The emergence of wide bandgap power devices has brought the attention back to the flying capacitor (FC) multilevel inverters with a large number of stages, in an effort to increase the power density by minimizing the passive components. The main challenge that such systems face, particularly the ones based on high-frequency Gallium-Nitride devices and small-value ceramic capacitors, relate to the stringent requirements for precise and fast capacitor balancing. Conventional natural balancing techniques exhibit poor settling times, while most improved natural balancing methods are not easily scalable to more than five levels. The alternative of active balancing normally requires one isolated sensor per FC which increases the overall system cost and footprint, or a single ac-side sensor that is more compact but calls for sophisticated PWMs that again are not available for multiple levels. In this paper we introduce a generalized pulse width modulation (PWM) strategy based on the phase-shift and carrier swapping principles for an arbitrary number of levels. We provide an easy and intuitive method for the extraction of the PWM pattern, the switching states, and their sequence. Simulations were carried out in Matlab/Simulink and experimental tests were conducted on a single-phase 7-level GaN inverter prototype. Not only is the extended PWM advantageous in natural balancing, but it also provides the right zero switching states for ac-side FC sensing in active balancing.