An independently reconfigurable dual-mode dual-band substrate integrated waveguide filter

In this paper, a novel perturbation approach for implementing the independently reconfigurable dual-mode dual-band substrate integrated waveguide (SIW) filter is proposed. Dual-frequency manipulation is achieved by adding perturbation via-holes (the first variable) and changing the lengths of the interference slot (the second variable) in each cavity. The independent control of the upper passband only depends on the second variable while the lower passband is independently tuned by combining the two variables. Using such a design method, a two-cavity dual-band SIW filter is designed and experimentally assessed with four via-holes and an interference slot in each cavity. The dual-band filter not only has a frequency ratio (fR) ranging from 1.14 to 1.58 but also can be considered as a single passband one with a tunable range of 40.5% from 1.26 GHz to 2.12 GHz. The scattering parameters |S11| and |S21| are in the range of -10.72 dB to -37.17 dB and -3.67 dB to -7.22 dB in the operating dual bands, respectively. All the simulated and measured results show an acceptable agreement with the predicted data.


Introduction
Multiband bandpass filters are of interest in many wireless applications for interference reduction in a two-way radio system, different frequency bands utilization in the congested spectrum of electromagnetic waves, and compatibility of wireless devices with different standards. Normally, integrating a bank of fixed-frequency filters in a wireless system will definitely add to the complexity. This factor inspires developing filters that can not only simultaneously work at multiple bands but also dynamically tune the operating bands if needed. Recent advancements in filter technology, tunable/reconfigurable bandpass filters have gained a remarkable research interest with reducing complexity/loss in signal routing and meeting the present requirements of system size, complexity and cost reduction.
Recently, some traditional materials are used to implement filters through different theoretical techniques. Besides, there are new materials which can be operated at microwave frequency band such as graphene [1][2] and topological insulator: Bi2Te3 [3]. Unlike traditional a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 substrates with metal plated on its surface, the topological insulator achieves conductivity by itself, while the devices about the topological insulator lack practical demonstrations. So far a few of tunable/reconfigurable filters with various materials and technologies have been realized to satisfy the increasing demands in multiband transceiver architectures for modern multistandard communication systems. The filters are mainly designed in these theories including graphene [2], substrate integrated waveguide (SIW) [4][5][6][7], coplanar waveguide (CPW) [8][9], microstrip [10][11][12], and cavity [13][14]. In [2,4,5,8,9,13], tunable passband filters are all designed based on a passband. Thus they cannot be operated at multiple passband simultaneously. The filters with two passbands in [6] and [10] are generated by dual modes, the lower passband can be reconfigurable without affecting the other one, but the upper passband cannot be tuned independently. Excitedly, with the continuous exploration of the researchers, in [7], [11][12] and [14], the lower and upper passbands of the designed filters can be tuned and are relatively independent of each other. Due to the advantages of the SIW technology such as easy fabrication, simple integration with active devices, higher quality factor, a few of SIW filters with single passband tunable have been proposed. However, few SIW filters with dual bands tuned independently have been put forward.
In this paper, we propose a novel simple approach, adding perturbation via-holes and changing the lengths of the interference slots, for designing a single-layer dual-mode dualband independently reconfigurable SIW filter. The approach, operating the electromagnetic distributions of one of two resonant modes (the TE 101 and the TE 102 modes) of the structure, are exploited to change its resonant frequency. In the following sections we will first give the traditional theoretical design of dual-mode dual-band SIW filter, and the influences of electromagnetic distributions of two resonate modes are analyzed for different disturbances on every original SIW structure. Second, put forward a new perturbation method and a set of dualmode dual-band SIW structures with different numbers of via-holes and lengths of the interference slots are applied to validate the design methodology. Finally, the dual-mode dual-band SIW filter with four via-holes and a fixed size of interference slot on each cavity is presented. The upper passband can be tuned individually only depending on the changed lengths of the interference slots, while the independent control of the lower passband needs to be combined the changed lengths of the interference slots and different numbers of via-holes. It can be found that this proposed SIW filter has a number of attractive features, which are: 1) flexible independently-reconfigurable dual bands; 2) simple via-holes and slots without any complex components; 3) easy integration with single-layer structure; 4) low-cost fabrication using the printed circuit board technology. structure of a single square SIW cavity directly excited by two 50 O microstrip feeding lines and the bottom of the used substrate is constructed completely by a metal. w m is the width of the microstrip feeding lines and h is the thickness of the chosen substrate. L c is the length of the single square cavity. d w is the diameter of metallized via holes. s w is the center spacing between two adjacent metallized via holes. To achieve dual-mode dualband SIW filter with the lower and the upper frequency generated by the TE 101 and the TE 102 modes, respectively, the initial sizes in Fig 1 can be calculated by the following equation [15]:

