a direct comparison to the RF co-designed ferritebased BPFC [28], this work presents higher order transfer functions (>3 poles) with similar IS levels (∼30 dB). Finally, the proposed approach is based on a comprehensive design methodology using the coupled-resonator formalism allowing the co-design of these multiport non-reciprocal networks with other RF front-end filtering and multiplexing components.

IV. CONCLUSION
This article reported on the RF design and practical development of co-designed, multiport BPFCs. The proposed concept is based on cascading dual-mode non-reciprocal FBRs with microwave resonators and frequency-dependent coupling elements. As such, highly selective transfer functions with high IS and frequency-selectivity can be created. A design methodology using coupled-resonator-based synthesis is provided to facilitate the design of higher order BPFCs as well as their co-design with advanced filtering and multiplexer topologies. For proof-of-concept validation purposes, four prototypes were designed, manufactured, and measured at S-band. They include: 1) two four-pole/two-TZ BPFCs; 2) a four-pole/six-TZ BPFC; and 3) a four-pole/six-TZ four-port BPFC. To the best of our knowledge, this is the first demonstration of CRDbased design applied to BPFCs. Furthermore, high-order RF co-designed BPFCs and multiport configurations using dualmode FBRs are uniquely presented in this work.