Convergence and stability analysis of a digital automatic gain control

Abstract

This paper is dedicated to the theoretical analysis of a digital automatic gain control (AGC), which feedbacks according to the desired output direct current (DC). First, we mathematically model the AGC, with the input signal interfered by AWGN. As it turns out, the loop model is a first-order varying-coefficient stochastic difference equation, and its solution consists of two parts, that is, the transient state and the steady state, which respectively explain the convergence and stability of the AGC. As is shown in the paper, the properties of convergence and stability of AGC are mutually contradictory, and both are determined by a key parameter in the loop, and the parameter is defined as the feedback sensitivity of the loop. The results of the paper are validated by numerical simulation, and they are of theoretical guide for practical digital AGC implementation on Application Specific Integrated Chips (ASICs) or Field Programmable Gate Arrays (FPGAs). Copyright