Theoretical design and modes analysis
Where m and n are the half-wave numbers propagating along the x-axis and the z-axis, respectively, f 101 and f 102 are the resonant frequencies of the TE 101 and the TE 102 modes, respectively, c 0 is the light velocity in vacuum, ε r is the relative dielectric constant of the chosen substrate. Note that the following conditions [16] should be considered to avoid dispersion loss of typical SIW structures: When d w /L c increases, a smaller s w /d w is needed.  The whole bottom and the top yellow area of the cavity is constructed by metal. L c is the length of the square SIW cavity, d w is the diameter of metallized via holes, s w is the center spacing between two adjacent metallized via holes. This SIW cavity is excited by two 50 Ω microstrip feeding lines, h is the thickness of a used substrate, w m is the width of the microstrip line. It is necessary to take appropriate values for s w , d w , and L c to avoid dispersion loss of typical SIW structure.
affect the electromagnetic distribution of the TE 101 mode. However, changing the interference slot to four perturbation via-holes in the same place, the situation is exactly the opposite. Despite that the TE 102 and the TE 201 modes are degenerate modes in a square cavity, the TE 201 mode is suppressed by the additional interference slot and perturbation via-holes.
The foregoing conclusions have been drawn from the papers [6] and [17]. Based on the conclusions, an inspiration is obtained that combining the additional interference slots and perturbation via-holes to achieve the tunable dual bands independently. However, there still exists an unsolved problem that it is difficult to achieve tunable dual bands independently when both perturbation via-holes and an interference slot are in the middle of the cavity at the same time. Thus the locations of the perturbation via-holes are changed symmetrically on both sides of the vertical bisector of each cavity. In contrast with Fig 2a and 2b, the perturbation via-holes symmetrically on both sides of the vertical bisector of each cavity have effects on the electromagnetic distributions of the TE 101 and the TE 102 modes in Fig 2g  and 2h. In addition, note that the influence on the TE 101 mode is greater than that on the TE 102 mode in Fig 2g and 2h.
In order to achieve independent controllable dual bands, a new way of interference needs to be found, which only affects the electromagnetic distribution of the TE 101 mode without affecting that of the TE 102 mode. Comparing Fig 2d with Fig 2h, it is found that the effects of the perturbation via-holes and an interference slot on the electromagnetic distribution of the TE 102 mode are reversed. Therefore, the effects of the specific number of perturbation viaholes and the specific length of an interference slot on the electromagnetic distribution of the TE 102 mode can be offset from each other. Besides, an interference slot has no influence on the electromagnetic distribution of the TE 101 mode. Therefore, the upper frequency generated by the resonate mode TE 102 will not be affected. Then the lower passband generated by the resonate mode TE 101 can be independently tuned by combining different additional numbers of perturbation via-holes and different lengths of the interference slots, and the upper passband can be independently tuned only by changing the lengths of the interference slots.
Inspired by the analysis and comparison of electromagnetic distributions in Fig 2, a twocavity dual-band SIW filter with four perturbation via-holes and an interference slot in each cavity is showed in    Fig 6c. Fig 6d and 6e illustrate the simulated and measured scattering-parameters of the dual-mode dual-band SIW filter in Fig 3 with two perturbation via-holes and different lengths of the interference slot in each cavity, respectively. One of the related fabricated PCBs is displayed in Fig 6f. The substrates of all the fabricated PCBs are the same as the simulated ones in Fig 2, except that the metal of the simulated substrates are all replaced by 1/2oz thick copper in measured ones.
When the number of perturbation holes and the length of the interference slot increase from 2 to 6 and 5 mm to 12 mm, respectively, the lower frequency shifts from 5.05 GHz to 5.48 GHz, meanwhile, the upper frequency keeps at 6.22 GHz. When the number of perturbation via-holes maintains 2 and the length of the interference slot increases from 4.8 mm to 13.8 mm, the upper frequency shifts from 6.26 GHz to 5.90 GHz, meanwhile, the lower frequency keeps at 5.06 GHz. Obviously, to control the lower resonant frequency shift individually, the length of the interference slot grows longer as the number of perturbation via-holes increases. To independently tune the upper resonant frequency, only the length of the interference slot needs to be changed.

