**1. Introduction**

Bandpass filter (BPF) is an essential component in transmitters and receivers. For anti-interference, high performance BPF with sharp selectivity as well as wide stopband is important and necessary. Due to limited and crowded spectrum nowadays, there are more and more challenges in designing such bandpass filters in modern wireless systems.

Traditionally, the selectivity of BPF can be improved by increasing the order at the expense of larger insertion loss. While quasi-elliptic function response can realize the same selectivity with fewer orders and thus quasi-elliptic filter has lower insertion loss with high selectivity [1]. In [2], stub-loaded half-wavelength resonators are electromagnetically coupled to form quasi-elliptic response. In addition to specific response functions, introducing multiple transmission zeros (TZs) near the passband can effectively improve the selectivity [3]. Source-load coupling [4,5] and mixed coupling [6] are both proved to be useful by introducing TZs at sidebands. In [7], capacitive dominant mixed coupling is used to create a lower stopband TZ while the upper stopband selectivity is enhanced by employing parallel source-load coupling. Mixed coupling is also common when designing high selectivity SIW BPFs [8–10]. Furthermore, merely several coupled line networks can introduce both transmission zeros and poles. In [11], a high selectivity bandpass filter with 5 zeros and 6 poles is obtained by six pairs of coupled lines. Another way to realize prescribed TZs is synthesis of the coupling matrix to generate the transfer and reflection polynomials for specific class of filter[12,13], and to simplify the computational complexity and eliminate redundancy, synthesis algorithms are invented to extract coupling matrix from zeros and poles[14,15].

In this paper, a multilayer bandpass filter with high selectivity is proposed. The second and third harmonics are eliminated by the quarter-wavelength resonators and discriminating coupling formed by quarter- and half-wavelength resonators respectively, resulting in a wide stopband as well. This discriminating coupling path has same amplitude as an extra coupled line path between feeding ports but they are out of phase. Thus transmission zeros are produced to not only improve the selectivity but also broaden the stopband performance of the proposed BPF. Furthermore, due to multilayer structure, source-load coupling is easily achieved to improve selectivity as well. Theoretical analysis of the proposed BPF is demonstrated in detail and a prototype is fabricated to validate the design. Both simulated and measured results are in good agreement, showing the good performance of the proposed BPF.
