We describe a supply modulator comprising a proposed delay-based hysteresis controller, proposed wideband class-AB amplifier, and class-D amplifier for an envelope tracking (ET) power amplifier (PA). We investigate the power dissipation and optimization method of the supply modulator for wideband applications taking into consideration the propagation delay, and show that a controller with zero threshold current not only improves the bandwidth of the supply modulator but also reduces its power dissipation. Based on our investigations, we propose a delay-based hysteresis controller embodying a novel high-speed current comparator whose reference current (threshold current) is zero, thereby achieving higher power-efficiency and simpler hardware. We further propose a class-AB amplifier, which features a high bandwidth and accurately controlled quiescent current. The proposed supply modulator features simultaneously the wide bandwidth (40 MHz), high output power (2.5 W), high peak efficiency (91%), high output voltage swing (3 V), and low output ripple noise (4 mVrms) at 3.6-V supply. The ET PA embodying our proposed supply modulator achieves a high power-efficiency of 41.4% at 28.5-dBm peak output power and 34.4% at 3-dB backoff—a significant >1.6× improvement over the radio frequency PA without the supply modulator.