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For practical design, it is useful to be able to determine in advance, from design parameters alone, the condition under which mutual inductances will not appear in ladder networks designed on the image-parameter or on the insertion loss basis. The present paper starts with some comments on Fujisawa's criterion and extends it to a class of image-parameter band-pass filters. It expresses Fujisawa's criterion in terms of the design parameters for the symmetrical, low-pass filter having Tchebycheff behavior in both the attenuation and transmission ranges and for some degenerate cases. Various approximations yield simple results of great practical importance.