Envelope tracking is widely used to raise the efficiency of PAs. An envelope tracking supply modulator (ETSM) modulates PA's supply voltage to tracks the RF waveform's envelope, so that the PA will operate in saturation all the time. A hybrid amplifier is commonly used to realize the ETSM, which, in effect, partitions the envelope bandwidth into a low and high subband. An efficient switching buck converter tracks the low band. In parallel with it, an op-amp supplies the current in the high band. In prior arts, the hybrid amplifier is realized with feedback using a hysteresis comparator, whose output actuates the buck converter to respond to the changing envelope; the continuous-time op-amp makes up for the error. But a comparator-driven buck converter produces a slew-rate limited current that always lags the envelope waveform. This forces the op-amp to produce a larger current to correct the error, and the arrangement cannot guarantee that the buck converter switches no often than is absolutely necessary. We replace the hysteresis comparator with a novel trellis-search that, first, finds the optimal sequence to switch the buck converter to minimize the RMS current that the op-amp must deliver; second, to lower the loss from switching the capacitance of FETs, it penalizes a large number of switching events in the buck converter.Meanwhile, with a conventional on-chip hysteresis comparator, we can demonstrate ETSM operation up to 160 MHz modulation bandwidth. This is the widest bandwidth reported so far for any ETSM.ii The dissertation of Weiyu Leng is approved.