M. Skopenkov gave a reference to criterion for a rectangle to be tilable by rectangles of a similar shape: C. Freiling, D. Rinne, Tiling a square with similar rectangles, Math. Res. Lett. 1 (1994) 547–558; M. Laczkovich, G. Szekeres, Tiling of the square with similar rectangles, Discrete Comput. Geom. 13 (1995) 569–572. This results related to construction of alternating-current circuits with given properties M. Prasolov, M. Skopenkov, Tiling by rectangles and alternating current, Journal of Combinatorial Theory, Series A 118 (2011) 920–937.
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