SIMULATION OF THERMAL EFFECTS IN OPTOELECTRONIC DEVICES USING COUPLED ENERGY-TRANSPORT AND CIRCUIT MODELS

2008 ◽  
Vol 18 (12) ◽  
pp. 2125-2150 ◽  
Author(s):  
MARKUS BRUNK ◽  
ANSGAR JÜNGEL
Keyword(s):  
Laser Diode ◽  
Energy Transport ◽  
Semiconductor Devices ◽  
Differential Algebraic Equations ◽  
Transport Equations ◽  
Hole Density ◽  
Algebraic Equations ◽  
Pass Filter ◽  
Electric Circuits ◽  
Photo Diode

A coupled model with optoelectronic semiconductor devices in electric circuits is proposed. The circuit is modeled by differential-algebraic equations derived from modified nodal analysis. The transport of charge carriers in the semiconductor devices (laser diode and photo diode) is described by the energy-transport equations for the electron density and temperature, the drift-diffusion equations for the hole density, and the Poisson equation for the electric potential. The generation of photons in the laser diode is modeled by spontaneous and stimulated recombination terms appearing in the transport equations. The devices are coupled to the circuit by the semiconductor current entering the circuit and by the applied voltage at the device contacts, coming from the circuit. The resulting time-dependent model is a system of nonlinear partial differential-algebraic equations. The one-dimensional transient transport equations are numerically discretized in time by the backward Euler method and in space by a hybridized mixed finite-element method. Numerical results for a circuit consisting of a single-mode heterostructure laser diode, a silicon photo diode, and a high-pass filter are presented.

Multirate partial differential algebraic equations for simulating radio frequency signals

2007 ◽  
Vol 18 (6) ◽  
pp. 709-743 ◽  
Author(s):  
ROLAND PULCH ◽  
MICHAEL GÜNTHER ◽  
STEPHANIE KNORR
Keyword(s):  
Radio Frequency ◽  
Time Scales ◽  
Differential Algebraic Equations ◽  
Fast Time ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Electric Circuits ◽  
Transient Behaviour ◽  
Partial Differential Algebraic Equations ◽  
Radio Frequency Signals

In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and frequency may change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. We outline the theory of this multivariate approach with respect to the simulation of amplitude as well as frequency modulated signals. Furthermore, a survey of numerical methods for solving the arising problems of MPDAEs is given.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

scholarly journals Memristors as Candidates for Replacing Digital Potentiometers in Electric Circuits

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 181
Author(s):  
Ivo Marković ◽  
Milka Potrebić ◽  
Dejan Tošić
Keyword(s):  
Phase Shifter ◽  
Voltage Divider ◽  
Frequency Characteristics ◽  
Phase Shifters ◽  
Pass Filter ◽  
Electric Circuits ◽  
Digital Potentiometer ◽  
Memristive Circuits ◽  
Parasitic Effects ◽  
Additional Level

Digital potentiometers are substantial components for the design of many mixed-signal electronic circuits and systems. Their capability to program resistance value almost instantly provides hardware designers an additional level of freedom. Unfortunately, this feature is limited to DC and lower frequencies, due to parasitic effects. Nowadays, memristors as continuously tunable resistors are becoming candidates for potentiometer successors. Memristors are two-terminal non-volatile devices which have less significant parasitic effects and a wide resistance range. The memristance value can be changed on the fly. Using nanotechnology, memristor implementation has a nanoscale footprint with nanosecond transition between resistive states. In this paper, we present a comparison between the frequency characteristics of digital potentiometers and the only commercially available memristors. Memristor parasitic effects dominate at higher frequencies which extends the bandwidth. In order to present the advantages of memristive circuits, we have analyzed and implemented tunable circuits such as a voltage divider, an inverting amplifier, a high-pass filter, and a phase shifter. A commercially available memristor by KnowM Inc. is used for this purpose. Experimental results obtained by the measurements verify that a memristor has equal or better characteristics than a digital potentiometer. Memristive realizations of voltage dividers and inverting amplifiers have a wider bandwidth, while filters and phase shifters with a memristor have almost identical frequency characteristics as the corresponding realizations with a digital potentiometer.

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