Introduction
Microwave filters are essential components in all types of telecommunication systems. Trends in future applications of wireless technologies require the filters to be compact, exhibit a high selectivity with low insertion loss, and be lightweight [1]. To achieve these desired features simultaneously, considerable filter design efforts are required. Advanced small size resonators with high quality factors are also needed to overcome the problems that arise in this regard.
High-quality Q resonators are important for high performance filters, duplexers, and wireless communication circuits and systems. It is well known that a passive microstrip or microstrip-like resonator generally yields poor Q-related performance, which drastically limits its circuit applications [2]. Waveguide resonant cavities have been popular in the design of devices and circuits that require a high Q. They exhibit numerous advantages such as high-Q and high sensitivity [3]. However, their non-integrability in planar form prevents their use in low-cost systems.
The Substrate Integrated Waveguide (SIW) presents an attractive solution for the production of planar resonators due to its ease of fabrication and relatively high-Q factor. Therefore, it is of great importance in modern technology for many practical applications [4]. This technology is a good compromise between the performance of classical waveguides and planar circuits, judging from the Q values and losses. For this reason, it raised a substantial amount of research in this field over the past several years. Various SIW passive microwave components and circuits have been successfully designed, demonstrated and deployed such as directional couplers [5], phase shifters [6], diplexers [7] and antennas [8]. The unloaded Q-factor of an SIW cavity can be determined by its losses, which depend primarily on the dielectric substrate dissipation, the finite metal conductivity, and the substrate radiation leakage through the gaps [9]. In fact, this is also closely related to the size, shape, and mode of the SIW cavity. The unloaded Q factor is usually limited in this case to a few hundreds [10]–[12]. The variation of the unloaded quality factor Q of a SIW resonator by changing the substrate parameters has been studied [12]. The results show that the energy stored in the resonator is related to the substrate thickness, the dielectric permittivity, and the loss tangent. A thicker substrate provides a lower loss, and for the same thickness, the SIW resonator provides significantly higher unloaded Q than did the microstrip resonator. The Q factor reaches a maximum of 580 with a substrate with
In this paper, an alternative SIW resonator showing higher Q factor is proposed and developed. The idea is based on a periodic artificial modification of the main line material with permittivity
Design Consideration
Fig. 1 presents a basic structure of the proposed SIW cavity resonator. This figure shows the periodicity between the main line material with permittivity
Proposed SIW cavity with periodic PDSIW (artificial synthesized dielectric): a) equivalent periodic cavity, b) perspective view with periodic cavity, c) unit cell.
The loaded quality factor (\begin{equation} Q_{l} =\frac {f_{0} }{\Delta f_{3dB}} \end{equation}
\begin{equation} Q_{e} =\frac {Q_{l} }{10^{-IL / {20}}} \end{equation}
\begin{equation} \frac {1}{Q_{u} }=\frac {1}{Q_{l} }-\frac {1}{Q_{e}} \end{equation}
In addition to dielectric and conductor losses, leakage loss may be present. However, the latter is nearly negligible with the appropriate selection of the size and spacing of the metallic via-holes or posts [9]. The conductor loss includes the contributions of metallic via-hole or post arrays as well as that of bottom and top metal surfaces. Since the substrate thickness is much smaller than the equivalent width or length of SIW cavity resonators and transmission lines, the loss caused by the metallic via arrays is negligible in the total loss for most cases. Since the propagation characteristics of SIW are quite similar to those of a classical rectangular waveguide, closed-form attenuation constant formulas of an SIW transmission line can be used to model the proposed periodic structure in terms of loss and other related parameters. The resonant frequency is evaluated by using a rectangular waveguide model for SIW cavities.
Air holes are used to decrease the substrate permittivity from
The waveguide dielectric loss can be calculated as an averaged function weighted by the drilled and undrilled surface in a periodic cell as follows:\begin{equation} \tan \delta =\frac {\tan \delta _{0} (\varepsilon _{r2} -1)\ast \varepsilon _{r1} }{(\varepsilon _{r1} -1)\ast \varepsilon _{r2} } \end{equation}
This assumption is valid in the case of total material removal (
To define the optimized parameters, a periodically dielectric slab of different length (
Fig. 3 suggests that the Q-factor increases as
The Q factor for a circuit is defined as the energy stored in the resonator and it is related to the power loss per oscillation period. Fig. 5 shows a comparison between the dispersion characteristics of the SIW waveguide and those of the periodic SIW/PDSIW waveguide with
E and H field’s distributions in the resonator: (a) With dielectric loading, (b) Without dielectric loading.
