Direct pulse‐width modulated (PWM) AC–AC converters are rapidly advancing, primarily because of their single‐stage power conversion and reduced footprint, achieved by eliminating the intermediate DC‐link capacitor. Z‐source AC–AC converters (ZSACs) especially have gained attention for their wide voltage range and reduced harmonic currents in applications where only voltage regulation is desired. Meanwhile, voltage regulation in PWM AC–AC converters necessitates effective closed‐loop control methods. Delta‐sigma modulation (DSM) has emerged as a promising technique, outperforming traditional methods. Nevertheless, the conventional DSM technique employs a fixed hysteresis band, resulting in the converter operating at a variable switching frequency. The variable switching frequency increases the switching losses, which puts more thermal stress on the switches. This paper introduces a CSF‐based DSM method for ZSACs that makes use of an adaptive hysteresis band. A four‐step commutation technique is utilized to prevent voltage and current spikes across the bidirectional switches, eliminating the need for snubber circuits. The proposed approach is validated through comprehensive simulation studies and experimental results on a modified quasi‐ZSAC topology using a 200‐W laboratory prototype, demonstrating significant improvements in source and load current total harmonic distortion (THD), dynamic response, and overall system performance while maintaining constant switching frequency.