This article proposes an advanced synthesis of the frequency-adaptive bandpass filter (FA-BPF) with constant absolute bandwidth (ABW). The proposed synthesis is based on the element-variable coupling matrix (EVCM), which is directly extracted from the classical filter polynomials. The extraction method is presented, investigated in detail, and confirmed by a set of numerical simulations. All frequency-dependent couplings between the resonators in an FA-BPF are uniquely modeled by the new coupling matrix, and the element variation of the EVCM directly accounts for the frequency tuning behavior of an FA-BPF. This one-to-one correspondence tackles the difficulty of the FA-BPF synthesis and design with a different center frequency tuning range (FTR), a different bandwidth (BW), and a different BW variation rate. This article also proposes the predefined coupling technique in the new synthesis. It allows both nonfrequency-dependent matrix and frequency-dependent matrix in an EVCM to be separately implemented in practice. For experimental demonstration, two four-pole/four-transmission zero (TZ) FA-BPFs with identical passband and constant ABW are implemented and then constitute a frequency-adaptive bandpass diplexer (FA-BPD) with two tunable channels that have identical passband and constant ABW. The measurement results exhibited performance superiority of the design and validated the proposed design method.