Design of Bandpass Multiplexer-Integrated Power Dividers

This study proposed a novel methodology for designing bandpass multiplexer-integrated power dividers (PDs) that provide frequency division, frequency selection, and power division. New coupling schemes for the multiplexer-integrated PDs were presented to ensure multifunctionality and compactness. Miniaturization was achieved through the common resonator technique. Dual-mode stub-loaded resonators serving as common resonators for various channel passbands were used in the multiplexer-integrated PD to reduce the required number of resonators and thereby considerably reduce the size. Each channel passband can be individually designed using the distributed coupling technique to decrease complexity. For validation, a third-order bandpass triplexer-integrated PD and third-order bandpass quad-channel diplexer-integrated PD were designed and fabricated using microstrip technology. Measurements of the devices were consistent with simulated results. The proposed circuits are compact, multifunctional, highly integrate, high performing, simple, and easy to fabricate; thus, they are suitable for the practical applications, such as multi-standard operation antenna array modules.


I. INTRODUCTION
Compact, high-performance, multifunctional microwave circuits have attracted widespread attention and are increasingly being applied in multiband wireless and mobile communication systems. Multifunctional circuits can facilitate system integration and reduce system size and cost. Numerous studies have reported multifunctional circuit design elements such as the filtering power divider (PD), duplexing filtering PD, balun filter, and filtering antenna; various design methodologies have also been proposed.
Filtering PD designs that integrate a bandpass filter (BPF) and PD into a circuit and offer frequency selection and power division have been proposed. The filtering PDs in [1]- [6] were designed using the coupled-resonator technique. Because these filtering PDs were constructed with miniaturized resonators, the overall circuit area was small. To further reduce circuit size, multimodal, resonator-based filtering PDs have also been investigated [7]- [20]. In [7]- [9], dual-and tri-mode resonators were used to produce a filtering PD. Strong isolation performance was achieved by including an isolation resistor between the two resonators. In [10], a single open-type dual-mode resonator and a resistor were integrated into a filtering PD design. Three open-ended stubs were introduced to increase the frequency selectivity and enhance the stopband response of the PD. In [11]- [14], multiway filtering PDs were explored for multichannel applications. Numerous examples of tunable filtering PDs [11], [15], [21]- [25] with wideband operations [7], [12], [15], [26]- [28] have been reported. In [11] and [15], varactortuned multimode stub-loaded resonators were used to design reconfigurable filtering PDs with tunable center frequencies, bandwidth, and power division. In [21] and [22], tunable filtering PDs produced using a varactor-loaded coupledresonator topology were proposed. In [23], filtering PDs based on quasi-bandpass sections were reported; these PDs feature frequency-controllable single-band and multiband operations. In [24], Wilkinson-type PDs with reconfigurable quasi-elliptic-type filtering characteristics were reported; the center frequency, bandwidth, stopband bandwidth, and outof-band attenuation of these PDs are reconfigurable through dynamic transmission-zero allocation. In [25], a reconfigurable filtering PD design method based on a flexible tunable coupling topology that ensured compactness and a wide frequency tunning range was proposed. In [26]- [28], wideband filtering PDs based on a parallel-coupled line structure were proposed; these PDs also achieved a satisfactory stopband response. In addition, [11], [13], [16]- [20], and [29]- [36] developed filtering PDs for dual-band applications. By assigning the resonance frequencies of one or more multimode resonators, filtering PDs with dual-band behavior have been created [11], [13], [16]- [20]. In [29], [30], and [34], dual-resonance resonators were applied to design PDs with dual-band filtering responses. In [31], Tjunction structures and quarter-wavelength stepped impedance resonators were employed in a Wilkinson PD design, which achieved dual-band power allocation and a bandpass response. The filtering PD in [32] was designed to achieve a dual-band filtering response with arbitrary power division, an arbitrary frequency ratio, arbitrary real terminated impedances, and independently controllable bandwidth by replacing the conventional quarter-wavelength transmission line with a dual-band filtering structure. The filtering PD in [33] was constructed using two open-stub resonators loaded on both side lines of a three-line coupled structure to ensure a dual-wideband bandpass response. In [35] and [36], dual-band filtering PDs based on single-layer substrate-integrated waveguide cavities were proposed.
To improve the functions of single circuits, various diplexer-integrated filtering PD (or duplexing filtering PD) designs that can provide frequency division, frequency selection, and power division have been developed [37]- [42]. The designs in [37]- [40] and [42] were for two-channel applications, and the design in [41] was for three-channel applications. Each of these circuits was designed to have a second-order bandpass response, resulting in poor selectivity. However, with the rapid development of modern wireless communications, the demand for multifunctional multiplexers with several operating channels and strong performance has increased. The conventional method for achieving frequency division, frequency selection, and power division typically requires numerous circuits, including a matching network, BPFs, and PDs (Fig. 1). These circuits increase the size and cost of a system. This problem can be resolved by integrating BPFs, PDs, and multiplexers into a single circuit, namely a bandpass multiplexerintegrated PD (Fig. 1). This study proposed a novel methodology for the design of a bandpass multiplexerintegrated PD. To the best of the authors' knowledge, no bandpass multiplexer-integrated PD operating on more than three channel bands has been reported in the literature. For proof-of-concept purposes, a bandpass triplexer-integrated PD and a bandpass quad-channel diplexer-integrated PD were designed and implemented in microstrip technology. The experimental results indicate that the proposed structures have excellent filtering performance and port-toport isolation. The proposed structures also have a small footprint and thus can be used for applications requiring miniaturization.
The remaining sections of this paper are organized as follows: Sections 2 and 3 detail the design methods, production procedures, and novel circuit topologies for the proposed novel bandpass triplexer-integrated PD and bandpass quad-channel diplexer-integrated PD, respectively. Design formulas for the proposed topologies are also provided. The results of two-port vector network analyzer measurements are also presented and compared with fullwave electromagnetic (EM) simulation results. In Section 4, the performance of the proposed circuits is compared with that of the state of the art, and the main contributions of the proposed bandpass multiplexer-integrated PDs are highlighted. Finally, Section 5 presents the conclusion. Fig. 2 presents the coupling scheme of the proposed triplexer-integrated PD with a third-order bandpass response. The circuit is a seven-port network. The multifunctional triplexer comprises only five resonators (resonators A, B, C, D, and E) and three isolation resistors (R1, R2, and R3), where S and L represent the input and output ports, respectively. To miniaturize the circuit, the first even-mode resonance frequency of dual-mode resonator A (node ) and the first  even-mode and odd-mode resonance frequencies of dualmode resonator B (nodes 2 I and 3 I ) were used to form the operating passband of channel I; the first odd-mode resonance frequency of dual-mode resonator A (node ) and the first even-mode and odd-mode resonance frequencies of dual-mode resonator C (nodes 2 II and 3 II ) were used to form the operating passband of channel II. Finally, the fundamental resonance frequency of resonator D (node ) and the first even-mode and odd-mode resonance frequencies of dual-mode resonator E (nodes 2 III and 3 III ) were used to form the operating passband of channel III. A third-order bandpass response can thus be achieved for each channel passband. In addition, because an additional crosscoupling path exists in the coupling scheme, a transmission zero above the passband was generated for each channel [43]. If the output coupling structure is designed to be symmetrical, equal-power division with the in-phase property can be achieved for each channel. Three resistors, namely R1, R2, and R3, loaded between the outputs enhance the impedance matching of and isolation between the output ports. The isolation resistors do not influence the power splitting or filtering performance [10]; thus, the resistances of the isolation resistors can be determined after all other design decisions are made.

