Design of a Multilayer Dual-Band Balanced Bandpass Filter on a Circular Patch Resonator

This letter presents a novel multilayer dual-band balanced bandpass filter (BPF) design by using two perturbed circular patch resonators. The TM11 mode and TM21 mode of the resonator with odd-symmetric field distributions are explored to realize the desired differential-mode (DM) transmission and common-mode (CM) suppression. Two circular patches are properly coupled in the back-to-back form to realize a dual-passband balanced response by virtue of coupling apertures etched on the ground. In addition to the internal coupling, the above apertures are also further utilized for the undesired degenerate mode harmonic suppression. Besides, slot perturbations on the patch are introduced to perturb the TM21 resonant mode to independently adjust the center frequency of the higher passband, while the lower passband remains almost unchanged. Thus, two passbands can be flexibly controlled by simultaneously tuning the above slots and size of the patch. For validation, a dual-band balanced BPF prototype is implemented. The results indicate 18 and 26% wide fractional bandwidths centered at 5.5 and 7.5 GHz with return loss higher than 20 dB under DM operation and CM suppression higher than 40 dB over an ultra-wide frequency band.


INTRODUCTION
Balanced filters play key roles in modern wireless communication systems, attributing to their superior immunity to the electromagnetic interference and environmental noise [1]. In the meantime, great development of modern wireless communication systems brings out an increased requirement for dual-band operations. To the end, dual-band balanced bandpass filters (BPFs) are desired.
Accordingly, much efforts have been made to explore a variety of high-performance dual-band balanced BPFs by using different transmission line structures, such as planar microstrip transmission line resonators [2][3][4][5], substrate-integrated waveguide (SIW) resonators [6][7][8][9], and dielectric resonators (DRs) [10]. On the contrary, the patch-type resonators are attracting much attention in balanced BPF designs due to their superior advantages of higher power handling capability and lower loss over the transmission line-based resonators and simpler and more straightforward analysis and design compared with the SIW and DR forms. However, to the best of our knowledge, only limited works have been carried out on design of single-band balanced BPFs, e.g., square patch resonator-based balanced BPFs [11][12][13] and triangular patch resonator-based balanced BPFs [14][15][16]. How to design a dual-band patch balanced BPF is still rarely reported and remains challenging. This letter is aimed at presenting a new dual-band balanced BPF design on a circular patch resonator. For this purpose, the TM 11 mode and TM 21 mode resonant properties of a circular patch are carefully analyzed and investigated with both differential-mode (DM) excitation and common-mode (CM) excitation. Two vertically coupled circular patches, via proper coupling apertures etched on the common ground, are explored to realize two passbands under DM operation. Furthermore, slot perturbations on the patch are designed to adjust the frequency ratio of the two passbands and attain high CM suppression. In order to demonstrate the design concept, a circular patch dualband balanced filter prototype was designed, manufactured, and tested. Measured and simulated results well coincide with each other.

