AC amplification circuit is an important type of circuit in electronic engineering, and its basicstructure and parameters have a significant impact on its performance.However, due to the coupling ofcomponent parameters and discontinuity issues in the design of AC amplification circuits,it is difficult toachieve the optimal performance target of the circuit.Therefore , this article presents a parameter optimizationmethod for AC amplification circuits based on Lagrange multipliers.Firstly ,the transfer function equation of theamplification circuit is derived using Kirchhoff's law.Then ,the main parameters of the AC amplifier,includingcenter frequency and amplification factor, are discussed, and finally, the quality factor is derived.Using theLagrange function, the maximum value of the quality factor is obtained under given center frequency andamplification factor,by treating them as constraints and solving for the maximum value of the function underthese two complete constraints.Based on a typical AC amplification circuit system, it explains the parameteroptimization method based on Lagrange multipliers, which provides a theoretical basis for the optimizationdesign of AC amplification circuits.