Unbalanced-/Balanced-to-Unbalanced Diplexer Based on Dual-Mode Dielectric Resonator

The design of compact unbalanced-/balanced-to- unbalanced diplexer (U2U/B2U) based on full dual-mode dielectric resonator (DR) is investigated for the first time. The relationships of the external quality factors (<inline-formula> <tex-math notation="LaTeX">$Q_{e}$ </tex-math></inline-formula>) under the two modes are analyzed. It is found that the <inline-formula> <tex-math notation="LaTeX">$Q_{e}$ </tex-math></inline-formula> of two modes can be controlled independently, which makes the design procedure simple and efficient. Based on the analysis, both of the proposed U2U and B2U diplexer can be easily built by properly adding feeding probes for the DR without increasing the circuit size by altering the location of the feeding probes according to the distribution of the electromagnetic fields. To verify the proposed design concept, the diplexers mentioned above are simulated, implemented and measured. The isolation is achieved by the orthogonality between modes while the low insertion loss is obtained due to the high unloaded quality factor (<inline-formula> <tex-math notation="LaTeX">$Q_{u}$ </tex-math></inline-formula>) of the dual-mode DR. The measurements are in accordance with the simulated results, showing low loss and good selectivity.


I. INTRODUCTION
With the rapid development of modern wireless communication systems, the features of miniaturization, low insertion loss and high performance are highly desired. As a key component of RF front end, the diplexer is essential in the multi-frequency transceiver [1]. Since a diplexer can simultaneously deal with the uplink and downlink signals, the number of filters can be reduced by half [2]. Due to the aforementioned advantages, various diplexers have been reported. In traditional designs, two independent bandpass filters are combined by a common T-junction which makes that one filter an open circuit at the frequency of the other passband [3]- [7]. However, the T-junction needs to be designed individually and occupies additional size. To miniaturize the circuit size, a common dual-mode resonator is used to replace the T-junction and act as the first level of the resonant circuit [8]- [12]. However, since the subsequently cascaded resonators in many reported works are still based on the The associate editor coordinating the review of this manuscript and approving it for publication was Abhishek K Jha . single-mode resonator, the advantage of dual-mode resonator for miniaturization is not fully realized. In recent years, the structure based on full dual/multi-mode resonator is proposed by replacing the subsequently cascaded single-mode resonators with dual/multi-mode resonators, which makes further miniaturization achieved [13]- [19]. In [15], a quadmode resonator is designed and applied to design compact dual-band diplexer. However, since the probe excites four modes simultaneously, the external quality factors (Q e ) under each mode can't be controlled independently, which makes the design procedure complicated. Therefore, how to achieve a balance between miniaturization and design efficiency is worth studying.
On the other hand, most of the works are based on the microstrip and SIW, showing various merits. However, due to the relatively low unloaded quality factor (Q u ) of the resonator, the insertion loss and selectivity of the passband are not good. The metal cavity can provide a high Q u [18]- [21], but the size is bulky. The dielectric resonator (DR) can be treated as a bridge between the microstrip line/SIW and metal cavity resonators in terms of Q u and volume. Accordingly, DR has been widely applied to design microwave circuits [22]- [25]. Among them, the diplexer based on DR also has been reported. In [26] and [27], an offcentered triple-mode DR is proposed to design the diplexer, achieving compact size and low insertion loss.
Balanced circuits, containing high immunity to interference distortion, are widely applied in antennas to achieve symmetrical radiation pattern, high common-mode rejection, low cross polarization, and good impedance matching [28]- [30]. As an interface between the single-ended and balanced components (i.e. the connector between a differential antenna and a receiver/transmitter), the balun diplexer is also highly desired. For the unbalanced-to-balanced (U2B) diplexer, differential signal can be realized by the halfwavelength transmission line [31], [32]. Most of the designs using this approach are based on the microstrip line which often suffers from high loss. For the balanced-to-unbalanced (B2U) diplexer, an effective approach is to excite a pair of differential modes at the input, which is effectively applied in the metal cavity [18]. However, up to now, the B2U diplexer based on DR hasn't been reported.
In this paper, the designs of the U2U and B2U diplexer based on full dual-mode DR are proposed. The full dual-mode structure effectively reduces the circuit size. Meanwhile, the design process is simple and efficient because the Q e values of the two modes can be controlled independently. The proposed U2U and B2U diplexers can be easily built by properly adding feeding probes for the DR without increasing the circuit size by altering the location of the feeding probes according to the distribution of the electromagnetic fields. Both of the two designs are fabricated and measured for demonstration. Multiple features are achieved, such as compact size, low insertion loss and good selectivity. Fig. 1 shows the topology of the proposed U2U diplexer. S and L i (i = 1, 2) represent the source and loads. The black and red lines represent the first and second channels. 1 A (2 A ) and 1 B (2 B ) represent the lower and higher resonant frequencies of the dual-mode DR, respectively. Based on this topology, a U2U diplexer is designed. The structure of the proposed U2U diplexer based on the dual-mode DR is shown in Fig. 2. A metal baffle is located in the middle of the cavity to form two paths for signal transmission. The width of apertures w 1 and w 2 are used to control the coupling coefficient between the two DRs. The probe length and the gap determine the coupling between the port and DR. Port 1 is the input port that excites the dual mode of the DR simultaneously. Port 2 and  The DR has the relative dielectric constant ε r = 38 with loss tangent tanδ = 2.5 × 10 −4 . Figs. 3(a) and (b) show the E-fields of the dual-mode DR with or without corner cuts. It can be seen that before the corner cutting where the DR is in square shape, the E-fields of the two modes distribute along the edge as shown in Fig. 3(a) while the E-fields distribute along the diagonal after the corner cutting as shown in Fig. 3(b). In both cases, the two modes are always orthogonal with each other. To excite the two modes separately, the feeding probe should be arranged along the direction of polarization. Fig. 4 shows the relationship between the dual-mode frequencies and the corner cuts. With the increase VOLUME 9, 2021  of s, the resonant frequency of Mode A remains unchanged while the frequency of Mode B increases. Fig. 5 shows the isolation between the two modes. Because of the orthogonality between the modes, the isolation between 1.35 GHz and 1.7 GHz is greater than 30 dB, which is suitable for diplexer design.

