# Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions

- 62 Downloads

## Abstract

This study describes the effect of hysteresis on the generation of the higher harmonics in the line voltage and current in a non-uniform transmission line when we include a quadratic non-linear term having memory to account for the hysteresis effect in the inductance part of line. The simulational analysis using MATLAB is presented which works with a non-uniform line having hysteresis. These simulations are based on a theoretical spatial Fourier analysis combined with perturbation theory which is used without bothering about source and load. The line differential equations are solved approximately in the space- time-frequency domain using perturbation theory and the numerical computations have been carried out for the voltage and current amplitude characteristics. In Appendix 1, some theoretical explanations that support our non-linear memory-based hysteresis model based on Landau’s equation of precession of a magnetic moment in a magnetic field are included. This paper also includes a brief derivation of atomic transition probability produced by e-m radiation from the transmission line falling on an atom in the far field zone. This calculation enables us to derive maximum likelihood estimation(MLE) of the hysteresis parameters by measuring which atomic transitions have occurred.

## Keywords

Non-uniform transmission line Perturbation theory Non-linear hysteresis and memory effect Volterra series Transition probability Quantum mechanical aspects of hysteresis## References

- 1.Khalaj-Amirhosseini, M.: Analysis of periodic and aperiodic coupled nonuniform transmission lines using the fourier series expansion. Prog. Electromagn. Res. PIER
**65**, 15–26 (2006)CrossRefGoogle Scholar - 2.Brachtendorf, H.G., Laur, R.: Simulation of skin effects and hysteresis phenomena in the time domain. IEEE Trans. Magn.
**37**, 3781–3789 (2001)ADSCrossRefGoogle Scholar - 3.Amharech, A., Kabbaj, H.: Wideband impedance matching in transient regime of active circuit using lossy nonuniform multiconductor transmission lines. Prog. Electromagn. Res. C
**28**, 27–45 (2012)CrossRefGoogle Scholar - 4.Shamaileh, K., et al: Non-uniform transmission line ultra-wideband wilkinson power divider. Prog. Electromagn. Res. C
**44**, 1–11 (2013)CrossRefGoogle Scholar - 5.Shamaileh, K.A., Dib, N.: Design of compact dual-frequency wilkinson power divider using non-uniform transmission lines. Prog. Electromagn. Res. C
**19**, 37–46 (2013)CrossRefGoogle Scholar - 6.Khalaj-Amirhosseini, M.: A closed form analytic solution for coupled nonuniform transmission lines. Prog. Electromagn. Res. C
**1**, 95–103 (2008)CrossRefGoogle Scholar - 7.Ghose, R.N.: Exponential transmission lines as resonators and transformerss. IRE Trans. Microwave Theory Tech.
**7**, 213–217 (1957)ADSCrossRefGoogle Scholar - 8.Collin, R.E.: Foundations for Microwave Engineering. Wiley, New York (1996)Google Scholar
- 9.Khalaj-Amirhosseini, M.: Analysis of coupled or single nonuniform transmission lines using Taylor’s series expansion. Prog. Electromagn. Res. PIER
**60**, 107–117 (2006)CrossRefGoogle Scholar - 10.Khalaj-Amirhosseini, M.: Analysis of coupled non-uniform transmission lines using Taylor’s series expansion. IEEE Trans. Electromagn. Compat.
**48**, 594–600 (2006)CrossRefGoogle Scholar - 11.Cheldavi, A., Kamarei, M., Naeini, S.S.: Analysis of coupled transmission lines with power law characterstic impedance. IEEE Trans. Electromagn. Compat.
**42**, 308–312 (2000)CrossRefGoogle Scholar - 12.Cheldavi, A.: Exact analysis of non-uniform transmission lines with exponential power law characteristic impedance. IEEE Trans. Microw. Theory Tech.
**49**, 197–199 (2001)ADSCrossRefGoogle Scholar - 13.Cheldavi, A.: Analysis of coupled Hermite transmission lines, . IEE Proc. Microw. Antennas Propag.
**150**, 279–284 (2003)CrossRefGoogle Scholar - 14.Khalaj-Amirhosseini, M.: Analysis of coupled or single non-uniform transmission lines using step by step numerical integration. Prog. Electromagn. Res.
**58**, 187–198 (2006)CrossRefGoogle Scholar - 15.Yan, H., et al.: Analysis of electromagnetic field coupling to microstrip line connected with non-linear components. Prog. Electromagn. Res. B
**51**, 291–306 (2013)CrossRefGoogle Scholar - 16.Tesche, F.M.: Development and use of the BLT equation in the time domain as applied to a coaxial cable. IEEE Trans. Electromagn. Compat.
**49**, 3–11 (2007)CrossRefGoogle Scholar - 17.Xie, L., Lei, Y.Z.: Transient response of a multiconductor transmission line with nonlinear terminations excited by an electric dipole. IEEE Trans. Electromagn. Compat.
**51**, 805–810 (2009)CrossRefGoogle Scholar - 18.Camassa, R., Findikoglu, A., Lythe, G.: Transmission, reflection, and second-harmonic generation in a nonlinear waveguide. SIAM J. Appl. Math.
**66**, 1–28 (2005)MathSciNetCrossRefMATHGoogle Scholar - 19.Kumar, L., et al.: Effect of non-linear capacitance on a non-uniform transmission line. Eur. Phys. J. Plus
**131**, 159 (2016)CrossRefGoogle Scholar - 20.Landau, L.D., Lifshitz, E.M.: On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sowjetunion
**8**, 101–114 (1935)MATHGoogle Scholar - 21.Parthasarathy, H.: Antennas and Wave Propagation. Ane Books, Delhi (2015)Google Scholar
- 22.Kumar, L., et al.: Quantum-mechanical estimation of rectangular waveguide parameters with atomic entropy computation. Eur. Phys. J. Plus
**132**, 285 (2017)CrossRefGoogle Scholar - 23.Schiff, L.I.: Quantum Mechanics. Tata Mcgraw-Hill Education Private Limited, Delhi (2014)MATHGoogle Scholar