Direct synthesis and design of high degree lowpass filters with ultra-wide stopband

A direct synthesis and design approach to lowpass filter (LPF) with ultra-wide stopband is proposed. The LPF consists of multiple radial stubs and capacitively loaded stubs, all connected with high impedance transmission lines in cascade. The capacitively loaded stubs with long electrical lengths not only produce transmission zeros (TZs) close to the band edge to sharpen the roll-off, but also produce TZs in the far stopband. The radial stubs, which can be approximated by series LCs and are spurious-free in a wide frequency range, are used to generate extra controllable TZs in the far stopband. The layout of LPF can be accurately modelled by a mixed lumped/distributed (MLD) equivalent circuit, which can be systematically converted from a generalized Chebyshev lowpass prototype. To demonstrate the proposed design approach, a 17-degree lowpass filter with cut-off frequency fc of 2 GHz and approximately 40 dB rejection stopband up to 9 fc is presented.