Optimizing compact Marx generator networks

Buchenauer, C.J.

doi:10.1109/ppc.2009.5386290

Cited by 7 publications

(22 citation statements)

References 2 publications

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“…These waveform symmetry requirements are summarized in Table 1 and were established during earlier work on optimizing Marx generator networks [1], [2]. They apply to the transformation of stored energy, either purely electrostatic or purely magnetic, into a different configuration of either purely electrostatic or purely magnetic stored energy [6].…”

Section: Network and Waveform Symmetriesmentioning

confidence: 99%

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Dispersionless charge transfer on lumped-element transmission lines synthesized via resonant frequency assignment

Buchenauer

2015

2015 IEEE Pulsed Power Conference (PPC)

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The uniform lumped element transmission line that exhibits translational symmetry is an inherently dispersive network. The dispersion properties can be transformed by imposing a harmonic symmetry that requires all of the resonant frequencies of the network to be integral multiples of some fundamental frequency. The resulting line will have spatially varying component values, thus breaking the network's translational symmetry. If mirror symmetry is imposed on the line such that right and left sides of the line have identical components, the natural resonant modes of the line will then be either spatially even or spatially odd. The even harmonic frequencies may be assigned to the spatially even modes, and the odd harmonic frequencies may be assigned to the spatially odd modes by methods similar to those used for Marx networks [1], [2], [3], [4]. The resulting network can then be shown to have several important properties: (a) All voltages and currents will be periodic in time with the fundamental period. (b) Starting with zero initial currents and finite charge voltages, the mirror image of the initial conditions on each side of the line will appear on the opposite sides at odd multiples of the half period. (c) A similar result can be stated when starting with zero initial voltages and finite initial currents.While many solutions can be found, the smoothly varying regular solution is of special interest. It possesses the property of having relatively spatially uniform impedance with a cutoff frequency that decreases away from the line center. Thus, higher frequency waves, which travel more slowly, are reflected further from the ends of the line, such that any narrow-band wave packet is reflected periodically without dispersing.This network may be used for efficiently transporting capacitive stored energy on ordinary transmission lines. The lumped-element line is cut at the symmetry plane, and an arbitrary length of conventional transmission line of appropriate impedance is inserted in the gap. Discharging the end capacitor into the resulting network generates a Gaussian-like pulse on the transmission line that is later converted to the identical capacitive charge on the network at the other end of the line.

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Section: Network and Waveform Symmetriesmentioning

confidence: 99%

“…Once conditions for conserving energy and charge are satisfied, ideal network designs often reduce to some form of resonant-frequency assignment [1]. Thus, this inherently time domain problem is recast as a problem in the frequency domain.…”

Section: Periodic Symmetrymentioning

confidence: 99%

Dispersionless charge transfer on lumped-element transmission lines synthesized via resonant frequency assignment

Buchenauer

2015

2015 IEEE Pulsed Power Conference (PPC)

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“…Following [1,35,6], the inductance and capacitor appearing in the rightmost loop take the values nℓ and c/n, respectively. We call this capacitor the "load capacitor".…”

Section: Marx Generator Design 21 Circuit Description and Problem Stmentioning

confidence: 99%

“…Marx generators (see [5, §3.2] or [7] for an overview) were originally described by E. Marx in 1924 and correspond to circuits enabling generation of high voltage from lower voltage sources. While many schemes have been proposed over the years for Marx generators, a recent understanding of certain compact Marx generators structures [6] reveals that their essential behavior can be well described by a suitable LC ladder network where certain components should be designed in order to guarantee a suitable resonance condition. In turn, such a resonance condition is known to lead to a desirable energy transfer throughout the circuit and effective voltage multiplication which can then be used for pulsed power generation.…”

Section: Introductionmentioning

confidence: 99%

“…In turn, such a resonance condition is known to lead to a desirable energy transfer throughout the circuit and effective voltage multiplication which can then be used for pulsed power generation. This paper addresses the mathematical problem of designing the lumped components of the compact Marx generator circuit well described in [6] and represented in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

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Design of Marx generators as a structured eigenvalue assignment

et al. 2014

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We consider the design problem for a Marx generator electrical network, a pulsed power generator. The engineering specification of the design is that a suitable resonance condition is satisfied by the circuit so that the energy initially stored in a number of storage capacitors is transferred in finite time to a single load capacitor which can then store the total energy and deliver the pulse. We show that the components design can be conveniently cast as a structured real eigenvalue assignment with significantly lower dimension than the state size of the Marx circuit. Then we comment on the nontrivial nature of this structured real eigenvalue assignment problem and present two possible approaches to determine its solutions. A first symbolic approach consists in the use of Gröbner basis representations, which allows us to compute all the (finitely many) solutions. A second approach is based on convexification of a nonconvex optimization problem with polynomial constraints. We show that the symbolic method easily provides solutions for networks up to six stages while the numerical method can reach up to seven and eight stages. We also comment on the conjecture that for any number of stages the problem has finitely many solutions, which is a necessary assumption for the proposed methods to converge. We regard the proof of this conjecture as an interesting challenge of general interest in the real algebraic geometry field.

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Measurement of Transition Frequency of Composite Transmission Line Model

Xia

Yao

et al. 2011

2011 Asia-Pacific Power and Energy Engineering Conference

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Optimizing compact Marx generator networks

Cited by 7 publications

References 2 publications

Dispersionless charge transfer on lumped-element transmission lines synthesized via resonant frequency assignment

Dispersionless charge transfer on lumped-element transmission lines synthesized via resonant frequency assignment

Design of Marx generators as a structured eigenvalue assignment

Measurement of Transition Frequency of Composite Transmission Line Model

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