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Kuroda Identities (aka
Kuroda Transforms) are used to convert a section of transmission line with an open parallel stub into an
electrically equivalent section of transmission line with a shorted series stub. As a result, an identical
S-parameter matrix is produced that performs the same function. The technique is handy when designing distributed
element circuits where one configuration is possible and the other is not. Filters are a good example, because in
the physical layout open parallel stubs are difficult (or impossible) to realize whereas series shorted series
stubs are.
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.
Kuroda Identity (Transform) Parallel Capacitor Input
Kuroda Identity (Transform) Series Inductor Input
Kuroda Identity (Transform) Parallel Inductor Input
Kuroda Identity (Transform) Series Capacitor Input
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