This paper presents an analysis and design strategy for a half‐bridge series resonant induction heating (HB SR‐IH) cooker powered by a rectified sinusoidal DC. The simplified equivalent circuit of an induction cooker is modelled by a train of rectified sinusoidal DC pulses chopped at the switching frequency. An average root‐mean‐square (RMS) method is proposed to calculate the RMS resonant voltage and current extrapolated to the power line frequency period. The stability of the cooker is achieved by properly setting the damping ratio in the root‐locus plane to keep the system running quasi‐resonantly at the required power. The power control of the SR HB‐IH cooktop is performed by forced commutation above the resonance frequency. A prototype of a 3 kW HB SR‐IH cooker was designed and implemented to validate the estimated results. Various waveforms from low power to high power are discussed and verified by damping ratio control. The SR HB‐IH cooktop achieves a high‐power factor of 0.95 to 0.995 when generating 300W to 3kW due to less filtered DC power. The power quality assessment showed that the total harmonic distortion (THD) of the line current and voltage measured at 3 kW was 4.1% and 3.5%, respectively.