Bandpass filter induced by imaginary resistance in the low-pass discrete electrical transmission lattice

Abstract

We examine a discrete low-pass electrical line in presence of imaginary resistance. The linear lattice is analyzed both from direct Kirchhoff law and classical points of view. The direct Kirchhoff law allows obtaining a linear Schrödinger equation which mimics quantum physics. From this point of view, it has been found that the imaginary resistance transforms the non-hermitian Hamiltonian due to the loss of pseudo-hermitian ones. The energy spectrum shifts from the low to the passband. The angular frequency is identical to the energy spectrum of the direct Kirchhoff law. The full integration of the lattice confirms the phase shift of the dispersion relation due to the imaginary resistance with the localization of the wave with a frequency equal to the cutoff frequency of the low pass filter and the propagation of the nonlinear voltage with the same frequency for different values of imaginary resistance.