Introduction To Modern Planar Transmission Lines - Anand K. Verma

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is images. For ωC = 0 also, the above equations are reduced to equations (3.4.17) and (3.1.18). Therefore, above the cut‐off frequency, i.e. for ω > ωc, the inductive loading of the transmission line shown in Fig (3.29) supports the backward slow‐wave outside the light cone and the backward fast‐wave within the light cone. Its dual structure, shown in Fig (3.27a), always supports the forward fast‐wave.

      Series Capacitor Loaded LC‐Line

Schematic illustration of series capacitor loaded L C-line.

      (3.4.23)equation

      The propagation constant of the capacitor loaded LC‐line is

      where the phase velocity of the unloaded LC‐line is images. The cut‐off frequency of the loaded line is images. For ω > ωc, the line behaves as the HPF. In absence of the series capacitance Cs loading, the line behaves like the LPF. The series‐arm impedance is capacitive at a frequency below cut‐off, i.e. for ω < ωc. The circuit of Fig (3.30) is reduced to the C‐C line, i.e. a line with capacitive elements in both the series and shunt arms. It corresponds to the mu‐negative (MNG) medium discussed in the section (5.5) of chapter 5. The C‐C line blocks the low‐frequency signal. Therefore, for the frequency ω < ωc, the propagation is in the evanescent mode with high attenuation. The phase and group velocities of the propagating waves are obtained as

      Additional numbers of configurations for the loaded transmission lines could be obtained. For instance, the L‐C section of a line, supporting the forward wave, could be cascaded with the C‐L section of a line, supporting the backward wave. The composite line forms an interesting kind of the transmission line structure [B.19, J.8]. Both the series and parallel reactive loading of the lines can be done. Such loaded line structures have been realized in the planar technology to obtain novel properties useful for the development of novel microwave devices. They form the so‐called metamaterials. The concept of metamaterials has been introduced in chapter 5 and elaborated in chapter 21. Chapter 22 considers the planar 1D‐metalines and 2D‐planar metasurfaces, and chapter 19 discusses the planar periodic transmission lines.

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