**Ke Lu, Guang-Ming Wang, Xiong Yin, and Tong Xu**

Dual-band bandpass filters are often used in modern communications systems to isolate different operating frequency bands within the same network. Conventional filter designs of this type usually suffer from large dimensions and the need for an additional combining network for the two filters. But the dual-band bandpass filter design approach detailed in this article can be made extremely small. It employs a relatively simple structure composed of two asymmetrical separated spirals resonators (ASSRs) cascaded with a microstrip line. The dimensions can be minimized due to the fact that the ASSRs can be completely embedded in the microstrip line due to its intrinsic convoluted geometry. an analysis for this novel design will be presented, along with a pair of prototypes fabricated to validate the design approach. The two dual-band filters operate at frequencies of 1.16 and 1.84 GHz as well as at 1.80 and 2.45 GHz.

Numerous attempts have been made to miniaturize the design of dual-band bandpass filters. For example, the cross-coupled filter presented in ref. ^{1} is a relatively effective solution. In that design approach, an equal-length split-ring resonator with a tworesonant- frequency response was proposed as the basis for the filter. In that report, one cross-coupled dual-band bandpass filter was synthesized by using four resonators whose relative positions must be adjusted carefully in order to get the appropriate coupling coefficients. Unfortunately, the use of four resonators leads to degraded insertion-loss performance, making it difficult to achieve compact dimensions (especially in the transversal dimension).

In another effort, an open-loop resonator was loaded with a shunt open stub as the basis for a compact dual-band bandpass filter; as detailed in that report, three dual-band filters with improved out-of-band rejection were designed and fabricated.^{2} In these prototypes, the second passband can be controlled by tuning the position and length of the given shunt open stub. additionally, miniature planar dual-band bandpass filters were proposed in ref. ^{3} based on meandered stepped impedance resonators (SIRs). The dual-band response of such filters is determined by the primary geometrical parameters of the sIRs while the compact dimensions are achieved by combining the u-shaped SIRs with a new coupling scheme. One miniature dual-band bandpass filter was also achieved by using the combined coupling structure of short and open quarter-wavelength sIRs.^{4} In summary, the dual-band operation of these various design methods all rely on a basic cell with two-resonant modes.

The current report offers a different design method for creating a compact, dual-band bandpass filter. In this new approach, the filter is composed of two cascaded ASSRs connected by a microstrip line. These ASSRs are improved versions of the uniplanar double spiral resonant cells and symmetrical separated spirals resonators detailed in refs. 5-7. Due to its special geometry, the ASSR can be completely embedded in the microstrip feed line, which directly renders the corresponding components in a compact transversal dimension. In general, an ASSR is a bandpass cell that operates by means of electromagnetic (EM) coupling. In the present design, the first passband is determined by the inherent passband of the ASSR, while the second passband is created by the combination of the equal-impedance networks formed by the ASSRs and the connected microstrip line. Thus, the second passband can be adjusted independent of the first by using the length of the connected microstrip line as the variable parameter. This conclusion will also be verified by circuit modal analysis.

Based on this analysis, two different dual-band BPFs will be designed and fabricated to demonstrate the validity of the analysis. To the best of the authors' knowledge, because of their extremely compact transversal dimension, these dual-band bandpass filters are the narrowest filters so far reported in the literature.

**Figure 1** shows layouts of the ASSRs (a) used in the dual-band bandpass filter, as well as the proposed filter (b). Each ASSR is composed of two separated rectangular spirals which are asymmetrical to each other. Due to the convoluted geometry of the rectangular spiral, the given unit can completely embedded in a microstrip line to achieve extremely compact transversal dimension. Thus, the width of ASSR, W1, is kept constant at 4.6 mm, which is equal to the width of 50-Ω microstrip line when fabricated on RT/duroid 5880 printed-circuit-board (PCB) substrate from Rogers Corp. with relative dielectric constant of 2.2 and thickness of 1.5 mm. These material values were also used in the simulations. Because of the limits imposed by circuit fabrication tolerances (about 0.1 mm for W1 = 4.6 mm), the values used for dimensions W3 and W4 are limited. For the design of these dual-band bandpass filters, values of W3 = 0.6 mm and W4 = 0.3 mm were used in this study. According to the general model for a coupled microstrip filter presented in ref. 8, these values will support effective bandpass properties through EM coupling. This prediction will be verified by means of parametric analysis of L1, the primary adjustment parameter for the bandpass filter, with results shown in **Fig. 2**.

As shown in **Fig. 2**, an ASSR exhibits a passband which moves downward in frequency with an increase in L1. Simultaneously, the frequency selectivity of the passband is enhanced with an increase of L1. Thus, L1 can be adjusted to achieve the required passband. It is a good starting point for designing the ASSRs and the associated microwave components needed for a dualband bandpass filter.