Results
The lower frequency can be tuned independently on condition that the perturbation holes are variable. Hence, to prevent perturbing holes linking the top metal layer directly, four perturbing holes of each cavity in However, the actual production may lead to a slight difference in the length (Vslot L ), width (Vslot w ) of the connected slots and the width (slot w ) of the interference slots. The interference slot at perpendicular bisector located on the z-axis in each cavity is equivalent to open-circuited perturbation and then the changes in slot w may result in shifts in the upper frequency. In Fig 2, the perturbation via holes symmetrically on both sides of the vertical bisector of each cavity influence the electromagnetic distributions of the TE 101 and TE 102 modes. We need to measure whether a small range of variations in Vslot L , Vslot w and slot w cause a shift in the two passband frequencies.   An independently reconfigurable dual-mode dual-band substrate integrated waveguide filter Note that '0' and '1' are considered to be disconnected and connected with perturbation holes, respectively. Fig 10a and 10c illustrate the simulated scattering parameters of the dual-mode dual-band independently reconfigurable SIW filter in Fig 9. Besides, Fig 10b and 10d illustrate the corresponding measured scattering parameters. Fig 10a and 10b show that the lower frequency is tunable while the upper frequency is unchanging . Fig 10c and 10d show that the upper frequency is tunable while the lower frequency is constant.
When the state varies from 00 to 11, and the corresponding length of the interference slot (slot L ) varies from 5.0 mm to 28 mm, the lower frequency (the resonant frequency of the TE 101 mode) is tuned with a range of 29.1% from 1.26 GHz to 1.75 GHz. Whereas the upper frequency (the resonant frequency of the TE 102 mode) has an offset of 0.50% at around 1.99 GHz. When the state keeps for 11 with the length of the interference slot (slot L ) varying from 5.0 mm to 28 mm, the upper frequency is tuned from 1.99 GHz to 2.12 GHz with a range of 6.5%, while the lower frequency is at around 1.75 GHz with an offset of 0.57%. It is shown that f R ranges from 1.14 to 1.58. An independently reconfigurable dual-mode dual-band substrate integrated waveguide filter Note that the state 11 and slot L = 28 mm are both applied in Fig 10b and 10d, thus, the independently reconfigurable dual-band SIW filter can be considered as a single passband one with a tunable range of 50.9% from 1.26 GHz to 2.12 GHz. The return loss |S 11 | and the insert loss |S 21 | are in the range of -10.72 dB to -37.17 dB and -3.67 dB to -7.22dB in the operating dual bands, respectively. Errors in processing and the loss of substrate may affect the ideal performance.

Discussion
In this paper, a novel perturbation approach for implementation of the dual-mode dual-band independently SIW filter is proposed by adding different numbers of perturbation via-holes and changing the lengths of the interference slots. The perturbation via-holes symmetrically on both sides of the vertical bisector of each cavity have effects on the electromagnetic distributions of the TE 101 and TE 102 modes. However, the interference slot on the vertical line of each cavity only influences the TE 102 mode. Thus, the lower passband is independently tuned with a range of 29.1% by combining the two variables, while the independent tunable range of 6.5% to the upper passband can be achieved only by the second variable. Besides, it can also be used An independently reconfigurable dual-mode dual-band substrate integrated waveguide filter as a single passband tunable filter with a wide range of 50.9%. The wide tuning range makes the proposed dual-mode dual-band SIW filter of the modern multiband and multistandard attractive in adaptable and cognitive radio systems.