【作者】 赵伟；

【导师】 赵永久；

【作者基本信息】 南京航空航天大学 ， 通信与信息系统， 2011， 博士

【摘要】 矢量网络分析仪(Vector Network Analyzer, VNA)的发展已有近60年的历史，已成为现代微波测量领域最重要的设备，校准和误差修正是矢量网络分析仪中的关键技术之一。由于任何的测量装置都不可能是理想的，特别是网络分析仪通常都工作在几十MHz到几十GHz的频率范围内，测量装置不可能在如此宽的频率范围内都具有理想的性能和良好的一致性，这些性能上的非理想和非一致性都将导致测量误差。而一味地追求硬件性能上的改进，一方面会造成设计难度的大大增加，另一方面也将使得仪器成本显著提高。因此，一个合理的解决方案就是允许直接的测量结果存在误差，而通过适当的方法得到各项误差并对测量结果进行修正，从而获得准确的测量结果。随着多端口器件在微波毫米波工程中的广泛应用，对多端口网络分析仪的需求不断增加。在利用二端口矢量网络分析仪测量多端口器件时，需要通过多次测量才能得到完整的散射矩阵，由于匹配负载的非理想性以及多次连接的非一致性，都会给测量结果带来误差。相比之下，多端口矢量网络分析仪只需一次连接就能获得完整的网络参数矩阵。但是由于其硬件结构和误差模型的复杂程度远远超过二端口矢量网络分析仪，所以，相应的校准和误差修正更加困难。本文针对n端口矢量网络分析仪(n≥2)的校准技术做了深入研究，主要工作及其创新成果包括：研究了两种三通道二端口矢量网络分析仪校准技术。第一种是基于波传播矩阵的10项误差模型校准技术。校准中不需要计算各个系统误差项，并且可以选择长度未知的50欧姆传输线作为校准件，不仅降低了测试成本，而且简化了校准步骤。第二种是基于引入开关补偿误差的8项误差模型校准技术。通过对考虑开关反射误差的8项误差模型进行深入研究，发现其远不能达到12项误差模型的校准精度，因此从实际的物理情况出发对8项误差模型进行了二次改进，并推导了相应的校准与误差修正公式。提出了三种n端口矢量网络分析仪校准技术。第一种是引入开关补偿误差的4n项误差模型校准技术。该误差模型更加符合实际情况，同时，利用矩阵形式简化了误差修正公式。第二种是基于广义节点方程的n端口矢量网络分析仪校准技术。校准中不仅考虑了串话误差对结果的影响，而且利用3个广义节点方程就可以完整地描述待测件网络参数的真实值与测量值之间的关系，很容易归纳出通用的n端口矢量网络分析仪误差修正公式。第三种是基于广义6项误差模型的n端口矢量网络分析仪校准技术。通过在流图中引入广义节点和广义增益的概念，使本来复杂的3n~2项误差模型在形式上与经典的6项误差模型相同，结合原始测量数据和节点方程，可以容易地计算出多端口待测件网络参数的真实值。讨论了由非理想校准件引入的多端口矢量网络分析仪测量不确定度的计算方法。计算过程只考虑不确定度来源于非理想SOLT校准件，并假设已知校准件的不确定度信息，采用B类评定方法计算出各标准不确定度分量。借助广义节点方程，推导了多端口待测件散射参数真实值(校准值)的偏差与校准件散射参数真实值(标定值)的偏差二者之间的数学关系，最终，可以得到各标准不确定度分量对应的灵敏系数。更多还原

【Abstract】 The vector network analyzer (VNA) has, for almost six decades, found frequent applicationwithin microwave measurement. Calibration and error correction have always been acknowledged tobe one of the key technologies. It is well known that measurement devices can hardly perform ideally,especially for the VNA, which works from several MHz to tens of GHz, the perfect characterizationand excellent consistency can not be achieved within such a wide frequency range, hencemeasurement errors is absolutely inevitable. Therefore, it is not feasible to emphasize improvement ofhardware performance blindly without considering the design difficulty and product costs. Inconclusion, the practical solution is to calibrate the measurement error with proper method toapproach the accurate result.With the frequent application of multiport components in millimeter-wave engineering, thewhole network parameter matrix of the device under test (DUT) can be deduced after severalmeasurements by the two-port VNA, hence will result in calculation complexity and accumulatederror, while with the help of multiport VNA, the whole network parameter matrix can be achievedwith single measurement. Therefore the demand of the multiport VNA increases explosively. However,its hardware structure and error models are more complicated than two-port VNA, hence thecorresponding calibration and error correction is far more difficult. In this paper, calibration methodsare proposed and studied for n-port VNA (n≥2), accordingly the research works and innovations are asfollows.Two calibration techniques for two-port VNA with three measurement channels are studied. Thefirst one is based on the10-term error model using the concept of T-matrix. In the calibrationprocedure the system errors are not required and the length-unknown50transmission line can beused as a calibration standard. By this method the measurement cost is decreased and the calibrationprocess is simplified. The second one is based on8-term error model with the offset error of theswitch. Because the calibration results based on8-term error model only considering the reflectioneffect of the switch are obviously worse than those based on the12-term error model, the8-term errormodel is further modified from the physical situation and corresponding formulas are deduced forcalibration and error correction.Three calibration techniques for n-port VNA are proposed. The first one is based on4n-termerror model with the switch offset error term at each unstimulated port. Fully considering theimperfect switch effect, the new error model is closer to the actual situation. The error correctionequation is also simplified by the matrix operation. The second one is a calibration algorithm based ongeneral node equations. With the crosstalk error term in the error model for high precision, themathematic relationship between calibrated S-parameters and raw S-parameters can be obtained byonly three general node equations. Thus the formula can be easily deduced for error correction. Thethird one is proposed for n-port VNA calibration by the general6-term error model. Using the general6-term error model to describe3n~2-term error model for n-port VNA, the nodes related to unexcitedports are rearranged as the complex vectors and coefficients in signal paths are accordingly replaced by the complex matrixes. From the node equations deduced from the general6-term error model, thescattering parameters of n-port device can be solved by a unified formula.The calculation procedure for the uncertainty of multiport VNA S-parameter measurement due tonon-ideal calibration standards is discussed. Only considering measurement uncertainties come fromnon-ideal SOLT standards, type B standard uncertainty components can be estimated by theuncertainty information of SOLT standards. Based on general node equations, the mathematicrelationship between the deviations of the S-parameters of DUT from their true values and of theS-parameters of non-ideal calibration standards from their ideal values can be got. Finally, thesensitivity coefficients can be obtained for establishing each standard uncertainty component.更多还原