диафрагмированные волноводные фильтры / b0b57036-0482-48fc-8baa-0683bd585b25

Fig. 29. Fabricated coupler. (a) Top-view photograph. (b) X-ray photograph of inside of LTCC. The X-ray photograph has been taken from downside to show the coupling apertures.

Fig. 30. Simulation and measurement results of V-LIW coupler.

results of the optimized coupler are illustrated in Fig. 30. As it can be seen from this figure, the designed coupler provides about 20-dB (22 dB measured) coupling from 58 to 62 GHz, and the return loss and isolation in this band are better than 17 dB (13.3 dB measured) and 32.5 dB (25 dB measured), respectively. It should be noted that the level of coupling is proportional to the size/number of the side apertures. In the vertical arrangement, these parameters are limited by the thickness of the LTCC stack. The more layers we use or the higher frequency we go to, the higher the maximum achievable coupling level becomes.

C. V-LIW Filter

The SIW has been widely used in the design of mmwave directed-coupled-cavity filters [43]–[47]. In these filters, the cavity resonators are usually coupled to each other using iris post walls [48] or apertures in case cavities are located in different layers [49].

Fig. 31. Geometry of V-LIW fifth-order W-band filter and sample layers.

In order to show the suitability of the proposed V-LIW in filter realization, we have designed two filters: a simple fifth-order fully V-LIW direct-coupled-resonator filter at W-band and also a ninth-order filter at V-band which has the 90◦ bend and transition to CPW.

1) Fifth-Order W-Band Chebyshev Filter: The geometry of the designed filter based on V-LIW is illustrated in Fig. 31. It is composed of five cavity resonators in a row. These cavities are coupled by iris discontinuities which are formed by printed metals. The design parameters of this filter are the length of cavities (li) and irises’ opening length (di). In order to determine these parameters, a method that is a combination of the methods in [50] and [51] has been used. The design procedure is quite straightforward and it can be summarized in the following steps.

Step 1: Solve the following equation to determine the midband guided wavelength λ0:

where λgl and λgh are the guided wavelength at lower and upper cutoff frequencies, respectively.

Step 2: Find the normalized iris reactances at λg0 by

where n is the order of the filter, gi is Chebyshev’s low-pass ith element [51], and L is defined by

in which ω is the passband edge of the prototype low-pass filter.

Step 3: Determine the length of cavity resonators (lci ) by

ISAPOUR AND KOUKI: V-LIW AND TRANSITIONS FOR mm-WAVE APPLICATIONS

Step 4: Obtain the iris’s opening length (di ). This is accomplished by finding di for which the following equation provides us the same Xi as in Step 2 [52]:

879

TABLE III

PARAMETERS OF W-BAND V-LIW FILTER FROM

THE THEORETICAL METHOD

TABLE IV

V-LIW OPTIMIZED DIMENSIONS AND RELATIVE

ERRORS TO THE THEORETICAL METHOD

where α is sin(π d/2a), β is cos(π d/2a), and F(α) and E(α) are complete elliptic integrals of the first and second kinds, respectively.

The design procedure is completed in Step 4; however, in most cases, (11) leads to cavity lengths that are not possible to realize by a discrete number of layers. To address this problem, we assign the closest feasible thickness as the cavity length and then modify the correspondent cavity width to keep resonance frequency the same at each resonator using the following equation:

where aci is the width of ith cavity.

This procedure has been used to design a filter with an operation bandwidth from 87 to 98 GHz and the passband ripples of 0.005 dB. Ferro A6M LTCC sheets with the dielectric constant of 6.21 and thickness of 93.98 μm have been utilized. An initial width of 960 μm has been chosen for the first and last sections of the V-LIW filter to be consistent with the one in V-LIW transition for W-band. Table III includes all parameters have been calculated following steps in the design procedure.

The designed filter is then simulated and optimized using ANSYS HFSS. The optimized values of V-LIW width and iris’ opening length along with associated errors are listed in Table IV. It should be noted that the error in the calculation of di is mainly due to the fact that (12) has been found for discontinuities between cavities with identical width; on the other hand, in our case, as we discussed earlier, we have modified the width of V-LIW. Fig. 32 shows the simulation results of optimized W-band filter.

2) Ninth-Order V-Band Chebyshev Filter: The previous filter shows the excellent performance of V-LIW in filter design; however, this configuration is not suitable to be integrated with other components of a communication circuit. In a new model, we combine the proposed transitions in Section III and the iris openings that have also been used in W-band filter to realize a filter with coplanar inputs in the same plane. Fig. 33 depicts the proposed filter. This filter has four sections: 1) CPW-to-V-LIW transitions; 2) V-LIW sections; 3) V-LIW-to-H-LIW transition; and 4) H-LIW section. The iris

Fig. 32. Simulation results of W-band V-LIW fifth-order filter.

openings and inductive posts are located in V-LIW and H-LIW sections, respectively, to form cavity resonators. Therefore, the transition sections are also used as resonators, which lead to having a more compact design.

