Harmonic-Assisted Parametric Excitation in Coupled Resonant Systems: Theory and Experimental Validation

The classical mass–spring–damper and inductor–capacitor–resistor analogy is extended from constant to state-dependent parameters and connected to an experimentally realized coupled Metglas AMCC-1000 resonant magnetic system. The formulation distinguishes externally varying inductance from intrinsic magnetic nonlinearity through secant and differential inductance and incorporates reversible, dissipative, and externally driven dynamics. The experimental study combines coupled-mode design with synchronized voltage and RF-current measurements. Measured component values establish a 32.016/16.461 kHz resonant pair with a frequency ratio of 1.9449, while calibrated RF-probe analysis quantifies the corresponding current components and broadband measurements reveal higher harmonic structure. A complementary 11–13 kHz controlled frequency sweep was performed at fixed 22 V, 388 mA supply conditions and 18% duty cycle. Coherent least-squares analysis identifies a common maximum of the second-order component at an 11.5 kHz drive frequency in two voltage channels and the RF-current channel, with A(2fd)/A(fd) ratios of 0.809, 0.870, and 3.665, respectively. The associated trigger-origin-invariant harmonic phase relation provides complementary phase-domain evidence of an organized frequency-selective nonlinear response. The results establish a reproducible connection between state-dependent oscillator theory, coupled-resonator design, and experimentally measurable harmonic dynamics.