1. Introduction

The fifth generation(5G) is no longer a technology in dreams, but a reality. A plenty of studies and researches are still under way. At the 2018 PyeongChang Winter Olympics, telecom companies of Korea performed 5G demonstrations for the first time in the world. Lately, frequency auctions were done on June 18, 2018. In the case of 5G sub-6-GHz area, SKT, KT and LG U+ were each assigned to 3.42 ~ 3.5 GHz, 3.5 ~ 3.6 GHz and 3.6 ~ 3.7 GHz. In addition, many countries such as the U.S, China, Japan and Europe allocated 5G frequencies to industries ^(1-3).

For systems of high data-rate transmission, digital components and software technologies are important. They are realizable by RF components and circuits. As the frequency bands flock side by side, the role of passive components such as filters are crucial.

In this paper, new small sized bandpass filters are proposed with a vertical split-ring as a novel resonator(VSRR). Unlike the conventional resonators and SRR(lying on a horizontal plane and used for bandstop)^(4-5), we make printable vertically standing split-ring resonators and then they are coupled through magnetic field, while others’ ring filters use electric coupling on the same horizontal plane. The proposed bandpass filter are designed with the Taconic TLY-5 substrate. The overall size is 23.7 × 19.3 × 1 $mm^{3}$. Based on the above structure, a total of three bands are designed for channel filters as a 5G core part.

The design method is verified by the equivalent circuit, EM-simulation and measurement of the fabricated filters. This will show good impedance match at the bands, insertion loss and stopband performances.

2. Design of the proposed bandpass filters

2.1 Electromagnetic design

To reduce the size, we proposed the not only the VSRR structure but also using the gap(or split) as the 0.5 pF for the three channels. The proposed filters are simulated and implemented with the Taconic TLY-5 substrate of the dielectric constant of 2.2, the thickness of 1 mm and loss tangent of 0.0002. The overall size is the 23.7 × 19.3 × 1 $mm^{3}$. All the design parameters in Fig. 1(a) $l_{s}, l_{1}, l_{2}, l_{3}, l_{4,1}, l_{4,2}, l_{5,1}, l_{5,2}, l_{5,3}, w_{s}, w_{1}$, and $w_{2}$ are 19.3, 3.5, 6, 14, 7.75, 7.4, 7.5, 7.2, 6.7, 23.7, 1.7, and 1.3. in mm. Furthermore, these numbers tell us the different length of the VSRR as the l4,n|n=1,..,3 and $l_{5,n|n=1,..,3}$ for each of the 3 channel filters. To emphasize the strength of the proposed methodology, the miniaturization effect is over 65%, compared to other designs like edge-coupled filters. Fig. 1(b) shows the H-field of the proposed filter. As shown in Fig. 1(b), the proposed filter is run by the magnetic coupling different from others’ filters. Furthermore, Fig. 1(c) shows the surface current at the stopband. Fig. 1(c) indicates that phase is reversed and this leads to the good attenuation at the stopband and almost no energy arrives at port 2.

그림. 1. 제안하는 대역통과 여파기 (a) 구조의 윗면 및 아랫면 모습 (b) 통과 대역에서의 자기장 결합 분포 (c) 차단대역에서의 전류분포 (@ 3.7 GHz)

Fig. 1. The proposed channel filter (a) Physical geometry(Top and bottom view) (b) H-field for coupling and energy transfer (c) Surface current at the stopband at 3.7 GHz

2.2 Equivalent circuit analysis and verification

그림. 2. 제안하는 대역통과 여파기 구조 모습 (a) 공진기 후면 모습 (b) 공진기 등가회로 (c) 제안하는 필터 등가회로

Fig. 2. The proposed channel filter (a) Physical geometry (b) The bottom view of the resonator (c) The equivalent circuit of the proposed filter

Fig. 2(a) shows the bottom view of the proposed VSRR structure. From the Fig. 2(a), the capacitor values are derived from equation (1). The total value of the capacitor is $C_{s}$+Clumped as shown in Fig. 2(b).

(1)

$C_{s}=\epsilon_{r}\left(\dfrac{\epsilon_{r1}+\epsilon_{r2}}{2}\right)\dfrac{(2l_{1}+2l_{2}-g_{1})\times t}{g_{2}}$

(2)

$f_{r}=\dfrac{1}{2\pi\sqrt{L(C_{s}+C_{lumped})}}$

(3)

$L=\dfrac{1}{(2\pi)^{2}\times(C_{s}+C_{lumped})\times f_{r}}$

Based upon equations (1)-(3), the inductances and capacitors of the channel 1 filter as the $L_{1}, L_{2}, C_{1}$ and $C_{2}$ are 4.13 nH, 4.13 nH, 0.52 pF and 0.52 pF, respectively. The $L_{3}$ and $C_{3}$ values are totally the same as L1 and C1 because the proposed filter is symmetry with the input- and output ports.

(4)

$K_{12}= M_{12}/\sqrt{L_{1}L_{2}}$

(5)

$K_{23}= M_{23}/\sqrt{L_{2}L_{3}}$

(6)

$K_{13}= M_{13}/\sqrt{L_{1}L_{3}}$

(7)

$M_{i,\:j}= M_{j,\:i}$

Where $K_{12}, K_{13}$, and $K_{23}$ are 0.1, 0.1, 0.08, respectively. Based upon the equivalent circuit, the transmission coefficient $S_{21}$ can be calculated by using coupling coefficient and transfer function method. Fig. 3(a) indicates the comparison results of the equivalent circuit result and full-EM simulated result. As shown in Fig. 3(a), between the equivalent circuit result and EM analysis result, the passbands are in good agreement and stopbands with a transmission zero also agree well.

그림. 3. 제안하는 대역통과 여파기의 주파수 응답 (a) 등가회로 및 전자기 모의시험 결과 비교 (b) 각 채널 필터 주파수 응답

Fig. 3. The proposed channel filter (a) The comparison of the equivalent circuit result and EM result (b) The frequency responses of the channel filters

The design method is checked initially by the comparison with the equivalent circuit. It is applied to the three channels and Fig. 3(b) shows the passbands are implemented as 3.42 ~ 3.5 GHz, 3.5 ~ 3.6 GHz, and 3.6 ~ 3.7 GHz.

3. The measured results

그림. 4. 제작된 대역통과 여파기 (a) 구조 모습 (b) 주파수 응답특성 (c) 전송계수

Fig. 4. The fabricated channel filters (a) Physical geometry (b) Frequency

Fig. 4(a) illustrates the fabricated proposed contiguous channel filters. As shown in Figs. 4(b) and (c), the slight frequency-shift is observed between the simulated and measured results. It is guessed that this comes from the discrepancy of the assumed and real dielectric constant and connector soldering. The measured levels of S11 are below 13 dB for the three channels, meaning good impedance matching. The measured insertion loss achieved is from 0.75 dB through 1.25 dB to 2 dB in the passbands, which is good compared to other printed filters and SAW filters with the insertion loss larger than 2 dB. The stopbands have attenuation larger than 20 dB.

4. Conclusion

The proposed channel filters have good performances in passbands and impedance matching as smaller footprints than the conventional ones. A good stopband property is obtained by a transmission zero. The proposed filter design methodology is proved by the equivalent circuit and EM simulation. These results show properness as the components of 5G telecommunication terminal and even base station systems.