Bandpass filter based on microstrip resonators with additional galvanic coupling

An expression is obtained for the coupling coefficient of microstrip resonators with inductive, capacitive, and galvanic interaction caused by an additional inductive element. It is shown that the capacitive coupling coefficient has a sign opposite to the galvanic coupling coefficient, and the inductive coupling coefficient can have both a positive and negative sign. Theoretically and experimentally, using two-order microstrip filters with the same conductor topology, the possibility of significantly increasing the bandwidth due to the introduction of galvanic coupling, as well as mutual compensation of three types of couplings, leading to the disappearance of the first passband, has been demonstrated. A sixth-order bandpass filter based on quarter-wave microstrip resonators with additional galvanic coupling has high frequency-selective properties due to the appearance of two transmission zeros on either side of the passband. The developed filter is made on a substrate with a permittivity $\varepsilon$ = 80, thickness 2 mm and dimensions 25 $\times$ 50 mm$^2$. The central frequency of the filter passband is $f_0$ = 0.5 GHz, and its fractional bandwidth $\Delta f/f_0$ = 15%.