A Self-Packaged Tunable <i>LC</i> Fourth-Order Filter With Cross-Coupling and Bandwidth Compensation

This letter presents a cross-coupled lumped LC tunable bandpass filter (BPF) based on novel LC electric coupling circuits and magnetic dominant mixed coupling circuits. The design enables control over the slope and magnitude of the electric and magnetic coupling coefficients to compensate the bandwidth. The magnetic dominant mixed coupling, serving as cross-coupling, generates a pair of adaptive transmission zeros (TZs) on either side of the passband and an additional mixed coupling TZ at low frequency. To validate this concept, two tunable LC filters—Filter I, based on low-cost FR4 substrate-integrated suspended line (SISL), and Filter II, based on low loss microwave substrate-integrated microstrip, are designed and fabricated. Both filters showcase a wide tuning range and compact size. The SISL filter is with a tuning range of 0.36–0.77 GHz and a size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.09\lambda _{\mathbf {g}} \times 0.04\lambda _{\mathbf {g}}$ </tex-math></inline-formula>, which stands out for its self-packaging capabilities and cost-effectiveness.