Extremely wideband signal shaping using one- and two-dimensional nonuniform nonlinear transmission lines

Abstract

We propose a class of electrical circuits for extremely wideband ͑EWB͒ signal shaping. A one-dimensional, nonlinear, nonuniform transmission line is proposed for narrow pulse generation. A two-dimensional transmission lattice is proposed for EWB signal combining. Model equations for the circuits are derived. Theoretical and numerical solutions of the model equations are presented, showing that the circuits can be used for the desired application. The procedure by which the circuits are designed exemplifies a modern, mathematical design methodology for EWB circuits.

Management of localized energy in discrete nonlinear transmission lines

“…The extensive theoretical and experimental work in this area focuses on the continuum-like soliton properties of nonlinear transmission lines [19][20][21][22][23][24][25][26]. Over the last decade two experimental studies have examined strongly localized excitations that require the discreteness of the nonlinear transmission line.…”

Ultrafast analog Fourier transform using 2-D LC lattice

“…Replace by and by , where and are, respectively, inductance and capacitance per unit length. Assuming that and stay constant in the limit, we arrive at the continuum dispersion relation (5) which is the exact dispersion relation for the scalar wave equation (6) In previous derivations [1], we started with (3), then posited a continuous function such that , expanded and in Taylor series about , and thereby derived precisely the same PDE model (6). The derivation of (6) as a continuum model of (3) on the basis of exact/approximate dispersion relations has its own utility, as we now show.…”

“…1, are a natural generalization of 1-D transmission lines. In our earlier work [1], general models for 2-D LC lattices were derived, starting from Kirchhoff's laws of voltage and current. These models consist of partial differential equations (PDEs) arising from continuum and quasi-continuum limits, which are valid for signals with frequency content below a certain threshold value.…”

“…In earlier work [1], the continuum limit of (3) was derived using standard Taylor series arguments. In the case of a uniform lattice, one can arrive at a continuum limit by examining the dispersion relation, a procedure we now describe.…”

Compact-Like Pulse Signals in a New Nonlinear Electrical Transmission Line

“…The development in NLTLs has demonstrated its capacity to work as signal processing tools [2,17]. To cite only a few examples, it has been demonstrated that the nonlinear uniform electrical line can be used: for extremely wide band signal shaping applications [18], for waveform equalizer in the compensation scheme for signal distortion caused by optical fibre polarisation dispersion mode [19], for doubling repetition rate of incident pulse streams [20] and in the scheme for controlling the amplitude (amplification) and the delay of ultra-short pulses through the coupled propagation of the solitonic and dispersive parts, which is important in that it enables the characterization of high-speed electronic devices and raises the possibility of establishing future ultra-high signal processing technology [21]. So, the emergence of compactons in nonlinear lattices can be a spring towards the important improvement of practical results concerning the distortion-less signal in ultrahigh-speed signal processing tools and in electronic devices where they may be used to codify data.…”