Compact microstrip bandpass filters with good selectivity and stopband rejection

Compact microstrip bandpass filters (second- and fourth-order) are proposed based on the folded quarter-wavelength (λ/4) resonators, which are mainly coupled through the shunt inductors connected to the ground. By introducing a cross-coupling capacitance directly between the input and output ports of the second-order filter, a pair of transmission zeros may be created to improve the selectivity. Moreover, by an extension of the proposed second-order filter with the incorporation of an additional cross-coupling capacitance, a fourth-order filter is also proposed in which two pairs of transmission zeros may be created to improve both the selectivity and stopband rejection. The proposed fourth-order filter also has the merits of small circuit area and no spurious response up to 3f₀, where f₀ is the passband center frequency. To provide effective design tools, simple equivalent-circuit models are also established.