The modulation bandwidth of a voltage-controlled oscillator (VCO) is a key design metric that defines its ability to respond to fast tuning voltages and change its frequency accordingly. While prior works have addressed practical methods for measuring it, particularly under sinusoidal excitation, the accuracy of these methods decreases for wideband VCOs due to their inherently nonlinear tuning behavior (i.e., non-constant tuning sensitivity). Our previous work focused on characterizing this bandwidth using periodic linear voltage excitation and presented only measurement results. The current paper significantly extends that study in three major ways. First, we apply FM theory to derive analytical expressions relating the modulation bandwidth to the tuning sensitivity and characteristics of the modulating waveform (i.e., periodic linear voltage excitation). This provides a theoretical framework for understanding the VCO’s behavior under non-sinusoidal excitations which are common in systems such as frequency-hopping transceivers, spread-spectrum clocking, certain phase-locked loops, and FMCW radars. These expressions confirm the dependence of the modulation bandwidth on the tuning sensitivity, VCO linearity and amplitude of the modulating waveform and help guide VCO design for fast signal excitations at the tuning port. Second, we present post-layout simulation results which agree with both theory and measurements, confirming the accuracy of the derived expressions. Third, we present more comprehensive comparisons with recent K-band SiGe BiCMOS VCOs to benchmark this work against state-of-the-art designs.