We constructed a coupled LC transmission line and studied the propagation of waves in it. We found asymmetric energy flow when we changed the driving conditions at the boundary. We analyzed this change and believe that it occurs because of the bandpass characteristics of the LC transmission line and high-order harmonic waves induced by nonlinearities. The LC transmission line could be used to simulate a microscopic crystal lattice. Therefore, we hope to observe thermal rectification in the system. We investigated the dependence of the system on different parameters, and then discussed the multi-frequency condition to aid in experimental verification. For numerical simulations of a coupled 1D lattice, it has been found that energy can flow through the channel from the high-temperature thermal bath to the lower-temperature bath in one direction. However, the lattice behaves as an insulator if the thermal baths are swapped. An experiment using a nanotube has shown this behavior with a 7% difference between heat fluxes in the two opposite directions [3]. However, nanotubes are not strictly 1D lattices in reality. In fact, we should be able to observe this abnormal phenomenon in experiments based on a macroscopic 1D lattice, which has the similar governing equations as the microscopic crystal lattice. In a macroscopic system, the energy of vibration (phonon) of each lattice can be measured directly. There are many types of macroscopic 1D lattice models, for example, pendulum chains [4] and nonlinear LC transmission lines [5]. While taking into account effect of thermal baths, we used the LC transmission line as our investigation model. The realization of random vibrations is much simpler to achieve with an electrical signal than in a mechanical system. In this work, we present a study of the propagation of waves in two coupled LC transmission lines, in which one line exhibits nonlinear transmission [5] and the other line is linear. First, we investigated monofrequency driving through numerical simulation and looked for possible abnormal energy transmission. Then we further discus multi-frequency driving (thermal bath) to aid ensuring experimental realization.
Coupled LC transmission lineThe coupled LC transmission line that we studied contains two sub-lines (Lines a and b), which have the same structure but different parameters. They are coupled by an inductor, L int . This is shown in Figure 1. Each cell of the transmission lines has the usual form [6], which consists of one capacitor and two inductors. In Line a, the capacitor is nonlinear. A variable capacitance diode, BB112, working at a DC voltage near V d =2.0 V, serves as the nonlinear capacitor. If |V n |<2.0 V, the capacitance is related to the AC voltage V n as follows [6]: