Funnel Resonance Theory: An Impedance-Matching Framework for Advertising Conversion Optimization

<div> This paper introduces Funnel Resonance Theory, a cross-disciplinary framework demonstrating that effective advertising conversion capacity is bounded not by budget allocation, but by the intersection of audience segments addressed across sequential funnel stages. Drawing on impedance mismatch theory from electrical engineering, we define a reflection coefficient for each stage boundary, quantifying traffic structurally unable to convert. Under independent stage targeting, the conversion-eligible population shrinks multiplicatively, establishing an audience intersection bound independent of spend. Applying resonance physics, simultaneous alignment across stages produces nonlinear conversion amplification described by a Lorentzian response function, with a Q-factor quantifying alignment precision. </div> <div> Meta-analytic evidence (751 econometric estimates) confirms average advertising elasticity of 0.12, while alignment interventions produce 47–212% conversion improvements at zero incremental spend. The Price of Anarchy bounds the cost of siloed funnel management; Braess's Paradox proves that adding channels without coordination can worsen performance. </div>