南邮电磁场第7章习题解答.doc

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第7章习题解答 7.6 如题7.6图所示相距为的平板金属波导，当时，沿方向可传播TEM模、TE模和TM模。试求：（1）各种模式的场分量；（2）各种模式的传播常数；（3）画出基本模式的场结构及其导体表面的传导电流。解：(1) 各种模式的场分量 对TEM模，在均匀波导横截面上的分布规律与同样边界条件下的二维静态场的分布规律是完全一样的。对静电场情况，无限大平板之间的电场强度为均匀电场，则对应的TEM模中电场为利用平面波电场与磁场关系，即 对TE模，，而满足的导波方程为式中，，则上式变成因此波动方程的解为由时可得到；由时可得到，即。因此式中取决于波源的激励强度。由于波沿着方向传播，则，因此利用各横向场分量与纵向场分量之间关系可以得到 对TM模，，而满足的导波方程为因此波动方程的解为由时可得到；由时可得到，即。因此式中取决于波源的激励强度。利用各横向场分量与纵向场分量之间关系可以得到 (2) 各种模式的传播常数对TEM模的传播常数相位常数：相速：波长：波阻抗：对TE模和TM模的传播常数截止波数、波长、频率：，，相位常数：波导波长：相速度：群速度：波型阻抗： (3) 导体表面的传导电流对于良导体表面的传导电流密度为，其中为导体表面法向方向，或，其中为导体表面的切向磁场。对TEM模，在平面上电流密度为在平面上电流密度为对TE模，在平面上电流密度为在平面上电流密度为对TM模，在平面上电流密度为在平面上电流密度为 7.8 已知空气填充的矩形金属波导()中的纵向场分量为式中，的单位为厘米。指出这是什么模式？写出其余的场分量，并求其和波阻抗。解：我们知道，TM模的纵向场分量为比较题中给出的纵向场分量，可以知道因此这是模。截止波数，因此也即角频率其余分量表示为截止波长波导波长相速度群速度波型阻抗 7.9 已知空气填充的矩形波导()中传播模。测得宽边中心处的最大磁场为，且工作频率为5，写出场分量的表达式。解：对模在宽边中心处，即处，，由此可得场分量的表达式为 7.10 空气填充矩形波导，。（1）当工作波长为6，4和1.8时，可能传播哪些模式？（2）当工作波长为4时，试求其主模的和波阻抗。解：(1) 矩形波导的截止波数和截止波长分别为对TE模，和不能同时为零，也即不存在，最简单的TE模是和模；对TM模，和不能为零，也即不存模在和模，最简单的TM模是模。我们可以利用截止波长分布图来分析波导中各种模式的传播状态。模式 TE10 TE20 TE30 TE01 TE02 TM11 TM21 TM12 …… () 4.56 2.28 1.52 2.03 1.01 2.16 1.52 0.99 …… TE模和TM模的传播模式的条件为。因此当工作波长为6 cm时，不存在传播模式，也即波导中所有模式都截止；当工作波长4.0 cm时，只存在的传播模式为TE10，即单模传播；当工作波长1.8 cm时，存在的传播模式为TE10、TE20、TE01和TM11，即多模传播。 (2) 所谓主模就是截止波长最大的模式，只有主模才能单模传播；对于的矩形波导，模是主模，且 cm。对 cm，和波阻抗分别为相位常数波导波长相速度群速度波阻抗 7.12 当工作频率为15时，取，，可使矩形波导更好地单模传播。试求该波导地宽边和窄边。若在该波导中填充的介质后，其最大的工作频率范围是多少？解：对15的工作频率，其工作波长为。截止波长可以表示为根据题意截止波长最大的模称为主模，截止波长仅小于主模的高次模称为最低型高次模。波导单模工作时，其工作波长必须介于主模的截止波长和最低型高次模的截止波长之间。对于矩形波导()，单模传播条件为时，时，由上述计算出结果可知，，因此最大工作波长范围为最大工作频率范围为 7.14 空气填充圆波导的半径为3。（1）试求模、模、模的截止频率；（2）当工作波长分别为7，6和3时，波导中可以传播哪些模式？（3）试求时，主模的和波阻抗。解：（1）模、模、模的截止波长和截止频率分别为（2）当工作波长分别为7，即时，波导中可以传播和模；当工作波长分别为6，即时，波导中可以传播，和；当工作波长分别为3，即时，波导中可以传播，，，，，，，和模；（3）时，主模模的，于是有波导波长相速度波阻抗 7.15 空气圆波导传播模，工作频率为5。若选取，试求该波导的直径及其各项传播参数。解：因为的截止波长为，所以该波导的半径为各项传播参数为相位常数波导波长相速度群速度波阻抗 7.18 空气填充矩形波导()中传播模，工作频率为20。保持相速不变，将其过渡到圆波导。若圆波导中传播模，试求半径是多少？若圆波导传播模，其半径又该是多少？解：为了使不同传播模式的相速度在同一工作频率时都是相同的，这些传播模式的截止波长就必须是相同的。由此可得，若圆波导中传播模，直径为若圆波导传播模，其半径又该是多少？技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋～12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，1～7栋建筑层数为11层，8～12栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed,5

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