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This paper discussed the design of rectangular spirals used to create an electrically small patch antenna with a μ-negative core (MNG) substrate and showed that varying the number of spirals placed on the individual boards provides added design freedom beyond selecting the number of turns. For an electrically small antenna with a fixed size, resonant frequencies were achieved from 220 MHz to 675 MHz by changing the parameters of the spirals that create the MNG substrate. Single spirals allow lower resonant frequencies than multiple spirals encompassing the same area with the same number of turns. This enables smaller antennas for a given wavelength.