Digital transmitters having improved characteristics are described. In one design of a digital transmitter, a first circuit block receives inphase and quadrature signals, performs conversion from Cartesian to polar coordinates, and generates magnitude and phase signals. A second circuit block (which may include a delta-sigma modulator or a digital filter) generates an envelope signal based on the magnitude signal. A third circuit block generates a phase modulated signal based on the phase signal. The third circuit block may include a phase modulating phase locked loop (PLL), a voltage controlled oscillator (VCO), a saturating buffer, and so on. A fourth circuit block (which may include one or more exclusive-OR gates or an amplifier with multiple gain states) generates a digitally modulated signal based on the envelope signal and the phase modulated signal. A fifth circuit block (which may include a class D amplifier and/or a power amplifier) amplifies the digitally modulated signal and generates an RF output signal.