II. DESIGN OF BANDPASS TRIPLEXER-INTEGRATED PD
The dual-mode stub-loaded resonator presented in Fig. 3(a) was employed in the design of the bandpass triplexerintegrated PD; , , and (i = 1, 2) represent the characteristic impedance, electric length, and physical length of the transmission line, respectively. Because of the symmetric circuit structure of the dual-mode stub-loaded resonator, the resonance conditions can be analyzed with the even-and odd-mode equivalent circuits in Fig. 3(b) and (c), respectively. By setting the imaginary parts of ( _ _ ) and equal to zero, the evenand odd-mode resonance conditions of the resonator can be expressed as follows: With these resonance conditions, the even-and odd-mode resonance frequencies of the dual-mode stub-loaded resonator and can be calculated by assuming as follows [8]- [10]: where is the speed of an electromagnetic wave in a vacuum and is the effective dielectric constant of the substrate. Equation (4) indicates that odd-mode resonant frequency depends only on . Therefore, in the resonator design, can be determined by adjusting . Subsequently, evenmode resonant frequency can be determined by adjusting accordingly.
To experimentally verify the proposed design, a bandpass triplexer-integrated PD was produced using microstrip technology. The Rogers RO4003C laminate with a dielectric constant of 3.55, thickness of 0.508 mm, and loss tangent of 0.0027 was used for design and fabrication. The design specifications of the bandpass triplexer-integrated PD are listed in Table 1. For each given specification, the coupling matrix for channel N can be synthesized and expressed as follows: To achieve an equal-split filtering response, the normalized coupling coefficient in (5) should satisfied the conditions of a n d , while and are the output couplings for a third-order BPF with a single output. Therefore, the external quality factors for two output ports are equal to each other, which are twice values of the output external quality factor for a third-order BPF with a single output. Fig. 4 shows the ideal response of the bandpass triplexer-integrated PD. Fig. 5 presents the layout of the proposed triplexer-integrated PD. Only five resonators are required for this design. Resonator D was a half-wavelength resonator; resonators A, B, C, and E were the dual-mode stub-loaded resonators. The distributed coupling technique was used to integrate the   three-channel filtering PDs without an extra matching circuit, thereby reducing circuit size. The loading effects between channel passbands were weak because of the use of this distributed coupling structure [42]. As a result, each of the three-channel passbands can be designed individually.
The desired resonance frequencies of each resonator can be derived as follows [44]: where and denote the center frequency of the passband and normalized coupling coefficient, respectively, for channel . On the basis of the specifications, the desired resonance frequencies of the resonators were calculated: , , , , and . The geometric parameters of the dual-mode stub-loaded resonators are determined using (3) and (4).
Coupling coefficient is given by the following: where and (the ratio of the passband bandwidth to the center frequency of the passband) are the normalized coupling coefficient and fractional bandwidth, respectively. The coupling coefficient depends on the distance between the adjacent resonators and can be extracted using a fullwave simulator through the following formula [44]: where for 1, 2 represents the self-resonance frequencies of two adjacent resonators and for 1, 2 denotes the two split frequencies for two resonators coupled with each other.
Input and output external quality factors and , respectively, can be derived as follows [44]: To achieve a third-order filtering response with equal power splitting at two output ports, the required external quality factors were as follows: , , , . To satisfy these desired external quality factor requirements, the geometric parameters, namely line width, line length, and spacing of the I/O coupled lines were adjusted. External quality factors can be extracted using a full-wave simulator through the following formula [44]: where is the group delay of S11 at resonance frequency .
