Unity-Based Auto-Limiting Oscillators: From Power-Ratio Feedback to Trigonometric Normalisation

Abstract

We introduce a family of digital oscillators whose amplitude is stabilised by enforcing algebraic identities of the form f (ratio) = 1. Three variants are detailed: (i) the Power- Unit Oscillator (PUO) based on multiplicative ratio-power feedback, (ii) the Trigonometric Normalisation Oscillator (TNO) exploiting the identity sin2 θ + cos2 θ = 1, and (iii) the Product-Unit Oscillator (PrUO) that jointly limits several modes via a single unity product. All designs achieve sub-0.001% total harmonic distortion (THD) with only one or two multiplications per sample, making them ideal for micro-controllers, FPGA soft-cores and low-power audio synthesis.