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

## 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.

- Authors:

- National Institute of Technology, Department of Electronics and Communication Engineering (India)
- National Institute of Technology, Department of Physics (India)
- Netaji Subhas Institute of Technology, Division of Electronics and Communication Engineering (India)
- G.B. Pant Engineering College, Department of Electronics and Communication Engineering (India)

- Publication Date:

- OSTI Identifier:
- 22771303

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Superconductivity and Novel Magnetism

- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 5; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; Article Copyright (c) 2017 Springer Science+Business Media, LLC; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1557-1939

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; ELECTRIC CURRENTS; ELECTRIC POTENTIAL; ENERGY-LEVEL TRANSITIONS; FOURIER ANALYSIS; HARMONIC GENERATION; HYSTERESIS; INDUCTANCE; MAGNETIC FIELDS; MAGNETIC MOMENTS; MAXIMUM-LIKELIHOOD FIT; NONLINEAR PROBLEMS; PERTURBATION THEORY; PRECESSION; QUANTUM MECHANICS

### Citation Formats

```
Kumar, L., E-mail: lalitkumar-khanna@yahoo.com, Pandey, V. Shankar, Parthasarathy, H., and Shrimali, V.
```*Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions*. United States: N. p., 2018.
Web. doi:10.1007/S10948-017-4368-Y.

```
Kumar, L., E-mail: lalitkumar-khanna@yahoo.com, Pandey, V. Shankar, Parthasarathy, H., & Shrimali, V.
```*Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions*. United States. doi:10.1007/S10948-017-4368-Y.

```
Kumar, L., E-mail: lalitkumar-khanna@yahoo.com, Pandey, V. Shankar, Parthasarathy, H., and Shrimali, V. Tue .
"Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions". United States. doi:10.1007/S10948-017-4368-Y.
```

```
@article{osti_22771303,
```

title = {Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions},

author = {Kumar, L., E-mail: lalitkumar-khanna@yahoo.com and Pandey, V. Shankar and Parthasarathy, H. and Shrimali, V.},

abstractNote = {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.},

doi = {10.1007/S10948-017-4368-Y},

journal = {Journal of Superconductivity and Novel Magnetism},

issn = {1557-1939},

number = 5,

volume = 31,

place = {United States},

year = {2018},

month = {5}

}