scholarly journals Derivation, Design and Simulation of the Zeta converter

2021 ◽  
Author(s):  
Asger Bjørn Jørgensen
Keyword(s):  
Fourth Order ◽  
Engineering Students ◽  
Electrical Engineering ◽  
Second Order ◽  
Component Sizing ◽  
Converter Topologies ◽  
Converter Topology ◽  
Detailed Derivation ◽  
Conduction Mode ◽  
Continuous Conduction Mode

The purpose of this paper is to guide electrical engineering students from analysing basic DC-DC converter topologies to more advanced topologies. Textbooks and free online papers include the derivation of second order DC-DC topologies such as buck, boost and buck-boost, while fourth order such as the Zeta converter are not as readily available as open knowledge online. This paper provides a detailed derivation of the Zeta converter topology in continuous conduction mode (CCM), it presents an example of component sizing and verifies the design by simulation in LTspice.<br>

scholarly journals Derivation, Design and Simulation of the Zeta converter

2021 ◽  
Author(s):  
Asger Bjørn Jørgensen
Keyword(s):  
Fourth Order ◽  
Engineering Students ◽  
Electrical Engineering ◽  
Second Order ◽  
Component Sizing ◽  
Converter Topologies ◽  
Converter Topology ◽  
Detailed Derivation ◽  
Conduction Mode ◽  
Continuous Conduction Mode

The purpose of this paper is to guide electrical engineering students from analysing basic DC-DC converter topologies to more advanced topologies. Textbooks and free online papers include the derivation of second order DC-DC topologies such as buck, boost and buck-boost, while fourth order such as the Zeta converter are not as readily available as open knowledge online. This paper provides a detailed derivation of the Zeta converter topology in continuous conduction mode (CCM), it presents an example of component sizing and verifies the design by simulation in LTspice.<br>

scholarly journals Derivation, Design and Simulation of the Single-Ended Primary-Inductor Converter (SEPIC)

2019 ◽  
Author(s):  
Asger Bjørn Jørgensen
Keyword(s):  
Power Electronics ◽  
Fourth Order ◽  
Engineering Students ◽  
Circuit Simulation ◽  
Second Order ◽  
Power Supplies ◽  
Boost Converters ◽  
Switch Mode ◽  
Converter Topologies ◽  
Detailed Derivation

The purpose of the paper is to guide engineering students and ease their transition from the most basic DC-DC converter topologies to more advanced types. The buck, boost and buck-boost converters are the usual suspects in textbooks and engineering classes to introduce students to the basics of power electronics and switch mode power supplies. There is a gap of how detailed such second order DC-DC converters are described and the more advanced fourth order such as the Cuk, Zeta and Single-Ended Primary-Inductor Converter (SEPIC). This paper gives a detailed derivation of the equations governing the SEPIC. An example of sizing of components is presented for a range of input voltages and power levels. Finally the design is verified by a circuit simulation using LTSpice.

scholarly journals Integrity basis for a second-order and a fourth-order tensor

1982 ◽  
Vol 5 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Josef Betten
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Tensor Function ◽  
Order Tensor ◽  
Isotropic Tensor ◽  
Anisotropic Properties ◽  
Isotropic Tensor Function ◽  
Fourth Order Tensor

In this paper a scalar-valued isotropic tensor function is considered, the variables of which are constitutive tensors of orders two and four, for instance, characterizing the anisotropic properties of a material. Therefore, the system of irreducible invariants of a fourth-order tensor is constructed. Furthermore, the joint or simultaneous invariants of a second-order and a fourth-order tensor are found. In a similar way one can construct an integrity basis for a tensor of order greater than four, as shown in the paper, for instance, for a tensor of order six.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

Sign in / Sign up

Export Citation Format

Share Document