## 1 Introduction  
The demand for wireless communication systems in the 4 th industrial revolution technology is steadily increasing. For human convenience, a wireless communication system is required to have high portability, low unit cost, high performance, and small size [1]. An important item in a wireless communication system is that it divides frequency bands and avoids interference in different frequency bands [2]. In this case, the band-pass filter (BPF) plays the role of frequency band distribution and interference blocking. The important components of a BPF are the low cost, bandwidth control, device size, skirt characteristic, frequency selectivity, and frequency response characteristics (low insertion loss and high return loss). For size reduction and bandwidth control, a BPF is used for the stepped impedance resonator (SIR), stub\(-\)loaded resonator (SLR), and multimode/band. In addition, to obtain sharp cut-off frequency characteristics, the filter is used to transmission-zero characteristics [2; 3; 4; 5; 6; 7]. To obtain an excellent skirt phenomenon, the filter increases the number of resonators [8]. However, if the filter is increased, the insertion loss is increased [8; 9]. In particular, a BPF using both SLR and SIR was able to obtain the tri\(-\)band characteristics of a wide bandwidth by adjusting the stub length and impedance ratio [10; 11]. In order to obtain tri\(-\)band characteristics, it would have been difficult to adjust the length and impedance ratio of the filter at the same time. Thus, the characteristics of the filter are quite attractive. However, it would not be easy to reduce the size of the device and this filter would still have the task of size reduction [2; 12]. Therefore, there is a case for using a sextuple\(-\)mode resonator to solve the bandwidth [13] however, the filter has many stubs. Therefore, the filter has the disadvantages of a complex structure and a size increase [9]. A dual-band BPF is used for the quad-mode SLR to obtain a sharp cut-off frequency response through transmission-zero characteristics [14]. However, this filter has a narrow band of the second band and low-frequency selectivity due to the improper location of the transmission\(-\)zero. It is very important to use transmission-zero characteristics to obtain excellent blocking characteristics. The reason is that multiple resonators must be used to obtain a good skirt phenomenon of the filter, but then the size of the device increases. To obtain tri\(-\)band response characteristics, it is analyzed that a spiral\(-\)shaped resonator has no transmission\(-\)zero characteristics, so the cut\(-\)off frequency characteristic is not excellent [15]. To improve the cut\(-\)off frequency characteristics, this filter connected various resonators, but the size of the device increased [9]. A band\(-\)pass filter with a coupled loaded self\(-\)SIR structure has dual\(-\)band characteristics and transmission-zero characteristics [16]. However, it is analyzed that the size of the device increases and the insertion loss is relatively poor due to the occupied area of the stub, the coupling structure, and the number of stubs. The tri-band BPF using the SIR-coupling structure has no transmission\(-\)zero characteristic. Therefore, the selectivity of the frequency is reduced between the second and third bands. Additionally, the bandwidth of the filter was reduced [9; 14]. Therefore, the transmission\(-\)zero technology is important enough to consider the blocking characteristics. On the other hand, the BPF is used for stub\(-\)loaded (SL)\(-\)SIR to obtain small\(-\)sized broadband through the input impedance of the even/odd mode in the resonant mode of the resonator [17]. However, in this filter, SL\(-\)SIR is spurious due to the parasitic component of the redundant structure [18]. On the other hand, it is analyzed that the BPF integrated with SLR and SIR obtained multi-mode and transmission\(-\)zero characteristics by controlling two impedance ratios and two length ratios [19].