The drawback of this new structure is, we achieve a more convenient design for integration, at the expense of a more complicated structure which makes almost impossible to provide a fully analytical design procedure. To find an acceptable starting point for optimization, one can follow the previous design procedure with certain considerations given in the following.

1)In the first (and last) resonator, the designed transition from CPW to V-LIW should be added. Then, the position of this transition in the XY plane and also the aperture diameter where the signal via comes into the V- LIW have to be adjusted to provide the external quality factor (Qext) and coupling factor (k) given by [53]

where BW is the bandwidth and f0 is the center frequency corresponding to mid-band guided wavelength found by (8). The external quality factor for these resonators can be extracted from ANSYS HFSS simulation in association with MATLAB code. This code has been written by the authors based on [54].

2)For the second transition, between V-LIW and H-LIW, like the first transition, with adjusting the lateral position of transition and the aperture diameter, the desired coupling between the third and fourth resonators can be achieved. It should be noted that the lengths of these cavities have to be optimized at the same time to keep the resonance frequency of the coupled resonators unchanged.

3)Two inductive posts are used to realize the coupling between the fourth and fifth resonators. The distance between these two posts determines the level of coupling. This distance can be estimated by (12) and then applying the formula for effective width of SIW, presented in [55].

Applying the presented method, we have designed and optimized a filter for unlicensed 60-GHz applications. The filter is targeted at 58–62 GHz with passband ripples of

Fig. 35. Fabricated V-band V-LIW filter. (a) Top-view photograph. (b) X-ray photograph of inside of LTCC filter.

0.005 dB. The filter has been designed following the analytical procedure presented in the previous part of this section, and then the steps, presented here, carried out one by one to have a fast and accurate optimization. Dupont 9k7 LTCC tapes with a permittivity of 7.1 are used to realize the desired filter. The LIW width in both sections, V-LIW and H-LIW, is 1428 μm. Table V includes the optimized dimensions for the proposed filter; the dimensions that are not listed in this table can be found from either symmetry of the filter or dimensions for the transitions presented in the previous sections.

Fig. 34 shows the simulation and fabrication of the V-LIW V-band filter. As it can be seen in this figure, the results are in good agreement. The measured filter has a return loss of better than 15 dB over the entire unlicensed band and an insertion loss of 2.1 dB at 60 GHz. A photograph of the fabricated filter and an X-ray photograph of inside LTCC are illustrated in Fig. 35.

V. CONCLUSION

In this paper, we proposed a new guiding structure, named V-LIW, for multilayer fabrication technologies. The proposed transmission line allows us to integrate the passive components in the perpendicular direction to the surface. The characteristics of V-LIW are fully presented, and three different transitions have also been proposed to interconnect this line to the standard rectangular waveguides, coplanar waveguides, and conventional horizontal SIW. Furthermore, the superior capabilities of V-LIW for designing compact 3-D circuits have been demonstrated through designing different elementary components: two filters, T-junction power divider, and a coupler. The transitions, as well as the 3-D circuits, are successfully fabricated and measured in LTCC. The authors envision that the proposed V-LIW to be an excellent candidate for the mmwave compact 3-D circuits, where highly integrated low-loss structures are desired.

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Aria Isapour (GS’13) received the B.Sc. degree in electrical engineering from the Iran University of Science and Technology, Tehran, Iran, in 2009, the M.Sc. degree in electrical engineering from the Sharif University of Technology, Tehran, in 2011, and the Ph.D. degree in electrical engineering from the École de Technologie Supérieure, Montréal, QC, Canada, in 2018.

He is currently a Staff RF Designer with the Infinera Corporation, Ottawa, ON, Canada. His current research interests include passive microwave

and millimeter-wave circuits, signal integrity, and low-temperature cofired ceramics for 3-D passive circuits and packaging.

Ammar Kouki (S’88–M’92–SM’01) received the B.S. (Hons.) and M.S. degrees in engineering science from Pennsylvania State University, State College, PA, USA, in 1985 and 1987, respectively, and the Ph.D. degree in electrical engineering from the University of Illinois at Urbana–Champaign, Champaign, IL, USA, in 1991.

the LTCC@ETS Laboratory, École de Technologie Supérieure, Montréal, QC, Canada. His current research interests include active and passive microwave and millimeter-wave

devices and circuits, intelligent and efficient RF front ends, 3-D circuits in lowtemperature cofired ceramics, applied computational electromagnetics, and antennas radio-wave propagation modeling.