Advances in power electronics have made it possible to achieve high power levels, e.g., reaching GW in grids, or alternatively high output bandwidths, e.g., beyond MHz in communication. Achieving both simultaneously, however, remains challenging. Various applications, ranging from efficient multichannel wireless power transfer to cutting-edge medical and neuroscience applications, are demanding both high power and wide bandwidth. Conventional inverters can achieve high power and high quality at grid or specific frequency ranges but lose their fidelity when reaching higher output frequencies. Resonant circuits can promise a high output frequency but only a narrow bandwidth. We overcome the hardware challenges by combining gallium-nitride (GaN) transistors with modular cascaded double-H bridge circuits and control that can manage typical timing and balancing issues. We developed a lightweight embedded control solution that includes an improved look-up-table digital synthesizer and a novel adaptive-bias-elimination nearest-level modulation. This solution effectively solves the conflict between a high power level and high output bandwidth and can--in contrast to previous approaches--in principle be scaled in both dimensions. Our prototype exhibits a frequency range from DC to 5 MHz with <18% total voltage distortion across the entire frequency spectrum, while achieving a power level of >5 kW. We conducted tests by sweeping the output frequency and two channel-mixing trials, which included a practical magnetogenetics-oriented stimulation pulse and an entertaining trial to reproduce the famous Arecibo message with the current spectrum.