现代通信系统中，微波双工器是重要组成部件之一，用于信道的选择和信道分离与合成，广泛应用于微波通信、卫星通信、遥测遥控，其性能优劣将直接影响整个通信系统的质量。随着微波技术的迅速发展，频谱日益拥挤，高性能滤波器、双工器在微波与无线通信系统应用中显得日益重要。高选择性、小尺寸、通带内低插入损耗、低成本等指标的严格限制，推动着微波滤波器设计方法和物理结构的深入研究。 在传统切比雪夫滤波器基础上，引入交叉耦合技术，构成广义切比雪夫滤波器。它可以在阻带产生有限传输零点，提高滤波器的带外抑制并减少滤波器的阶数。 本文详细介绍了广义切比雪夫滤波器组成双工器的原理,研究了与广义切比雪夫滤波器相关的理论。介绍广义切比雪夫多项式的推导，从等效电路模型入手提取广义切比雪夫滤波器全耦合矩阵。详细论述了常见的交叉耦合拓扑结构产生传输零点的原因及零点的分布，利用梯度优化算法优化出预设拓扑结构滤波器的耦合矩阵并采用Matlab实现。最后设计了一个特高频频段800MHz的同轴腔体双工器,利用三维电磁场仿真软件HFSS对双工器收发端滤波器的谐振频率、耦合系数、外部品质因数进行了仿真，从而确定双工器的物理尺寸,并给出了双工器的等效电路仿真图。最后研制出该款双工器，测试数据表明该双工器具有高选择性、高隔离度、低插入损耗等优点，测试指标均满足指标需求,已成功应用于某微波无线通信系统中。

Microwave diplexers are very a important part of modern communication system, and usually select and join channel. So they are generally used in microwave communication, satellite communication and remote sensing system. With the rapid development of microwave technology, the microwave communication frequency resources are becoming precious and crowded. The high performance microwave filters and diplexers have played more important roles in the microwave and wireless communication system. The high performance of high selectivity, small size, low inserts loss and low cost accelerate development of filter design and physical structure. The generalized Chebyshev filter which was composed by traditional Chebyshev filter and cross coupling technology can produce finite transmission zeros in filter stopband. This technology can increase stopband attenuation and reduce filter order. The issue expatiatory introduces theory about diplexers composed by Chebyshev filters, and research theory about Chebyshev filter, and also deduces the Chebyshev polynomial. The full coupling matrix of filter was calculated from equivalent circuit model of filter. The usual filter topology structure and the distribution of their transmission zeros were simply introduced. The procedure deduced the coupling matrix of filters which were prescribed in advance by using gradient-based Optimization technique. And all the steps were programmed by Matlab language. Using the above synthesis design a coaxial cavity diplexers working in 800MHz. Using 3D electromagnetism software HFSS simulates resonant frequency of diplexer’s receive/transmit filter, coupling coefficients of each two resonator, and external quality factor. It is easy to make sure the diplexer physical structure and dimension form above steps. And the simulation result of equivalent circuit is given. Finally, the diplexer was manufactured and tested. The test data shows the diplexer has high selectivity, small size and low inserts loss. The example is reported which validates the proposed synthesis procedure. At last, the diplexer has been successfully used in a microwave wireless communication system.