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Kuroda's Identities (Transforms) | ||||||
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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.
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