The initial geometric parameters for the bandpass triplexer-integrated PD were determined when the extracted values of coupling coefficients and external quality factors corresponded to the theoretical values. By using to this design procedure, the initial geometric parameters for the bandpass triplexer-integrated PD can be obtained. When an equal-split filtering response was achieved at each channel, the isolation between the output ports and the impedance matching of the output ports for each channel was enhanced by changing the resistances of isolation resistors R1, R2, and R3. Fig. 6(a)-(c) displays the simulated frequency responses with various resistances for R1, R2, and R3, respectively.  Output return losses |S22|, |S44|, and |S66| and port-to-port isolations |S32|, |S54|, and |S76| change with the resistances of R1, R2, and R3, respectively, with a negligible effect on the equal-power splitting and filtering performances. The initial values of the resistances can be obtained using the matching condition of the output for each channel. The optimized resistances of the three resistors were R1 = 182 Ω, R2 =194 Ω, and R3 =168 Ω to achieve high isolation and impedance matching. A fine-tuning procedure can be performed to optimize performance if required; the produced multifunctional PDs were fine-tuned in this study. The proposed bandpass triplexer-integrated PD has been fabricated using a conventional printed circuit board (PCB) process. A photograph of the fabricated bandpass triplexerintegrated PD is displayed in Fig. 7, and its physical dimensions are presented in Table 2. The circuit size was 0.63 × 0.48 (93.9 mm 72.1 mm), where is the guided wavelength at 1.31 GHz.
Simulations were performed with a full-wave EM simulator (Keysight Advanced Design System, ADS), and measurements were performed with the Agilent N5230A network analyzer. And a short-open-load-thru method was used for calibration. The S-parameter measurements have been performed from 0.8 up to 2.6 GHz. Since the proposed bandpass triplexer-integrated PD is a seven-port device, 50-Ω loads need to be used generally. During measurements, ports and ( , = 1 to 7) of the device are connected to the 2-port network analyzer for obtaining input and output matching, transmission, and phase response between ports and , while the other ports should be loaded at 50-Ω loads. Figs. 8, 9, and 10 present plots of the EM simulated and measured frequency responses of the proposed bandpass triplexer-integrated PD. A filtering response with equalpower division was accomplished in each channel. The experimental results indicate that the in-band return losses (−20 log |S11|) were higher than 15 dB and that the in-band insertion losses (−20 log |S21|, −20 log |S41|, and −20 log |S61|) at channel passbands I, II, and III, respectively, including the 3-dB equal-power division loss, were approximately (3 + 1.0), (3 + 0.9), and (3 + 2.9) dB, respectively. The isolations between the output ports (−20 log |S32|, −20 log |S54|, and −20 log |S76|) were greater than 25 dB over the entirety of the channel passbands. The port isolations between channels (−20 log |S42|, −20 log |S62|, and −20 log |S64|) were greater than 31 dB. A transmission zero generated above the passband was observed, which greatly increases the skirt selectivity for each channel. The measured in-band group delay for the first, second, and third channel passbands are 4.92-6.44 ns, 4.04-4.99 ns, and 7.44-9.31 ns, respectively. In addition, the amplitude and phase imbalances within the passbands were <0.25 dB and <2°, respectively. As a result, the measured and simulated results were consistent, which validates the proposed design method. Fig. 11 presents the coupling scheme of the proposed thirdorder bandpass quad-channel diplexer-integrated PD, which mainly comprises eight resonators (resonators 1 I,III , 2 I , 2 III , 3 I,III , 1 II,IV , 2 II , 2 IV , and 3 II,IV ) and two isolation resistors (R1 and R2), where S and L denote the input and output ports, respectively. The circuit is a five-port network. In this design, the fundamental resonance frequency of the resonator 2 I (node 2 I @ f01) and first even-mode resonance frequencies of dual-mode resonators 1 I,III and 3 I,III (nodes and @ f01) were used to form the operating passband of channel I; the fundamental resonance frequency of resonator 2 II (node 2 II @ f02) and first even-mode resonance frequencies of dualmode resonators 1 II,IV and II,IV (nodes and @ f02) were used to form the operating passband of channel II; the fundamental resonance frequency of the resonator 2 III (node 2 III @ f03) and first odd-mode resonance frequencies of resonators 1 I,III and 3 I,III (nodes and @ f03) were used to form the operating passband of channel III; the fundamental resonance frequency of the resonator 2 IV (node 2 IV @ f04) and first odd-mode resonance frequencies of resonators 1 II,IV and 3 II,IV (nodes and @f04) were used to form the operating passband of channel IV. A third-order bandpass response can thus be achieved for each channel passband. The filter order and selectivity can be increased by adding resonators to each coupling path. Because the proposed circuit has an independent signal coupling path for each operating frequency band, each of the channel passbands can be created individually. The topology of the symmetrical output feeding structure enables an equal-power division function with the in-phase property for each channel. In addition, two resistors, namely R1 and R2, were loaded between the outputs to improve the isolation between output ports and the impedance matching of the output ports for each channel.

