A novel SIGGW dual post band-pass filter for 5G millimeter-wave band applications with a transmission zero

Integration of planar circuits been considered a credible technique for low-cost mass production of microwave and millimeter-wave circuits and systems. For the first time, in this research a dual-post band-pass filter is designed and simulated in a three-layer substrate integrated gap groove waveguide (SIGGW) for 5G millimeter-wave frequency band applications. The filter includes 12 posts (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$6 \times 2$$\end{document}6×2). Also, the structure facilitates to use resonant posts and so we can design the posts to add a transmission zero in lower rejection band. The design theory algorithm and its limitations are investigated based on the circuit model of filter. The results shows that FBW of 5% and a lower band transmission zero for the proposed 12 posts filter. Also, the results are verified by simulation using CST. According to the results, the proposed filter is a good option for Ka-band applications and can be used as the building block for suppressing the LO leakage that is commonly used for up-converting the 5G signal to Ka band.


Substrate integrated groove gap waveguide (SIGGW) structure
The geometry of the SIGGW is shown in Fig. 1.Unlike classic waveguides, the SIGGW doesn't require electrical contact between the upper and lower planes.The dimensions and positions of metallic bars are designed to create a metamaterial gap at desired frequency band to prevent propagation in the x-direction and virtually act as a wall in that band.As a result, EM wave propagates through the space between top plane, metal pins, and lower plane which is filled with a dielectric.Here, we use RO4003 with ǫ r =3.55 and tanδ=0.002as dielectric.The dimensions of metal pins are designed to achieve a band gap around 28 GHz 25 .The designed parameters are depicted in Table 1.
The simulated results for values in Table 1 are shown in Fig. 2. The dispersion curve indicates that the first bandgap is between 20.5GHz to 42GHz.In Fig. 3, the s-parameters of the designed SIGGW are displayed, revealing excellent return loss and transmission coefficients in the range of 24GHz-32GHz.

Dual post filter design
One of candidates for band-pass waveguide filter is inductive dual-post structure 28 .In section 3, we designed the SIGGW, and in this section, we use those results to design our filter.The filter is designed at center frequency of 28GHz and fractional bandwidth of about 5 We use posts at distance about g 2 from each other, where g is guided wavelength at center frequency, taking into consideration the ǫ r of structure.For designing dual-post filters in classic rectangular waveguide, we use posts connecting bottom to top of the waveguide, but in this case the posts are shorter than the height of SIGGW.The post lengths, denoted as L from the bottom, as shown in Fig. 1.Since the L is shorter than waveguide height, there will be a gap between the top of the posts and the upper plate.A capacitance is formed between the posts and upper conductor.This can be so useful to generate a transmission zero in rejection band of filter.The posts are inductive and having a capacitance in series cause a resonance frequency which short circuit the SIGGW and current is maximum in this case.Nevertheless, we need inductances for our filter topology and fortunately, as the frequency increases, the behavior of series inductance and Table 1.Desired parameter for design SIGGW.T x and T y are distance center to center of metal pins and D is diameter of metal pins.www.nature.com/scientificreports/capacitance becomes more inductive, so in this case we expect that if the frequency increases this design behaves perfectly as an inductive post.This means we have a resonant frequency at lower rejection band that could be useful if we can control it at proper frequency.So here, we introduce an algorithm to control this transmission zero.The equivalent circuit of waveguide filter is shown in Fig. 4.
The ABCD matrix and input impedance of transmission line is given by Eqs.
where, x = Z 02 Z 01 so: Y in = jY 02 We mentioned that distance between posts is about g 2 so the ABCD matrix of total structure is Eq. ( 4).
where Z 0 and βl , is characteristic impedance and electrical length of resonators respectively.If l 11 < /4 from taylor series we have cotβl 11 ≈ 1 due to Fig. 5 it is a reasonable assumption.As a result, with βl = π: If we convert ABCD matrix to S-matrix due to 29 : At resonance frequency we choose |S 11 | = 0 and |S 21 | = 1 .
In this case we have Quasi-TEM mode so we compute inductance and capacitance of posts.It is assumed that the inductance of l 1 and capacitance of l 11 are dominant.First, we compute inductance, form Ampere law we have: On the other hand, we know the energy of inductance is W= 1 2 LI 2 so: So, the resonance frequency due to the post is: Electric field and magnetic field are minimum and maximum respectively on posts, so assuming that the waveguide is strip line the radius of R 1 and R 2 related to Z 01 and Z 02 .The impedance Z 0 of a transmission line consist- ing of a circular signal conductor having a diameter D and centered between parallel ground planes separated by distance T is given by Eq. ( 7) 30 .

