A sigma-delta-modulated (SDM) power amplifier implemented by a simple cycle-by-cycle integral control is presented. The SDM pulse train for simulating the input signal is polarity-dependent. There is a leading negative bit pulse followed by a positive pulse for the train pulse formation converted from a positive input amplitude, or, a leading negative pulse followed by a positive bit pulse formed from the negative one. Analytic modelling to describe the signal conversion and system analysis is conducted thoroughly. The proposed conversion strategy provides group-mode harmonics randomly scattered over the spectrum with low amplitudes for reducing the EMI problem. An experimental demonstration to verify the performance of a 1 kVA SDM AC power amplifier is conducted. The resulted efficiency is up to 90% and the total harmonic distortion less than 2% before the EMI filtering.