Design and Simulation of Sine-Gordon Lattice System
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The sine-Gordon equation is one of the nonlinear and integrable partial differential equations that can be solved exactly and has soliton solution. This equation was first introduced for Josephson junction propagation and has been applied to many other scientific fields. Based on three discretized forms of the sine-Gordon equation, i.e. conventional discrete sine-Gordon equation, Orfanidis’s discrete sine-Gordon equation and sine-lattice equation, we create and simulate three sine-Gordon lattice systems. By taking the difference between the adjacent outputs as the transmitting soliton signal, it is shown that all three systems could propagate the bell-shaped signal constantly and the sine-lattice equation system gives the best results. Due to the low-voltage, low-power feature, we choose the MOS translinear circuit that exploits bulk voltages under weak inversion to realize the sine function in the sine-Gordon lattice system and the complete circuit of the sine-Gordon cell is also created utilizing this MOS translinear sin(x) circuit.