Analytical method of triplate transmission lines configuration
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摘要: 在考虑不等宽度三平板传输线的极板边缘效应和极板厚度的条件下，建立了单位长度电容、特性阻抗和各位置电场强度幅值的解析求解方法。该方法利用保角变换，将三平板传输线的不规则场边界变换为规则边界，所得结果是不带有任何近似的准确值。该方法计算结果与利用商业软件Ansoft进行模拟所得结果一致，证明该方法正确且可行。Abstract: Triplate transmission line is widely used in huge pulsed power facilities. However, the accurate circuit parameters of the triplate transmission line are difficult to obtain because of three factors. The first one is that the widths of the anode and cathode plates are different, the second one is that the plates’ thickness cannot be ignored, and the third one is that the electromagnetic field near the edges of the plates is seriously distorted. Taking all these three factors into consideration, an analytical method was established to obtain the capacitance per meter, the characteristic impedance, and the electric field magnitudes of the triplate transmission line. In this method, the distorted boundaries are transformed into regular boundaries based on conformal mapping and accurate results are obtained without approximation. Results obtained by this method are the same as those obtained by electromagnetic simulation with a commercial code called Ansoft, which indicates the correctness of this method.
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图 1 大型脉冲功率装置中的三板线示意图
Figure 1. Triplate transmission lines in huge pulsed power facilities
图 3 三板线的保角变换过程
Figure 3. Processes of conformal mapping of the triplate transmission line
图 4 解析方法得到的三个不同模型z平面实轴上各点的电场强度幅值
Figure 4. Electric field magnitudes of three different models obtained by analytical method
图 5 Ansoft模拟得到的三个不同模型z平面实轴上各点的电场强度幅值
Figure 5. Electric field magnitudes of three different models obtained by Ansoft simulation
表 1 三个阴阳极板间距不同的三平板传输线模型的单位长度电容C和特性阻抗Z0计算结果
Table 1. C and Z0 of three different triplate transmission lines with different distances between the anodes and cathodes
model h1/m h2/m d1/m d2/m d3/m C/nF Z0/Ω analytical method Ansoft analytical method Ansoft 1 1.0 2.0 0.1 4.0 4.1 1.85 1.86 16.0 15.9 2 1.0 2.0 0.1 3.0 3.1 2.18 2.19 13.5 13.5 3 1.0 2.0 0.1 2.0 2.1 2.81 2.81 10.5 10.5 
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