How do I design a microstrip to SIW transition for integrating waveguide filters with planar circuits?

A microstrip-to-SIW transition is a critical interconnection structure that converts between the quasi-TEM mode of microstrip and the TE10 waveguide mode of the substrate integrated waveguide, enabling integration of high-Q SIW filters with microstrip-based active circuits on the same PCB. The most common transition design is the tapered microstrip feed: the 50-ohm microstrip line enters the SIW through a linearly tapered section where the trace width gradually increases from the microstrip width to a width that excites the TE10 mode of the SIW. The taper length is typically lambda_g/4 to lambda_g/2 (guided wavelength at center frequency). The taper width at the SIW end is approximately W_SIW/2 (half the SIW width) for optimal field matching. Alternative transition designs include: stepped impedance transition (discrete width steps instead of continuous taper; easier to fabricate but narrower bandwidth), probe coupling (a short section of microstrip extends into the SIW cavity through a slot in the SIW top wall, acting as a probe antenna that excites the TE10 mode; provides very compact transition), and CPW-to-SIW transitions (the CPW ground-signal-ground structure interfaces with the SIW through a slot in the SIW wall). Design performance targets: insertion loss < 0.3 dB per transition over the SIW operating bandwidth, return loss > 15 dB across the band, and bandwidth covering the full single-mode range of the SIW (f_c to 2 x f_c).