# Nonlinear analysis of PLL by the harmonic balance method

## TL;DR

This paper explores the use of the harmonic balance method for analyzing the global stability and pull-in range of classical PLL circuits, highlighting its advantages and limitations.

## Contribution

It applies the harmonic balance method to classical PLL analysis, providing insights into stability and solution existence without rigorous proofs.

## Key findings

- Harmonic balance offers a practical approach for PLL analysis.
- The method helps estimate the pull-in range.
- Limitations include lack of rigorous justification.

## Abstract

In this paper we discuss the application of the harmonic balance method for the global analysis of the classical phase-locked loop (PLL) circuit. The harmonic balance is non rigorous method, which is widely used %,often without rigorous justification, for the computation of periodic solutions and the checking of global stability. The proof of the absence of periodic solutions is a key step to establish the global stability of PLL and estimate the pull-in range (which is an interval of the frequency deviations such that any solution tends to one of the equilibria). The advantages and limitations of the study of the classical PLL with lead-lag filter using the harmonic balance method is discussed.