The unloaded Q-factor is also determined by the resonator conductor and dielectric losses. To estimate this factor, the different losses mechanisms effects are estimated. The slab is substituted by PDSIW as illustrated in Fig. 1(c); the radiation effect by the air holes in the drilled SIW has been studied. Fig. 7 presents the results of this study and concludes that radiation losses are not significant with air hole diameters of 0.05 mm, which corresponds to the first Q-factor max spike (
Simulated Q, reduction factor, radiation loss and metallic loss in function of via diameter.
An unloaded Q factor of 815 is achievable with the proposed method. The effect of this enhancement on the filter performance should be studied further.
Filter Structure
Fig. 8 shows the horizontal cross section of the proposed filter with three-cavity resonators. In this figure, separate rows of metallic via slots are used to synthesize the three rectangular cavities.
The insertion loss IL within the bandpass filter depends on three principal factors: the unloaded quality factor of resonators \begin{equation} IL(f_{0} )\approx 4.343\frac {N}{Q_{u} \frac {\Delta f}{f_{0}}} \end{equation}
The optimal dimensions of the simulated filter of order 3 with dielectric loading (according to the parameters annotation in Fig. 8) are:
To demonstrate the effectiveness of this design, the insertions losses of filters without dielectric loading of orders 3 and 4 and of filter with dielectric loading of order 4 are compared in Fig. 9. This figure also shows the comparison between the return losses. For the filter with three-cavity SIW without dielectric loading, the center frequency is 10.05 GHz, bandwidth
Simulated and Measured Results
Following a parametric optimization through Ansoft HFSS, a cavity is designed and fabricated to validate the proposed concept and is compared to the simulated results. The optimized dimensions of the fabricated cavity shown in Fig. 10 are as follows:
Fig. 11 shows the simulated and measured S parameters of the proposed resonator. A good agreement is observed between the simulated and experimental values. The resonance frequency of the SIW cavity is shifted to 9.97 GHz with respect to the simulated value of 10 GHz and the measured insertion loss is higher than the simulated counterpart. The measured unloaded Q-factor of the cavity is higher than 800, as expected.
The measured results show a loaded Q factor of 60 and unloaded Q factor of 815 with the dielectric loaded SIW resonator. It can be observed that in Table 1, the unloaded Q-factor of the proposed SIW resonator is greatly improved compared with same cavity without dielectric loading (with the same loaded Q factor of 60), with an increase in size of approximately 5%. Compared with the same type of SIW cavities reported in previous studies over the same frequency range, the Q-factor of the proposed SIW resonator is greatly improved. However, the Q-factor is still higher in the standard rectangular resonator in which the height is larger.
The proposed filter with three cavities is designed using the same substrate of resonator cavity. The optimized dimensions of the fabricated filter shown in Fig. 12, were presented in the simulation section. The simulated and measured responses of the proposed filter are shown in Fig. 13. A good agreement is observed between the simulated and experimental values.
As shown in Fig. 13, the center frequency for the simulated results is 9.98 GHz, with a difference of approximately 0.01 for the measured results (9.99 GHz). The bandwidth
Figure 14, presents the simulated results of the group delay of S21 for the two structures (standard SIW, PDSIW). The first structure attains a maximum group delay of 0.19 ns, and the minimum group delay of 0.08 ns. About the proposed design (PDSIW) the maximum group delay is less than 0.2 ns and the minimum is 0.09 ns, throughout the passband. In all this duration, the proposed design present a phase behavior of the signal remains linear, which is very smooth for the microwave filter. Comparison of the group delay of S21 with other types of filters is not available here because most of the filters presented in references haven’t been reported.
Conclusion
In this paper, a synthesized resonator based on a hybrid structure of substrate integrated waveguide and periodically drilled substrate integrated waveguide is developed and used to implement a filter. The operating principle and design procedure have been discussed. The resonator and filter have been designed, fabricated and measured to verify the proposed scheme. The periodicity is able to increase the stored energy, and it has been shown that the Q-factor can be increased. An optimal ratio of 0.9 between the main waveguide and the artificially synthesized substrates permittivity with an optimal periodicity of