Abstract: 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.

Key words: carbon nanotubes, structural parameter, equivalent transmission line, dielectric property, complex permittivity