基于拉格朗日乘子的交流放大电路参数优化方法  

Optimizing Parameters of AC Amplification Circuit Based on Lagrange Multiplier

作　　者：蒋乐群 陈冰雪 褚良宇 李青青 赵梦浩 李泓钢 洪葳 JIANG Lequn;CHEN Bingxue;CHU Liangyu;LI Qingqing;ZHAO Menghao;LI Honggang;HONG Wei(MOE Key Laboratory of Fundamental Physical Quantities Measurement&Hubei Key Laboratory of Gravitation and Quantum Physics,PGMF and School of Physics,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学物理学院,精密重力测量国家重大科技基础设施,基本物理量测量教育部重点实验室,引力与量子物理湖北省重点实验室,湖北武汉430074

出　　处：《大学物理实验》2023年第6期6-10,22,共6页Physical Experiment of College

基　　金：国家自然科学基金(52275056);华中科技大学教学研究项目(2018096);基础学科拔尖学生培养计划2.0研究课题(20212067)。

摘　　要：交流放大电路是电子工程中重要的一类电路,它的基本结构和参数对于其工作性能有着重要的影响。然而由于交流放大电路设计中存在元器件参数耦合以及不连续问题,导致电路设计无法达到最优性能,即品质因数不能取最大值。为此提出了一种基于拉格朗日乘子的交流放大电路参数优化方法。首先介绍了采用基尔霍夫定律推导放大电路的传递函数方程。随后讨论了交流放大器的主要参数,包括中心频率和放大倍数,最终推导出品质因数。最后,使用拉格朗日函数来求解在给定中心频率和放大倍数下品质因数的最大值问题,即通过将中心频率和放大倍数视为约束,在这两个完整约束下求解函数的最大值。基于典型交流放大电路系统地阐述了基于拉格朗日乘子的参数优化方法,为交流放大电路的优化设计提供了理论基础。AC amplification circuit is an important type of circuit in electronic engineering,and its basic structure and parameters have a significant impact on its performance.However,due to the coupling of component parameters and discontinuity issues in the design of AC amplification circuits,it is difficult to achieve the optimal performance target of the circuit.Therefore,this article presents a parameter optimization method for AC amplification circuits based on Lagrange multipliers.Firstly,the transfer function equation of the amplification circuit is derived using Kirchhoff's law.Then,the main parameters of the AC amplifier,including center frequency and amplification factor,are discussed,and finally,the quality factor is derived.Using the Lagrange function,the maximum value of the quality factor is obtained under given center frequency and amplification factor,by treating them as constraints and solving for the maximum value of the function under these two complete constraints.Based on a typical AC amplification circuit system,it explains the parameter optimization method based on Lagrange multipliers,which provides a theoretical basis for the optimization design of AC amplification circuits.

关 键 词：交流放大器电路 基尔霍夫定律 传递函数 中心频率 放大倍数 品质因数 拉格朗日函数乘子法 

分 类 号：O41[理学—理论物理]