Compact Self-Packaged Dual-Band Filter Using Multilayer Liquid Crystal Polymer Technology

A compact self-packaged dual-band filter structure using multilayer liquid crystal polymer technology is presented in this paper. The frequency and bandwidth of each passband can be more conveniently controlled by means of vertically embedded elements, i.e., metal patches, placed above the coupled folded multi-stepped impedance resonators. The packaged solution is connected to the outer environment through a coplanar waveguide that allows flip-chip interconnection to a host board. The proposed design is validated with the fabrication of two prototypes. The measured results show good agreement with the simulations.


I. INTRODUCTION
A S wireless communications penetrate more and more in our daily lives, different systems and transmission technologies have to be developed to fit them properly. Mobile phones or laptops, as an example, often integrate technologies like WiFi, Bluetooth, GSM, or GPS. Each of these services has receivers/transmitters operating in different frequencies that have to be accommodated in a small, portable device. Multiband radio frontends are often employed for this matter, and, here, multiband filters play a key role.
Extensive work has been carried recently in the field of dual-band filters [1]- [16], and different approaches on how to produce the passbands have been reported. The most common approach is to employ multimode resonators and locate the passbands at the resonant frequencies [2], [3], [5]- [7], [11], [12]. The resonant modes are split by means of inter-resonator coupling in order to control the bandwidth. The separation between the bands depends on the modes of the resonator, placing some design constraints. Alternatively, in [10], only one ring resonator is used to produce the two passbands. In this case the split of each resonant mode is obtained by a pair of open-circuited stubs attached to the resonator. Even though it has the advantage of using only one resonator, it also has the limitations of a small frequency ratio between the passbands. In the other hand, the use of four resonators is reported in [8], [9]. Additionally, methods for producing each band independently, combining two bandpass filters, have been covered in [4], [14]. Finally, a method based on successive transformations from a lowpass prototype is presented in [1], and a semi-lumped element approach cascading several bandpass cells in reported in [13]. These methods simplify the design process usually at the cost of increased footprint.
The multilayer structure proposed in this work ( Fig. 1) consists of four metal layers. On the central layer, two coupled dual-mode resonators are placed next to each other in a mirrored disposition. The coupling between them is produced first by this proximity between them and, second, by a pair of metal patches , placed on the layer above them, that controls the coupling coefficients for each of the passbands. Finally, the coupling between the resonators and the input/output ports is achieved by a second pair of patches whose area determines the external quality factor for each band. The top and bottom layers are the ground planes, also providing electromagnetic shielding to the filter. Furthermore, the top layer contains a pair of coplanar waveguide (CPW) lines that connect the filter to the external environment through a vertical via transition. The whole packaged filter is implemented using liquid crystal polymer (LCP) material.
The remainder of this paper is structured as follows. In Section II, the critical design parameters of the proposed filter are described and analyzed. Section III explains the design process of the discussed dual-band filter, following two design examples and the results after fabrication in Section IV. Finally, conclusions are presented in Section V.

