Analysis and Design of Wideband Microstrip-to-Microstrip Equal Ripple Vertical Transitions and Their Application to Bandpass Filters

This paper first presents two types of wideband microstrip-to-microstrip equal ripple vertical transitions designed with the uniform and folded slotline structures, respectively. By solving the characteristic function with differential calculation, the condition for realizing the constant equal ripple frequency response but different bandwidths (BWs) for the proposed transition is determined with resorting to the characteristic impedances of the coupled open-circuited microstrip line and slotline. Then, a vertical transition with the uniform slotline is synthetically analyzed and designed with Chebyshev polynomial function and another similar vertical transition with the same in-band ripple level but different BWs is also comparatively presented. By modifying the normalized impedances of the proposed transition to make the theoretical result close to the simulated one with the initial normalized impedances, the transformer turns ratios of the microstrip-to-slotline intersection is exactly calculated by the impedance ratios between two corresponding sets of normalized impedances. Due to the degraded high-frequency performance caused by the radiation loss of the uniform slotline, two vertical transitions with the folded slotline structure are further analyzed and the related turn ratios are extracted with the proposed approach. To verify the effectiveness on the reduction of radiation loss for the folded slotline structure, a six-pole wideband bandpass filter is presented with high-frequency performance greatly improved. In final, wideband vertical transitions with different slotline structures and a six-pole wideband bandpass filter are synthetically designed, simulated, fabricated, and measured.