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A combined linear and delta-modulated (DeltaM) switch-mode PA supply modulator for polar transmitters in wireless handsets is designed in a 0.25 mum CMOS process. The modulator employs a DeltaM switch-mode DC-DC buck converter to enhance the efficiency of a linear regulator at backed-off supply voltages and powers. The delta-modulator's noise-shaping characteristic, linear regulator's power supply rejection, digital pre-emphasis of the input envelope, and a closed-loop amplitude path from the PA output are simultaneously used to achieve state-of-the-art modulator performance. The presented supply modulator follows the input signal's envelope with 20 dB output dynamic range, maximum efficiency of 75.5% at an output power of 30.8 dBm, and 75 dB SFDR for envelope signals up to 4 MHz occupied RF bandwidth. For a 1625 kb/s 8 PSK RF input signal at 900 MHz, polar modulation of a commercial low-power GSM-900 PA provides 10 dB ACPR improvement.