A. Dual-Mode Resonator
The essential resonator deployed in the dual-band filter design can be seen as a folded multi-stepped impedance resonator (FMSIR) with four sections alternating high and low This alternating structure allows for a compact layout when folding two sections over the other two [as depicted in Fig. 2 by adding extra length to some of the sections . Spurious coupling is expected when folding the resonator in such a manner between adjacent lines, as it is stronger where the current density is higher and the distance between them smaller. However, at FMSIR resonant frequencies, most of the current density is accumulated at the high-impedance sections, which are always next to a low-impedance section, with low current density [cf. (8)]. This property makes the coupling between adjacent lines negligible, avoiding significant interaction even if the gap between the lines is small. Hence, the width of the slotline can be reduced down to fabrication tolerances without having a direct impact on the resonant frequencies. Variations to the resonant frequencies respect to the ideal model [ Fig. 2(a)] are mainly due to the length of the sections [ Fig. 2(b)] and larger as this length increases. Since is directly related to , it is desirable to design them to be as small as possible.
Conventional quarter-wavelength resonators with uniform impedance (UIR) resonate at integer odd multiples of the fundamental frequency , i.e., with It is well known that a quarter-wavelength SIR (single step) is able to shift the first harmonic frequency away from depending on the impedance ratio of its two sections [17]. In this study, it will be demonstrated how the FMSIR enhances this property by offering more control over the positioning of the second harmonic . Ignoring the effects of the step discontinuities and the increased lengths of the sections with , the input impedance , looking into the open end of the resonator, can be determined as (1) where is the impedance ratio between the lines. From (1), the resonance condition is described as (2) By defining the line length ratio as , the resonator's behavior can be fully determined according to , and the total electrical length of the resonator described in terms of its total electrical length as follows: ( For comparison, the normalized length of the unfolded resonator with respect of that of a conventional UIR is defined as (4) Fig. 3 shows for several combinations of and . Note that, when , the FMSIR becomes an UIR and the lengths are equal. Also, special cases are and , corresponding to single SIR with both sections equal in length and inverted . For the purpose of designing a dual-band filter, the second passband will be determined by the frequency of the first-harmonic mode . In Fig. 4, it can be observed how can be controlled depending on the design parameters and . For , the most determining parameter is , while for both and are equally relevant. Another conclusion from Fig. 4 is that, when , the frequency variation is less sensitive to impedance variations, and this can be used as an advantage in the fabrication process, especially when dealing with etching tolerances.
Providing a wide stopband after the second passband is also a desirable property in a dual-band filter. This width is mainly determined by how far in frequency the second harmonic can  be pushed away from the first harmonic. Fig. 5 shows that, for , the maximum bandwidth is obtained for , while for the maximum is for .

B. I/O Coupling
The resonator is coupled to the input/output ports through the capacitance created by two metal patches placed above the lowimpedance sections of the resonator (Fig. 6). The amount of coupling is determined by the capacitance created between the metal patches, as a parallel-plates capacitor (5) where 8.854 10 F/m, is the relative dielectric constant of the substrate, is the area of the parallel plates, and is the separation between them. In this case, is determined by the area of or and by the thickness of the dielectric layer between the resonator and the I/O coupling layer. It is important to note that (5) is only valid for low frequencies. The actual value of the capacitance created between the patches and the resonator will grow as frequency is increased until the capacitor's self-resonant frequency is reached. From that point, modelling the coupling as a pair of capacitors is not possible.
In general, increasing the size of the patches will increase the coupling and hence reduce the external quality factor . However, the variation of each patch will affect both bands, meaning that the value of the set is a function of both coupling patches, i.e., and (cf. Figs. 11 and 15). is extracted using a technique described in [18]. When loading the FMSIR with and , a shift of the resonant modes towards lower frequencies is expected. As the capacitance is increased, the loaded resonant modes approach those of the unloaded FMSIR.

C. Inter-Resonator Coupling
In order to produce the two desired passbands, proper couplings need to be facilitated. This is achieved by two different means: by the proximity of the resonators on the same layer and by two metal patches placed on the layer above the resonators along the symmetry plane. The individual equivalent patches for each resonator are joined together to form one single piece of metal [ Fig. 7(b)].
The coupling coefficient between the resonators may be electric (or capacitive) or magnetic (or inductive), being always a mix of both with one of them being dominant. To determine the between two resonators, the circuit is analyzed by separately inserting a magnetic and an electric wall in the plane of symmetry. These two separate experiments provide two different resonant frequencies: and for electric and magnetic walls, respectively. From [19] and [20], it can be found that, if , the coupling is predominantly magnetic and,  if , it is predominantly electric. The effective is calculated by (6) The coupling produced by the proximity of the resonators is predominantly magnetic and is stronger as the separation (GAP) is reduced. Fabrication tolerances place a limitation in the amount of coupling that can be obtained. Furthermore, by solely modifying the gap it is not possible to control independently for each band.
Independent control over the coupling of each band separately comes from the coupling patches and . These two patches create the capacitances and , respectively [ Fig. 7(a)] contributing to and differently. This property makes tuning for each band possible. The type of coupling they produce is also different due to their positioning on the symmetry line. From Fig. 8, it is seen how the current density is higher in the high-impedance sections, and minimum at the other end of the symmetry line. Coupling between the high-density current sections contribute towards magnetic coupling, and low-density current sections, towards electric coupling. Hence, by placing at the left end of the symmetry line it will be adding electric coupling, in different amount, to and . As the position of is shifted towards the other end, its contribution to the coupling progressively turns into magnetic. Similarly, from , the contribution is initially magnetic when placed at the rightmost of the symmetry line, turning into electric as shifted away from that point.
In general, the coupling will be stronger as their area of and is increased. However, since the effective is a mix of both types of coupling, it could happen that they cancel each other when electric and magnetic coupling are equally strong. Getting the desired and is a combination of tuning GAP, areas of and , and their position along the symmetry line.

