Frequency Dependence of Bloch Impedance in Left-Handed Transmission Line

In this study, the frequency dependence of Bloch impedance in a left-handed transmission line (LH-TL) is investigated using the F-matrix formulation and Bloch-Floquet theorem. The artificial LH-TL formed by periodic lumped elements is described and then the F-matrix and Bloch impedance are formulated according to this description. The numerical results are provided to understand the behaviour of Bloch impedance in LH-TL. Although LH materials have been extensively analyzed in literature, there is no work which directly relates to Bloch impedance of LH-TL. The analysis is structured in two main steps; firstly the concept of artificial LH-TL formed from composite periodic structure is presented. Then, F (ABCD)-matrix parameters for the unit-cell of artificial LH-TL are derived. The formulation of the frequency dependence of Bloch impedance is determined using F-matrix with the Bloch-Floquet theorem and the constructed model. The numerical investigation for the frequency dependence of Bloch impedance in a LH-TL is considered for the application of the theoretical formulation. It is seen that numerical results support the theoretical formulation found which is successfully applied to calculate the frequency responses of Bloch impedance. By using these results the behaviour of Bloch impedance on LH-TL can easily be investigated and the cut-off frequency and the stop band region are observed. The effect of the unit cell numbers to the cot-off and stop band region is also analysed. The theoretical and numerical results obtained here can easily be extended for further studies especially for periodic structures.