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We present a systematic, empirical design technique to obtain optimum broadband impedance, axial-ratio (AR) and gain bandwidths for a singly-fed electromagnetically coupled patch antenna for circular polarization. Our investigation has also revealed tradeoffs amongst obtainable AR, impedance bandwidth and AR bandwidth. Using two design examples at different frequency bands and for different senses of circular polarization, we have demonstrated the effectiveness of the proposed knowledge-based tuning method. We have obtained at C-band measured values of impedance bandwidth (VSWR≤2) equal to 43%, 3-dB AR bandwidth of 8%, AR of less than 0.3 dB and a mean gain level of 7 dB. For the Ku-band element, a 40% impedance bandwidth and a 17.3% of 3-dB AR bandwidth have been obtained with a peak gain of 7.2 dBic.