III. DESIGN OF BANDPASS QUAD-CHANNEL DIPLEXER-INTEGRATED PD
To verify the proposed design methodology, the thirdorder bandpass quad-channel diplexer-integrated PD was implemented using microstrip technology. Rogers RO4003C with a dielectric constant of 3.55, thickness of 0.508 mm, and loss tangent of 0.0027 was used as the dielectric substrate. The design specifications of the bandpass quad-  channel diplexer-integrated PD are listed in Table 3. Fig. 12 shows the ideal response of the bandpass quad-channel diplexer-integrated PD. The required coupling coefficient between adjacent resonators and the I/O external quality factor can be calculated using the following formulas [44]: where is the lumped circuit element values of the lowpass prototype filter and superscript is the channel number ( I, II, III, or IV). Output external quality factor is two times input external quality factor because the energy is equally split into two outports for each channel. The layout of the third-order bandpass quad-channel diplexer-integrated PD is displayed in Fig. 13. Resonators 2 I , 2 II , 2 III , and 2 IV were created with the U-shaped halfwavelength resonator, and resonators 1 I,III , 3 I,III , 1 II,IV , and 3 II,IV were created with the dual-mode stub-loaded resonator in Fig. 3. The design was miniaturized because of the reduction in number of resonators to eight (in general, twelve resonators are required for a third-order quad-channel diplexer). The design does not require a matching network at the input because the distributed coupling technique was used. Moreover, the four channel passbands can be designed individually.
On the basis of the specifications, the desired coupling coefficients between adjacent resonators can be calculated u s i n g ( 1 2 ) : , , , a n d  coupling coefficients can be extracted using the full-wave simulator through (8). If the extracted value of the coupling coefficient is equal to the theoretical value, the distance between the adjacent resonators can be determined. The desired I/O external quality factors can be calculated using (13) and (14): The external quality factor, which depends on line width, line length, and spacing of the I/O coupled lines, can be extracted using a full-wave simulator through (11). If the extracted external quality factors are equal to the theoretical values, the I/O coupling structure can be determined.
After an equal-split filtering response was achieved at each channel, the isolation between the output ports and the impedance matching of output ports for each channel was improved. Resistors R1 and R2 were loaded between the output feeding lines (Fig. 13). Fig. 14 presents the simulated frequency responses for various values of R1 and R2. Output return losses |S22| and |S44| and port-to-port isolations |S32| and |S54| change with the resistances of resistors R1 and R2, respectively, with a negligible effect on the equal-power splitting and filtering performance. For channels I and III, both return loss (|S22|) and isolation (|S32|) increase if R1 is changed from 340 to 148 Ω. Similarly, for channels II and IV, both return loss (|S44|) and isolation (|S54|) increase if R2 is changed from 340 to 191 Ω. The initial values of the resistances can be obtained using the output matching condition. The optimized resistances for the two resistors were R1 =148 Ω and R2 =191 Ω. Finally, a fine-tuning procedure can be performed to optimize performance. A photograph of the fabricated bandpass quad-channel diplexer-integrated PD is displayed in Fig. 15, and its physical dimensions are listed in  16,17, and 18 present the simulated and measured results for the proposed bandpass quad-channel diplexerintegrated PD. The proposed five-port circuit provides a third-order filtering function with equal-power division for each channel passband. The measured in-band return loss (−20 log |S11|) was larger than 17 dB. Including the 3-dB equal-power division loss, the insertion losses at channel passbands I and III (−20 log |S21|) were approximately (3 + 2.3) and (3 + 2) dB, respectively, and those at channel passbands II and IV (−20 log |S41|) were approximately (3 + 2.1) and (3 + 2.9) dB, respectively. The measured in-band group delay for the first, second, third, and fourth channel   Table 5 presents a comparison of the proposed bandpass triplexer-integrated PD (case 1) and the proposed bandpass quad-channel diplexer-integrated PD (case 2) with similar devices reported in other studies. The advantages of the proposed bandpass multiplexer-integrated PD are as follows:

