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Kirt Blattenberger - RF Cafe WebmasterCopyright
1996 - 2016
Webmaster:
Kirt Blattenberger,
 BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

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Kuroda's Identities (Transforms)

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 - RF Cafe

Kuroda Identity (Transform) Parallel Capacitor Input



Kuroda Identity (Transform) Series Inductor Input - RF Cafe

Kuroda Identity (Transform) Series Inductor Input



Kuroda Identity (Transform) Parallel Inductor Input - RF Cafe

Kuroda Identity (Transform) Parallel Inductor Input



Kuroda Identity (Transform) Series Capacitor Input - RF Cafe

Kuroda Identity (Transform) Series Capacitor Input