III. UNBALANCED-TO-UNBALANCED DIPLEXER
Figs. 6(a)-(d) show the Q e of the three unbalanced ports versus probe location, probe length and the coupling gap between the DR and probe. Figs. 6(a)-(b) show the extracted Q e at the common input port (port 1) for the two modes (Q u eA and Q u eB ). It is shown that the two modes can be excited simultaneously and controlled independently, i.e. Q u eB varies within a small range while the value of Q u eA can be changed in a large range. Q u eA increases as l increases or h 1 decreases while Q u eB keeps almost unchanged from l = 10 mm to 18 mm. The similar relationship between Q u eA (Q u eB ) and l (or g 1 ) can be obtained. By adjusting the three parameters (l, g 1 , and h 1 ), the required Q e can be easily obtained at port 1. Figs. 6(c)-(d) show the extracted Q e under each of the two modes against different h 2 (h 3 ) and g 2 (g 3 ). In this case, the port should be arranged along the corresponding polarization direction as shown in Fig. 3. Fig. 7 shows the coupling coefficient k versus w 1 with different w 2 .
According to the design specification, the lower and higher center frequencies are respectively 1.52 GHz and 1.64 GHz, which corresponds to s = 8.7 mm. Through calculation, we obtain k 1 A 2 A = 0.006 and Q u eA = 190.2 for the lower passband while k 1 B 2 B = 0.0067 and Q u eB = 167 for the higher passband. Accordingly, the coupling matrix of U2U diplexer can be obtained as shown in (1), as shown at the bottom of the page.
Since there is actually a small amount of coupling between the orthogonal modes and the two output ports, the coupling coefficients of M 2 B L 1 and M 2 A L 2 are not zero. Fig. 8 shows the theoretical and simulated results with good agreement.
The design procedure of the U2U diplexer can be summarized as follows.
(1) Calculate the Q e and the coupling coefficient according to the design specification.
(2) Select the lengths of the feeding probes and the gap between the feeding probes and DR according to Figs. 6(a)-(d).
(3) Select the w 1 and w 2 of the metal baffle according to Fig. 7.
(4) Optimize the dimensions according to the response. According to the required k and Q e , the dimensions of the proposed U2U diplexer after optimization can be determined as follows: m 1 = 83 mm, m 2 = 40 mm, m 3 = 32 mm, a = 25 mm, q = 20 mm, l = 12.5 mm, g 1 = 3 mm, g 2 = 3 mm, g 3 = 0.8 mm, w 1 = 11.8 mm, w 2 = 11.8 mm, w 3 = 3 mm, h 1 = 27.3 mm, h 2 = 20 mm, and h 3 = 20 mm. The simulated and measured results are shown in Fig. 9. The center frequencies of the dual band are 1.52 GHz and 1.64 GHz, respectively. The simulated dual-band return losses are better than 18.5 dB and 15.2 dB while the measured return losses are better than 14.5 dB and 14 dB. The simulated dual-band insertion losses are both less than 0.54 dB while the measured insertion losses of the dual bands are both less than 0.8 dB.  The simulated and measured isolations (S 23 ) are better than 34 dB and 33 dB, respectively. The comparisons with other diplexers are summarized in Table 1. As can be seen, this work shows many advantages such as low insertion loss, small size and minimum fractional bandwidth (FBW). Compared with the other 3-D structures using the T-junction [26], [27], [34], [35] and the starjunction [36], the design of full dual-mode DR can achieve the size reduction. Compared with the other implementations that need 2 coupling matrices to synthesize the two bands separately, only one coupling matrix is used in this design, which improves the design efficiency.

