微波传输线中导体粗糙表面轮廓影响的精确建模

Nowadays in the trend toward miniaturization of microwave components, conductor surface roughness has significant effects on the signal degradation over the wide frequency range from tens of Megahertz to 20+ GHz, or for data rates above 10+Gb/s. Often conductor surface roughness is accounted for using correction factor from the well-known Hammerstad-Bekkadal equation. With a much rougher surface, the equation "saturates" at high frequencies, which leads to an significant error compared to the performance from the actual components . However, the approach of measurement is expensive and time consuming since plenty of samples must be fabricated and measured in extracting the effect of conductor surface roughness. As typical microwave transmission line with broad applications, microstrip and waveguide are used to characterize the effect of conductor surface roughness. The project has two main challenges. Firstly, considering the boundary of conductor surface roughness, the numerical method should be investigated about co-simulating of multiscale structures in solving Maxwell equations; Secondly, the rules of the electrical performance of the microwave transmission with the conductor rough surface are extracted with the results from the numerical simulations. The adapted filament model in frequency domain, hybrid implicit-explicit finite difference time domain method and electromagnetic field integral equations with lossy conductor boundary in closed domain are adopted to modeling the microwave transmission lines with large scales; To modeling the conductor surface roughness in small scales accurately and efficiently in numerical simulation, the period boundary condition from a geometrical view and a layer with an effective lossy dielectric material from a material view are studied. The accurate of the numerical methods are validated with measurements. Based on the simulation results from the numerical methods, the effect of the conductor surface roughness can be separated with the differential extrapolation method, then the modeling of the effect of conductor surface roughness on the electrical parameters of microwave transmission line can be derived. Finally, the physical explanation of the effects of the rough surface can be obtained, and the correction factors for the different electrical parameters of microwave transmission lines due to the surface roughness can be established. With the achievement of accurate modeling of conductor surface roughness, the performance parameters in planar microwave circuits can be modelled accurately, the information of PCB dielectric substrate materials can be characterized over a wide frequency range, the electromagnetic reliability and the age can be improved for the space microwave components, the measurement range of microwave instruments can be extended to more higher frequencies. In summary, the investigations of the project have more potential applications in varied engineering problems.

在微波器件小型化趋势下，随着信号带宽或数字速率的持续增大，导体粗糙表面成为影响微波器件工作性能的重要因素。在高频段时粗糙表面影响趋于显著，传统方法的预估结果和实际器件的电性能相比误差较大；而采用实验测试方法时周期长、成本高。本项目以微带线和闭域波导为模型，考虑导体粗糙表面轮廓，研究多尺度结构共存时Maxwell方程的数值求解问题。采用自适应导体细线模型，混合隐式显式时域有限差分方法和闭域有耗边界条件下的电磁场积分方程实现大尺度微波传输结构建模，采用周期结构和有耗介质材料层等效实现小尺度粗糙导体边界表征。采用微分外推方法提取分离导体粗糙表面对微波传输线电特性的影响关系，并建立导体粗糙表面轮廓对微波传输线电特性参数的影响规律及光滑等效修正关系。导体粗糙表面的精确建模在提高微波电路性能指标、实现PCB板介质材料参数宽带建模、提高空间微波器件工作可靠性和拓宽微波测量仪器量程等问题中具有应用价值。

项目背景：随着器件小型化和频率提高，微波毫米波器件中导体有限电导率，导体表面粗糙对微波器件的电性能影响不容忽视。项目针对微波传输线导体表面粗糙的精确建模和数值计算方法开展研究，提高了微波毫米波器件的建模精度，可应用于微波仪器测量和基板介质材料提取的精度提高。. 研究内容：1. 波导型传输线导体粗糙表面的精确建模。采用坐标变换法、电导率梯度模型等实现了导体粗糙表面的精确建模；采用有限元法、频域有限差分方法、直线法结合等效电导率仿真了波导模型的传输性能参数；利用导体粗糙表面的等效表面阻抗及应用软件可计算谐振腔，滤波器等微波器件的电性能参数。2. 平面传输线导体粗糙表面的精确建模。利用微扰法、电导率梯度模型计算平面传输线导体粗糙表面的等效表面阻抗；利用等效介质层表征导体粗糙表面；利用直线法、频域有限差分方法或应用软件计算平面传输线和平面微波器件的电性能；利用测量结合传输线RLCG理论模型计算了导体粗糙表面影响的修正因子。利用多项式混沌展开计算了传输线加工参数不确定时电性能参数的统计特性。3. 平面传输线基板介质材料参数的提取。利用微分外推方法结合遗传算法提取了宽频带下介质材料参数；利用基片集成波导谐振腔模型，提取了粗糙导体表面的等效电导率，基板介质材料参数。. 重要结果：1. 实现了微波传输线中粗糙导体表面的精确建模，得到了等效电导率和等效表面阻抗；2. 利用直线法、频域有限差分等方法可计算导体粗糙表面时微波传输线的性能参数；3. 宽频带下提取了基板介质的材料参数。研究方法具有通用性，计算精度较高。. 关键数据：微波器件中导体表面粗糙的加工模型数据；导体表面粗糙时的等效电导率和等效表面阻抗；导体表面粗糙时微波传输线传播参数；平面传输线基板介质材料参数的提取数据。. 科学意义：项目研究方法对微波毫米波器件的精确建模具有通用性，对研究器件加工参数对其电性能影响具有科学意义，提高了宽带下材料参数的提取精度。