D. Transmission Zeros (TZs) Mechanism of Generation
Several TZs are excited due to the different resonating modes of the FMSIR. A low-frequency TZ is generated by the resonance of the SIR formed by the transmission-line sections C and D [ Fig. 2(a)]. This mode is excited when section B acts as a virtual connection to ground, making the aforementioned sections C and D behave as a SIR. This mode will typically show between the two passbands. Moreover, a second resonant mode from this structure is also excited in the stopband. The frequencies for these modes can be calculated using the equations for SIR found in [17]. These two TZs are split into two pairs when inter-resonator coupling is put in place, and further control over them can be made by specifically coupling the sections C and D of both resonator. In this case, this is achieved by adding the capacitor [ Fig. 7(a)]. Depending on the position of the pair and , two modes are excited. From the I/O patches looking into sections B and C, the resultant section behaves as an open-ended UIR with length . This section anti-resonates at odd multiples of . As previously discussed, the inter-resonator coupling is also able to split this TZ in two.

E. Packaging
Following the work carried in [21], the filter structure is enclosed within two ground planes in a stripline configuration. Additionally, a conductive paste is applied in the surrounding walls in order to achieve a full electromagnetic shielding.
The filter is connected the outer environment by means of a CPW, printed on one of the ground planes, and via transition (Fig. 1). This kind of packaging allows easy interconnection of the device to a hosting board in a flip-chip manner, as well as allowing easy matching of the input impedance by modifying the width and gap in the CPW.

III. DESIGN PROCEDURE
Due to the structure being so compact, the designs of resonator, I/O coupling and inter-resonator coupling are not really independent. Nevertheless, the design procedure described below can be useful.
First, depending on the substrate to be used, fix for the design. Then, depending on the required fundamental frequency, the length for a UIR is calculated using (7) Fig. 9. Low-pass prototype filter.

Once
is computed, from Fig. 4 obtain the value for that matches the required ratio and . With this value, from Fig. 3 obtain the value for to calculate the length of the MSIR, and physical length for and , since is already known. Finally, is calculated as plus .
With the resonator tuned for , the I/O patches have to be put in place for the required for each band. While tuning the I/O patches, the resonant frequencies will be affected and have to be retuned accordingly, as discussed in Section II-B.
Values for and are calculated based on a low-pass, second-order Chebyshev prototype ( Fig. 9) with normalized parameters , and for a return loss of 20 dB. These parameters can be calculated by [18] (8) (9) where and are the input and output external quality factors, is the coupling coefficient, and is the fractional ripple bandwidth. Index represents the band. Even though calculations are intended for a single-band, they can be applied separately for each band, since both external quality factors and coupling coefficient is independently controlled for each band. Finally, inter-resonator coupling patches are included to provide the required coupling coefficient.

IV. PROTOTYPE DESIGN AND RESULTS
In order to validate the previous analysis and parameter extraction, two prototypes are designed and fabricated following the same process. LCP substrate with the same layer distribution (Fig. 10) and fabrication technique is also applied for both designs.
For the given layer distribution and thickness of substrate (0.4 mm) the high and low impedance have a width of 0.2 and 1.6 mm, respectively, yielding 48 and 12 . These dimensions are chosen bearing in mind etching tolerances and compactness, and so is , which is fixed to 0.2 mm. To reduce the number of via holes required in the circuit, both resonators share the same grounding via [cf. Figs. 13(a) and 17(a)]. The patch for the ground via takes away some length from the line section A, producing some frequency shifting that needs to be compensated accordingly.

