碳纳米管是一种应用非常广泛的电磁材料，研究其复介电常数的计算不仅能了解其介电性能规律，而且对材料的设计具有重要意义。基于碳纳米管的等效传输线模型，建立了微波场作用下多壁碳纳米管管壁间电容和量子电容的联接模型,推导了多壁碳纳米管等效传输线的阻抗公式。基于复电导率与复合材料阻容网络模型，建立了多壁碳纳米管复合材料复介电常数的计算公式。根据所得结论，模拟计算了2~18GHz频率下，管长为20μm、管外径分别为25、40、70nm的碳纳米管复合材料的相对复介电常数，以及管外径为20nm，管长分别为60、100μm、 厚度为4mm的碳纳米管复合涂层的微波反射损耗，结果与文献实验值能较好吻合；计算结果也表明，随碳纳米管管径、管长增大，其相对复介电常数的虚部均增大，而且管长对相对复介电常数的影响明显大于管径。

Carbon nanotubes (CNTs) is widely used as electromagnetic materials. Study on the calculation of complex permittivity of carbon nanotubes not only can make us understand the characteristics of the dielectric properties of CNTs materials, but also has an important significance for material design. Based on the equivalent transmission line model of CNTs, the connection model of the wall capacitance and quantum capacitance of multi-walled carbon nanotubes (MWCNTs) in the microwave field was established, and the impedance expression of MWCNTs equivalent transmission line was derived. Based on the complex conductivity and the resistance capacitance network model of composite materials, the analytical expression of complex permittivity of MWCNTs composites was established. The complex permittivity of CNTs composites with the tube length of 20μm, the pipe outer diameter of 25nm, 40nm and 70nm respectively ,and the microwave reflection loss of CNTs coating with the pipe outer diameter of 20nm, the tube length of  60μm, 100μm respectively,  and the thickness of 4mm were calculated with this analytical expression at the frequency of 2~18GHz. The calculated results are well agreed with the experimental results in reference. The calculation results also show that the imaginary part of the complex permittivity increases with the increase of the diameter and the length of the CNTs, and the effect of the tube length on the complex permittivity is greater than that of the tube diameter.