IV. BALANCED-TO-UNBALANCED DIPLEXER
The topology of the B2U diplexer is shown in Fig. 10. Based on the U2U diplexer, the B2U diplexer can be achieved by adding an additional port to the input port to form a balanced input port. In this design, the Q e of the two kinds of input ports must satisfy Q b eA = Q u eA and Q b eB = Q u eB [23], [33]. This can be achieved by only changing the probe length of the balanced input port while other parameters are the same as the U2U counterpart. Fig. 11 shows the extracted Q e of the balanced input under the two modes (Q b eA and Q b eB ) versus     The simulated and measured results of the B2U diplexer are shown in Figs. 12(a)-(b). The simulated and measured center frequencies of the dual bands are 1.52 GHz and 1.64 GHz, respectively. The simulated return losses of the dual bands are larger than 15.9 dB and 15 dB. The measured dual-band return losses of them are larger than 14.27 dB and 14.31 dB. The simulated dual-band insertion losses are both less than 0.53 dB and the measured dual-band insertion losses are both less than 0.67 dB. The simulated and measured isolations are better than 33 dB and 26 dB, respectively. The simulated and measured common-mode rejections (CMR) are better than 31 dB and 22 dB, respectively. The difference 53330 VOLUME 9, 2021 between the simulated and measured results can be due to the fabrication errors, the measuring errors and the loss of the SMA connectors. Table 2 shows the comparisons with other balun diplexers. The same with the U2U diplexer proposed above, the B2U diplexer also has the lowest insertion loss in the case of minimum FBW, showing good passband performance.

V. CONCLUSION
In this paper, we proposed the compact U2U and B2U diplexers. By using dual-mode DR, the circuit size is effectively reduced. Since the Q e of two modes can be controlled independently, the design procedure is simple and efficient. The proposed U2U and B2U diplexers can be easily built by properly adding feeding probes for the DR without increasing the circuit size by altering the location of the feeding probes according to the distribution of the electromagnetic fields. Both of the two prototypes are verified by the simulation and experiment. Good performance, such as low insertion loss, high selectivity, and compact structure, has been realized, which makes the diplexer attractive in modern wireless communication systems. If wider bandwidth is required, higher filtering orders can be considered properly.