The implementation of novel, stable, accurate, and wideband infinite impulse response fractional order microwave integrators (FOMIs) is presented. The formulation of FOMIs is employed with equal length line elements in cascading. The optimum values of characteristic impedances of the line elements are determined by approximation to the ideal fractional order integrator (FOI). The hybrid algorithm (HPSO‐GSA) combining particle swarm optimization (PSO) and gravitational search algorithm (GSA) which integrates PSO's exploitation and GSA's exploration ability is used. The comparison of HPSO‐GSA with PSO and GSA is carried out for the proposed FOMIs. The performance criteria used are magnitude response, absolute magnitude error, phase response, pole‐zero response, percentage improvement graph, and convergence rate. The simulation analysis affirms the superiority of proposed FOMI using HPSO‐GSA. The absolute magnitude error of proposed 0.5 order HPSO‐GSA‐based FOMI is as low as 0.9436. The structure of the designed FOI is implemented with microstrip configuration on RT/Duroid substrate with permittivity 2.2 and thickness 0.762 mm that is eligible for wideband microwave integrator. The designed FOMI is compact in size and suitable to cover microwave applications. The measured results are established in fine agreement with simulation results in the frequency range of 2‐9 GHz in MATLAB and Advanced Design Software environment.

中文翻译：

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紧凑型分数阶微波积分器的优化设计与实现

提出了新颖，稳定，准确和宽带无限脉冲响应分数阶微波积分器（FOMI）的实现。FOMI的公式在级联中使用等长的线元素。线元素的特征阻抗的最佳值是通过逼近理想的分数阶积分器（FOI）来确定的。使用结合了粒子群优化（PSO）和重力搜索算法（GSA）的混合算法（HPSO-GSA），该算法融合了PSO的开发和GSA的探索能力。对提议的FOMI进行了HPSO-GSA与PSO和GSA的比较。使用的性能标准是幅度响应，绝对幅度误差，相位响应，零极点响应，百分比改进图和收敛速度。仿真分析证实了使用HPSO-GSA提出的FOMI的优越性。建议的基于0.5阶HPSO‐GSA的FOMI的绝对幅度误差低至0.9436。设计的FOI的结构是在RT / Duroid基板上以微带结构实现的，其介电常数为2.2，厚度为0.762 mm，适合宽带微波积分器。设计的FOMI尺寸紧凑，适用于微波应用。在MATLAB和Advanced Design Software环境中，在2-9 GHz频率范围内的仿真结果与测量结果完全吻合。设计的FOI的结构是在RT / Duroid基板上以微带结构实现的，其介电常数为2.2，厚度为0.762 mm，适合宽带微波积分器。设计的FOMI尺寸紧凑，适用于微波应用。在MATLAB和Advanced Design Software环境中，在2-9 GHz频率范围内的仿真结果与测量结果完全吻合。设计的FOI的结构是在RT / Duroid基板上以微带结构实现的，其介电常数为2.2，厚度为0.762 mm，适合宽带微波积分器。设计的FOMI尺寸紧凑，适用于微波应用。在MATLAB和Advanced Design Software环境中，在2-9 GHz频率范围内建立的测量结果与仿真结果完全吻合。