Algorithm of design:
(1) Choose the frequency that want to have transmission zero out of band and compute ω c (2) From Eq. ( 7) compute R 11 and R 1 according to Z 01 and Z 02 . (1) The final design parameters are depicted in Table 2 We must mention that there are limitations to this structure.At lower frequencies, designing and building this structure will become difficult due to the increase in substrate thickness.Similarly, at higher frequencies, it will also be challenging to design and build this structure because of the shrinking dimensions of the filter.The final structure and results are shown in Figs. 5 and 6 respectively.

Simulation of SIGGW filter
For verifying our results, we use sweep parameters in CST.If we reduce the radius of capacitors from Eq. ( 6), we see that resonance frequency is increased.It can be seen from Fig. 7 that if radius of each capacitor is decreased about 0.02 mm the resonance frequency increased about 100MHz.Figure 8 illustrates the primary objective of this paper, which is to present the design of the SIGGW filter in the Ka band with finite transmission zero in the lower band.This analysis method can also be employed for designing other resonant filters that incorporate finite transmission zero.

Discussion
In this research, a dual-post band-pass filter in the 5G Ka-band has been designed and simulated using a threelayer substrate integrated gap groove waveguide (SIGGW).After interpreting the dual-post filters, we proceeded with the SIGGW filter design.The most crucial advantage of gap waveguide structures compared to conventional rectangular waveguides is that the posts are not connected to the top wall of the waveguide.In SIGGW, the multilayer PCB etching and plating technology forces us to provide some pads on both sides of the via holes.These pads play the role of capacitor plates when we realize the posts as blind vias.We have shown that this can be efficiently controlled and facilitates the utilization of the resonant frequency of the filter posts to synthesize a transmission zero at a lower reject band.The realized transmission zero improves the lower side rejection slope and can be used for suppressing the LO leakage, which is commonly employed for up-converting the 5G signal to the Ka-band.We have proposed an algorithm to control this transmission zero, verified using CST simulating software.This algorithm can create transmission zero in other gap waveguide resonant filters and obtain a suitable initial solution.The results agree with the introduced simple circuit model for the resonant frequency.Finally, Table 3 compares the BPFs that were recently reported and fabricated using different technologies (the mass of the construction was not included due to a lack of available data).

Figure 1 .
Figure 1.The geometry of SIGGW.(a) Front view of structure with RO4003 (b) Perspective view of SIGGW without dielectric.

Figure 2 .
Figure 2. The bandgap between first and second mode of excitation.

Figure 3 .
Figure 3.Return loss and transmission coefficient of designed SIGGW.

Figure 5 .
Figure 5. Final structure of filter.(a) Perspective view of SIGGW with cuting plane (b) Enlarged view of posts.

Figure 6 .
Figure 6.Final result of filter.

Figure 7 .
Figure 7. Effect of changing the area of capacitors in the location of transmission zero.

Figure 8 .
Figure 8. Flow chart of the main steps in the SIGGW filter design with finite transmission zero in lower band.

Table 2 .
Design parameters for posts.Index 1 and 11 is for the first post, index 2,22 and 3,33 is for second and third posts respectively.

Table 3 .
Performance comparisons between proposed filter in this paper with other filters in different technologies.