**8. Conclusion**

*7.3.2. Frequency multiplier*

Generally to raise the frequency in electronic systems, it is necessary to use oscillators which present increasingly raised (brought up) frequencies of vibration. Since a few years, the NLTL combined with an amplifier, which amplifies the signals stemming from the noise of the electronics.

**Figure 23.** Compression of a signal effect observed in the cell 101 (full lines) for an input signal of sinusoidal form

*f* = 169.4 KHz frequency and amplitude V = 1.75 V (dashed), polarization of the line voltage is V0 = 1.5 V.

**Figure 22.** Evolution of a solitary wave sech2 profile in the bi-inductance line. Note the conservation of cohesion of the

wave; the decrease amplitude is due to losses by Joule effect and the presence of the oscillatory tail.

180 Advanced Electronic Circuits - Principles, Architectures and Applications on Emerging Technologies

We present in this work a selection of experimental results which we reached and which concerns essentially the system of study of our choice, worth knowing, the electrical nonlinear transmission line.

We notice that our experimental device was proved to be a powerful tool of work characterized by its flexibility and its robustness. Qualities essentially owed to our strategic choice who allowed us to make our investigations on sections of lines in the modest size by comparison to other systems constituted by hundreds or even thousands of cells. This arrangement also allowed us to reduce considerably the sources of drift or of artifacts, which increase with the number of components of the line.

From the point of view of the experimental results, we determined, at first, experimentally the dispersion curve of the line by an original method, which consists of determining the phase velocity of the wave between two consecutive cells. We determine the dispersion curve with a very good precision.

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We proof the reality of the transmission of the waves in electrical lines not shelf spaces. We observed the effects of the waste and the dispersion of the waves. On the other hand, even our device was not designed and optimized to produce certain effects on the signals; we observed the modification of the shape of the signals like the compression of signal and the multiplication (increase) of frequency.

Finally, it is recognized today unanimously that the nonlinear physics was born with the remarkable work of Fermi, Pasta, and Ulam, who concerned an abstract system and the study which was made by numeral calculation, the collection what it was advisable today to call the FPU recurrence is a constant current events whatever is the system. We observed the FPU recurrence in the NLTL in BF mode and in HF mode. Hence, we brought a completely original explanation that gets off the beaten track.

The device carried out during this work makes possible to carry out in future work on the investigations on the nonlinear transmission lines and on the dynamics of the solitary waves in various applications as: characterization of the periodical loaded transmission lines, use of the nonlinear reactance of thin layers superconductive, resolution of the Ginzburd-Landau equations for a tangential magnetic field, supraconductivity in the forbidden band in a bimodal nonlinear system; and so on.
