# Parallel-Coupled-Line Bandpass Filter with Notch for Ultra-Wideband (UWB) Applications
## 1 Introduction  
In 2002, a marvelous opportunity was unrolled for researchers and scientists of the ultra-wideband (UWB) technologies by the U.S Federal communication commission (FCC) in terms of the release of a very-wide-frequency band with a fractional bandwidth (FBW) of 110% at a mid-band frequency of 6.85 GHz for unlicensed commercial usage [1]. One significant component that plays a significant part in determining the UWB systems' overall behavior is the UWB bandpass filter. The UWB bandpass filters are required to exhibit high selectivity, low insertion loss, higher out-of-band rejection, and flat group delay. For these reasons and to meet these specifications, huge efforts have been executed in the last two decades to develop various UWB filters [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. One of the approaches for the design of very-wide-band bandpass filters with small footprints is implementing multi-mode resonators (MMR) [2; 3; 4; 5; 6; 7]. In [2], a multiple-mode wideband bandpass filter was developed using a rectangular waveguide cavity and split ring resonators. The filter showed only the first two resonant modes inside the anticipated passband and, therefore, its bandwidth is limited. In [3], a very wideband bandpass filter was developed using a stepped-impedance configuration. The filter is constructed of two identical high-impedance line sections and one low-impedance line section. The electrical lengths of the high- and low-impedance sections were quarter-wavelength and half-wavelength at the center frequency, respectively. The wideband passband was achieved by creating the initial three resonant modes inside the required passband where the first-order resonant frequency was used to form the lower cutoff frequency while the third-order resonant frequency was used to form the upper cutoff frequency of the passband. To improve the stopband behavior, the low-impedance line unit can be replaced with a stub-loaded multiple-mode resonator [4]. Another way to improve the performance of this kind of filter is by including two short-circuited stubsin the low-impedance line section [5]. As a result, the first four resonant frequencies were evenly allocated inside the UWB passband, which significantly improved the stopband performance. The passband skirts can be improved by increasing the number of resonant modes inside the passband. This can be achieved by adding two side stubs to the stepped-impedance resonator [6] or by implementing a stub-loaded resonator [7]. In both cases, five-mode UWB filters are designed with good filtering performance and sharp selectivity. The UWB filters can also be designed using different topologies such as low-temperature co-fired ceramic technology [8], multilayer printed-circuit-board configuration [9; 10], parallel-coupled-lines [11; 12], and double-ridged half-mode SIW and ridged half-mode folded substrate-integrated waveguide [13]. Another common way to design UWB bandpass filters is using shunt short-circuited stubs. As a way to reduce the physical size and enhance the performance of this type of filter, the short-circuited stubs can be tapered to provide a wider controlled operational bandwidth and better stopband characteristics [14]. Due to the interference that may occur between the UWB systems and the existing wireless local-area network (WLAN) radio signals such as IEEE 802.11a, IEEE 802.11b, and IEEE 802.11g, UWB bandpass filters with single or multiple notched bands are necessary to avoid interferences from the undesired signals. To achieve this, various wideband bandpass filters can be designed and developed using diverse notched configurations [15; 16; 17]. In Ref. [15], short-circuit stepped-impedance stubs were used to develop a wideband bandpass filter with a notch where the notched band was attained by implementing short-circuit stepped-impedance stubs that have different electron length ratios. In Ref. [16], a narrow notched band was generated by embedding open-circuited stubs into the transmission unit elements of the wideband bandpass filter.