Kuroda's Identities (Transforms)
I remember learning of the Kuroda Transform right after graduating and being assigned to do a set of four bandpass filters for an L-band switched filter. Those were the days of Touchstone on a Unix box where net list inputs were the norm rather than handy GUI interfaces. It was mesmerizing to watch the optimizer crank through successive iterations and draw increasingly perfect bandpass responses - with the necessary group delay parameters - in an impressive array of colors (16-color CGA everyman's PC display of the era). But then I digress.
The Kuroda Identities shown here are custom reproductions of versions that can be found in hundreds of other sources.
For all four transforms, use n2 = 1 + Z2/Z1, and the rectangular boxes are λ/8 transmission line sections with the indicated characteristic impedances.