1) Multifunctionality and high integration:
The proposed bandpass multiplexer-integrated PD offers frequency division, frequency selection, and power splitting without a considerable increase in size. It can improve system integration and thereby reduce the system size and cost. Thus, the multifunctional PD can be used in numerous applications.

2) More operating channels:
The device in this study has more operating channels than do those in [37]- [42], which increases its applicability to multiband and multiservice wireless communication systems.

3) Strong performance and compactness:
All devices in [37]- [42] had a second-order filtering response. In this study, both the proposed triplexerintegrated PD and quad-channel diplexer-integrated PD were designed to have a third-order filtering response with favorable port-to-port isolation to increase responsiveness and selectivity. Because the dual-mode stub-loaded resonators (that serve different channel passbands) were used in the bandpass multiplexerintegrated PD, the number of resonators was low, enabling a considerable size reduction.

4) Simple design and layout:
The proposed design procedure is simple; the traditional coupled-resonator design method described in [44] can be directly applied. In addition, the structures do not require any via holes or slotted ground planes; thus, the device is easy to fabricate.

V. CONCLUSION
This study presented a novel methodology for designing bandpass multiplexer-integrated PDs. A bandpass triplexerintegrated PD and a bandpass quad-channel diplexerintegrated PD were designed, fabricated, and measured to verify the methodology. The experimental results were consistent with the EM simulation results. The proposed multifunctional bandpass multiplexer-integrated PD is compact, highly integrated, high performing, easy to design, and easy to fabricate.