The dual-band bandpass filter proposed in this article is synthesized by cascading two ASSRs with a microstrip line whose length is denoted as W5 (**Fig. 1**). In order to explain the given operating principle of these ASSRs clearly, **Fig. 3** shows a corresponding equivalent-circuit model. The connecting microstrip line is represented by inductance L2, while the ASSR is represented by capacitance C1 and inductance L1, along with mutual inductance Lm. It can be seen that one passband is primarily determined by the ASSR while the other passband results from a combination of inductance L2 and the equal impedance networks of the ASSRs.

Based on this circuit model, it is apparent that one of the dual passbands is determined primarily by the intrinsic passband of the ASSR and the other passband is produced by the combination of the connected microstrip line and the equalimpedance networks of the ASSRs. It is clear that passband 2 can be adjusted independently through L2. Moreover, the geometrical parameters of the ASSRs can influence both passbands. To demonstrate that this model is valid, the extraction process aimed at three different prototypes is implemented using the curving-fitting method. The geometrical parameters of the three prototypes and the corresponding center frequencies of the two passbands are listed in **Table 1**. The full-wave simulation results and the circuit simulation results are compared in **Fig. 3**, respectively. The extracted results of the lumped elements are listed in **Table 2**.

Within the given frequency ranges of interest, the full-wave EM simulations agree closely with the circuit-level simulations in all three cases. Both simulators demonstrate quite clearly the dual-band phenomenon of the ASSR-based designs, helping to validate both the circuit model and the proposed dual-band bandpass filter design approach. Comparing the values in Tables 1 and 2, it is clear that the increased value of L1 makes the two passbands move downward in frequency and affects all the elements to a great extent (cases 1 and 2). On the other hand, an increase in W5 only lowers the center frequency of the second passband, with a strong influence on L2. Obviously, the guidelines derived from the circuit model are verified once again by the given compared results. To summarize, just two geometrical parameters, L1 and W5 (**Fig. 1**), are sufficient to control the dualband operation of this filter design effectively.

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Based on this analysis, it would appear that compact dualband bandpass filters can be designed using ASSRs in conjunction with microstrip transmission lines. The optimization process only requires the adjustment of two primary geometric parameters, L1 and W5, allowing for great flexibility in tuning and optimization for these filters. To demonstrate the effectiveness of the software analysis with actual hardware, the prototype represented by Case 1 in Table 1 was fabricated and measured; this will be called prototype A for convenience. In addition, a second dual-band bandpass filter, which will be called prototype B, will also be fabricated and characteristized to further validate this design approach. This second filter was designed to operate with passbands within the DCS1800 band from 1710 to 1880 MHz and within the Industrial-Scientific-Medical (ISM) band from 2400 to 2483 MHz.

The tuning process was found to be quite effective for both filters, with the target passbands and performance levels achieved with both prototypes. **Figure 5** shows photographs of both prototype filters, with a millimeter-scale ruler as a reference for size. The prototype filters were characterized by a model ME7808A microwave vector network analyzer (VNA) from Anritsu Co., with models capable of operation through 110 GHz. Simulated and measured results for the prototype filters are shown in **Figure 6** and **Figure 7**.

As **Figure 6** and **Figure 7** show, the simulated and measured results agree well within the given frequency bands of interest. The minor discrepancies in the sets of results are due to fabrication inaccuracies and/or tolerance errors in achieving the required values for the circuit elements. Compared with the lower passband, the bandwidth of the higher passband is relatively narrow, with a considerably smaller fractional bandwidth. For prototype A, the band ratio is about 1.58 while the 3-dB fractional frequency bandwidths of the dual passbands are roughly 3% and 0.5%. The band rejection between the dual passbands is about 36 dB. For prototype B, the measured results indicate that the center frequencies of the dual passbands are about 1.81 and 2.44 GHz while the band ratio is about 1.34. The corresponding 3-dB fractional frequency bandwidths are 12.7% and 0.8%. The band rejection between the dual passbands of prototype B is about 17 dB, which is an acceptable level of isolation between the two passbands. These results show the effectiveness of this novel design method for creating dual-band bandpass filters with compact dimensions, with tuning accomplished by adjusting only two primary geometric parameters.

In summary, this use of ASSRs with standard microstrip circuitry allows the fabrication of relatively compact dual-band bandpass filters at microwave frequencies with good passband responses and adequate isolation between the passbands. The equivalent-circuit model developed for these filters appears to be accurate, with simulated results bearing close agreement with measurements on fabricated prototype filters. Any deviations between the performance expected from computer simulations and the measured performance of fabricated filters can be attributed to process variations and the difficulty in achieving the precise circuit-element values employed in the computer simulations. Nonetheless, with a growing number of applications in wireless communications where many closely placed frequency bands must coexist, this novel design approach shows great promise for creating both discrete and integrated-circuit (IC) filters in miniature sizes where dual passbands are required.

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China under Grant No. 60971118. The authors would also like to thank the China North Electronic Engineering Research Institute for fabrication of the dual-band bandpass filter prototypes.

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