About the Phasor Pathways in Analogical Amplitude Modulation

TL;DR

This paper explores the geometric patterns formed by phasor diagrams in analog amplitude modulation, revealing various algebraic curves and their dependence on modulation parameters.

Contribution

It introduces a detailed analysis of phasor pathways in amplitude modulation, deriving diverse algebraic curves and clarifying the influence of modulation index and frequency ratios.

Findings

Identifies multiple algebraic curves in phasor pathways.

Shows how modulation index affects geometric figures.

Analyzes effects of frequency ratio on pattern shapes.

Abstract

The Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard Amplitude Modulation Systems (e.g. A3E, H3E, J3E, C3F). A cornucopia of algebraic curves is then derived assuming a single tone or a double tone modulation signal. The ratio of the frequency of the tone modulator (fm) and carrier frequency (fc) is considered in two distinct cases, namely: fm/fc<1 and fm/fc>=1. The geometric figures are some sort of Lissajours figures. Different shapes appear looking like epicycloids (including cardioids), rhodonea curves, Lemniscates, folium of Descartes or Lam\'e curves. The role played by the modulation index is elucidated in each case.