DESIGN AND ANALYSIS OF THE PROPOSED DUAL-BAND BALANCED FILTER
Figures 1A-E describe the configuration of the proposed dualband balanced BPF. Two layers of RO4003C substrates (ε r 3.55, h 0.508 mm, and tanδ 0.0027) are used. Two differential input ports (Ports 1 and 1′) are placed at the top layer, while two output ports (Ports 2 and 2′) are at the bottom layer. Two coupling apertures of length l 2 and width w 2 are arranged along the main diagonal line (A-B) on the square common ground of Figure 1D. Besides, two perturbation slots with length l 1 and width w 1 are placed along the diagonal line (C-D) of a circular patch with radius r as shown in Figures 1C,E. The dual-band response of the proposed balanced BPF is realized by the utilization of two diagonal modes: TM 11 mode (Mode 1) and TM 21 mode (Mode 3), in the patch resonator. In this context, the first DM passband is made up of a pair of TM 11 modes (Mode 1), while the second DM passband is formed by two TM 21 modes (Mode 3) from the two top-and bottom-layer patches, respectively. Detailed working mechanisms are illustrated as follows. Figure 2 and Figure 3 indicate simulated electrical and magnetic fields of the first three resonant modes in the circular patch: a pair of degenerate TM 11 modes (Mode 1 and Mode 2) and TM 21 mode (Mode 3), respectively. As observed in Figure 2, the electrical-field patterns of these modes are oddsymmetric inside the patch. In other words, almost same intensity and opposite direction can be found with respect to the corresponding symmetric plane. Therefore, when input ports 1 and 1′ are injected with DM signals, the fields of the TM 11 mode (Mode 1) and TM 21 mode (Mode 3) can be simultaneously excited in the top-layer patch. Meanwhile, the magnetic-field  Two coupling apertures placed in the above regions are utilized for the internal coupling of both passbands in a vertically stacked form. Accordingly, the same field patterns from the TM 11 mode (Mode 1) and TM 21 mode (Mode 3) on the bottom-layer patch will be excited. When the feeding output ports are chosen to place at two sides of the symmetrical plane as Ports 2 and 2′, balanced outputs can be attained for both the TM 11 mode (Mode 1) and the TM 21 mode (Mode 3) in the bottom-layer patch.
It should be mentioned that, under CM excitation, the TM 11 mode (Mode 1) and TM 21 mode (Mode 3) cannot be supported on the patches, while the TM 11 mode (Mode 2) can be activated. Thanks to the fields of Mode 2 that are weak around coupling apertures as shown in Figure 3, the CM signals can hardly be coupled to the bottom-layer resonator. Therefore, the CM suppression will be obtained with this structure.
Based on the above analysis, the corresponding coupling scheme is depicted for the dual-band balanced filter, as shown in Figure 4. In the scheme, 1 A and 2 A represent the coupled TM 11 modes (Mode 1) of the top and bottom patch resonators, respectively, to form the first passband. On the contrary, 1 B and 2 B denote the coupled TM 21 modes of the top and bottom patch resonators for the second passband. As is known, for the intact circular patch, the resonant frequency (f nm ) of each mode (TM nm ) is determined by the radius r of the circular patch, and the formula is provided as follows [17]: x 11 1.841184, x 21 3.054237, a r 1 + 2h πrε r ln πr 2h + 1.7726 where c is the speed of light. According to Eqs. 1-3, the two resonant frequencies of the interested modes for the dual-band balanced BPF are simultaneously changed with various radii r. Therefore, it is impossible to independently control two passbands by just changing the radius r. To further improve the flexibility of the design, two slot perturbations on the patch are carefully introduced in the patches as shown in Figure 1 to perturb the    Figure 3. Therefore, the higher passband can be independently tuned, while the lower passband remains almost unchanged. In other words, two passbands can be flexibly controlled by simultaneously tuning the above slots and size of the patch. For more clear illustration, Figure 5 provides the effect of changing the length of the slot l 1 on the passbands. It can be seen that the first passband stays remained, while the second passband shifts to lower frequency with an increase in slot length l 1 . Herein, it is worth mentioning that, with the involvement of the introduced slot perturbations, the field distributions of the TM 11 mode (Mode 2) will be affected. As such, the resonant frequency of the TM 11 mode (Mode 2) under CM excitation will be shifted away from that of the TM 11 mode (Mode 1) under DM excitation. For better understanding of this principle, Figure 6 gives the performance of CM suppressions with and without slot perturbations on the bottom and top patches. As can be seen, due to slot perturbations, the resonant frequency of the TM 11 mode (Mode 2) is shifted from 6.0 to 4.5 GHz when compared to the design without slots. The CM suppression has been highly enhanced from 19 to 40 dB for the lower passband, while it remains above 48 dB for the second passband in both cases.
To verify this design concept, a dual-band balanced BPF that can operate at the center frequencies of f 1 5.5 GHz and f 2 7.5 GHz with bandwidths BW 1 1,000 MHz and BW 2 2,000 MHz, and in-band return loss higher than 20 dB, is designed. The corresponding design parameters are calculated as M Ⅰ Superscripts I and II denote the two passbands, respectively. Firstly, the initial value of the radius r is determined by the center frequency f 01 of the first passband and Eqs. 1-3. Secondly, the length l 1 of the slot is determined by the center frequency f 02 of the second passband. Thirdly, the final parameters of the feedline (l F ), slots (w 1 ), and internal coupling apertures (w 2 and l 2 ) are optimized to achieve a compromise for calculated external quality factors (Q ext ) and internal coupling coefficients (M ij ) of both passbands. Herein, it is worth mentioning that as the internal coupling is obtained using the same coupling apertures for both passbands, the two passband bandwidths will not be able to be independently controlled.

MEASUREMENT AND DISCUSSIONS
Based on the given specifications and design procedures discussed above, the size of the proposed dual-band balanced filter can be determined as follows: r 8.0, l 1 6.0, l 2 4.9, l F 5, w 1 0.3, and w 2 0.68 (unit: mm). A dual-band balanced filter is designed and manufactured. Simulation and measurement results are shown in Figure 7. The measured results show that the CFs are 5.5 and 7.5 GHz and the 3 dB BWs are 1.0 GHz (18%) and 2.0 GHz (26%). In the two passbands, the measured insertion loss is both less than 1.4 dB and the return loss is both higher than 22 dB. Common-mode inhibition is higher than 40 dB. Table 1 compares the proposed dual-band balanced filter with other state-of-the-art designs. The present work not only exhibits a new effective design method for a dual-band balanced patch filter but also achieves nice operation performance in terms of much wider bandwidths, independently controllable center frequencies, better return loss, competitive common-mode suppression, compact size, etc.

CONCLUSION
A new dual-band balanced patch filter has been designed and implemented in this letter. The resonant modes of circular patch TM 11 mode and TM 21 mode are explored to design the dual-band balanced filter. By wisely etching coupling apertures on the ground and introducing slots on the patch, a nice controllable

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/supplementary material, and further inquiries can be directed to the corresponding author. CMS, common-mode suppression; RL, return loss; IL, insertion loss; λ g , guided wavelength at its first center frequency.