Based on the cavity model and Greenberger's addition theorem, a theory is formulated to analyze stacked circular microstrip patch antennas (S-CMPAs) for low-coupling array design. Expressions for electric fields are given. In general, the calculated electric fields agree with those simulated. Our theoretical analysis demonstrates that if the electric fields E-x excited by the stacked circular patches completely cancel each other out, the S-CMPA array will exhibit the self-decoupling characteristic. The vector fitting technique is adopted to extract the zeros and poles of the S-21 curve to get a deeper insight into the mutual coupling between the two S-CMPA elements. The zeros are desirable and account for self-decoupling characteristics. For experimental validation, a two-element S-CMPA array was designed, fabricated, and measured. Results show that both elements achieve a wide impedance bandwidth of 14% (3.32-3.82 GHz) and a low coupling level of less than -25 dB between the two elements for the free-space half-wavelength spacing at the center frequency. In addition, the designed antenna is extended into a four-element linear antenna array, which still maintains broad impedance bandwidth and low coupling levels.