A. Design I
The chosen center frequencies/FBW are 1.2 GHz/10% and 2.4 GHz/8%. As described in the previous section, in order to find the dimensions for the resonator, first for 1.2 GHz is calculated from (7), which is 36.08 mm. From Figs. 4 and 3, the values and are obtained, so . Finally, including mm, the final length of the FMSIR is 14.63 mm. With the help of an EM simulator [22], the FMSIR has to be tuned to compensate for the effects of impedance steps and extra lengths in the lines , with changing to 14.35 mm and to 3.2. Furthermore, in order to accommodate a patch for the common ground via, section A is reduced by 0.8 mm, forcing further modifications to the resonator.
From (8), the values and are obtained. Following the discussion from the previous section, from Fig. 11, the point where the curve crosses shows the required values for and : 6 mm and 0.7 mm , respectively, with mm. As previously discussed, the inclusion of this two patches modifies the resonant frequencies, as well as the use of a common ground via, so at this stage, the dimensions of the resonator have to be adjusted to compensate this effect and match the desired center frequencies, which are 1.2 and 2.4 GHz in this case. The final value for is set to 12.6 mm and , to 1.47 (ignoring the length reduction in line section A to include the grounding via patch). Regarding , from (9) the values and are calculated. As in the previous step, the dimensions of and can be obtained from Fig. 12, being the point where both curves cut each other, i.e., 0.6 mm and 0.4 mm .
Once the sizes for the resonators and patches are fixed, the stopband can be expanded by moving the coupling patches along the symmetry plane. As the structure is so compact, additional coupling paths are generated, producing additional transmission zeros. However, the values for the coupling patches would require further tuning. The completed design and dimensions are shown in Fig. 13. Furthermore, the physical  realization for (see Sections II-B and II-C) for splitting the inter-band TZ is also shown.
Results (Fig. 14) show good agreement between the simulated and measured results. It is demonstrated how the in-band  second-order TZ splits into two TZ, with a separation proportional to the capacitance . A slight shift in the second band's center frequency can be appreciated, due to small over-compression of the 25 m core-film layer.
The prototype has been manufactured in LCP substrate with a dielectric constant of 3, following a standard fabrication process. The layer distribution is shown in Fig. 10. Results obtained show a very good agreement with the simulations (Fig. 14) on a compact design of 15.8 10.2 0.4 mm , packaging included.

B. Design II
The same design routine as in the previous section is followed, in this case aiming at 2.4/5 GHz WiFi bands with FBW's of 8% and 5%, maintaining the same layer distribution and . In this case, and are changed to 6 mm and 1.57, respectively, and the width for the ground via patch is 0.6 mm.
Required values for and are 8.3 and 13.3 from (8), corresponding to and calculated as 0.95 and 0.3 mm (Fig. 15). Regarding the coupling coefficient, required values of and correspond to 0.15 mm and 0.16 mm . As discussed for the previous design, further improvement can be obtained for the stopband by adjusting the position of the patches, and eventually, their sizes. The final design has a footprint of 7.5 11.2 0.4 mm , including the self-packaging. A summary of the dimensions is shown in Fig. 17 and the results in Fig. 18.

V. CONCLUSION
In this paper, a novel compact structure for designing selfpackaged dual-band filters has been presented. This structure exhibits flexibility in terms of choosing the spacing between the bands by modifying the parameters of the two coupled dualmode FMSIR. The coupling coefficient for each band can be controlled independently by means of the areas of a pair of conductor patches over the resonators. Finally, the external quality factor is controlled by a second set of conductor patches. For the demonstration, two different designs have been presented. This type of packaged dual-band filter exhibits high rejection between the two passbands and a wide upper stopband. The validity of this approach has also been demonstrated by fabricating two prototypes. The results obtained show good agreement with the simulation results. Comparison to other reported filters is summarized in Table I.