diff options
Diffstat (limited to 'OSCAD/LPCSim/report/simulationReport.tex')
| -rw-r--r-- | OSCAD/LPCSim/report/simulationReport.tex | 173 |
1 files changed, 173 insertions, 0 deletions
diff --git a/OSCAD/LPCSim/report/simulationReport.tex b/OSCAD/LPCSim/report/simulationReport.tex new file mode 100644 index 0000000..2e06242 --- /dev/null +++ b/OSCAD/LPCSim/report/simulationReport.tex @@ -0,0 +1,173 @@ +\documentclass[a4paper,10pt]{report} +\pagestyle{plain} +\usepackage{graphicx} +\usepackage{caption} +\usepackage{algorithmic} +% Title Page +\title{Half-Wave Rectifier} +\author{Generated by SMCSim} + +\begin{document} +\maketitle +\hrule\vspace{5mm} +\begin{center} {\bf Simulation of ckt/HWRectifierFilter.ckt} \end{center} +\hrule\vspace{5mm} + +{\bf Circuit Diagram:} \\ +\vspace{2mm} +\hrule\vspace{5mm} + +{\bf NetList:} \\ +{\it * Half-Wave Rectifier} \\ +V1 1 0 sine (5 50) \\ +D1 1 2 mymodel (1e-8 0.026) \\ +R1 2 0 10000 \\ +C1 2 0 10e-3 \\ +.tran 0 100 0.5 \\ +.plot v(1) v(2) \\ +.end +\vspace{2mm} +\hrule\vspace{5mm} + +{\bf System of Equations representing the electrical circuit:} +\vspace{2mm} +\begin{equation} + i_{V_1} + D_{1f}(v_1,v_2) = 0 +\end{equation} +\begin{equation} + (R_1)v_2 + (C_1)\frac{dv_2}{dt} + -D_{1f}(v_1,v_2) = 0 +\end{equation} +\begin{equation} + v_1 = V_1 +\end{equation} +\vspace{2mm} +$$ D_{nf}(v_a,v_b)=Is_n(1-e^{(v_a-v_b)/vt_n})$$ + where $Is_n$=reverse saturation current and $vt_n$=threshold voltage of diode $n$\\ +\hrule\vspace{5mm} + +{\bf Matrix form:}\\ +The system of equations $\mathbf{A}\mathbf{x}+\mathbf{D}_f(\mathbf{\widehat{x}})+\mathbf{C}(d\mathbf{x}/dt)=b$ (Symbolically)\\ +Where $\mathbf{A}$, $\mathbf{D}_f$ and $\mathbf{C}$ represent matrices corresponding to linear, + nonlinear and time dependent electrical elements respectively. + $\mathbf{b}$ represents the vector corresponding to sources. + +\begin{equation} +\mathbf{A}= +\left[ +\begin{array}{ccc} +0 &0 &1 \\ +0 &\widehat{R}_1 &0 \\ +1 &0 &0 +\end{array} +\right] +\end{equation} +\begin{equation} +\mathbf{b}= +\left[ +\begin{array}{c} +0 \\ +0 \\ +V_1 +\end{array} +\right] +\end{equation} +\begin{equation} +\mathbf{D}_f= +\left[ +\begin{array}{c} +D_{1f} \\ +-D_{1f} \\ +0 +\end{array} +\right] +\end{equation} +\begin{equation} +\mathbf{C}= +\left[ +\begin{array}{ccc} +0 &0 &0 \\ +0 &C_1 &0 \\ +0 &0 &0 +\end{array} +\right] +\end{equation} +\begin{equation} +\mathbf{x}= +\left[ +\begin{array}{c} +v_1 \\ +v_2 \\ +i_{V_1} +\end{array} +\right] +\end{equation} +\begin{equation} +\mathbf{\widehat{x}}= +\left[ +\begin{array}{c} +(v_1,v_2) +\end{array} +\right] +\end{equation} +Note that the matrix contains $\widehat{R}$ entries (corresponding to resistors) whose values are equal to 1/$R$\\ +\hrule\vspace{2mm} +The number of equations are $3$ \\ +Unknowns: \\ + Node potentials: $2$ Current Variables: $1$ \\ +\hrule\vspace{5mm} + +{\bf Operating Point (DC) Analysis: } \\ +{\it All capacitors are open circuited and inductors are short circuited.} +\vspace{2mm} + +{\bf System of Equations representing the electrical circuit:} +\begin{equation} + i_{V_1} + D_{1f}(v_1,v_2) = 0 +\end{equation} +\begin{equation} + (R_1)v_2 + -D_{1f}(v_1,v_2) = 0 +\end{equation} +\begin{equation} + v_1 = V_1 +\end{equation} +\vspace{2mm} +$$ D_{nf}(v_a,v_b)=Is_n(1-e^{(v_a-v_b)/vt_n})$$ + where $Is_n$=reverse saturation current and $vt_n$=threshold voltage of diode $n$\\ +\hrule\vspace{5mm} + +{\bf Application of Newton-Raphson method: }\\ +\vspace{2mm} +{\it Nonliner models: }\\ +See linearized model for diode $D_1$ in diode\_D1.eps +\begin{figure}[h] +\centering +\includegraphics{diode_D1.eps} +\caption{linearization of diode $D_1$} +\end{figure} +\vspace{2mm} + +{\bf System of Equations representing the electrical circuit:}\\ +\begin{equation} + (R_{D_1})v_1 + (-R_{D_1})v_2 + i_{V_1} = -i_{D_1} +\end{equation} +\begin{equation} + (R_{D_1})v_1 + (R_{D_1}+R_1)v_2 = i_{D_1} +\end{equation} +\begin{equation} + v_1 = V_1 +\end{equation} +\hrule\vspace{5mm} + +{\bf Transient Analysis:} \\ +\hrule\vspace{5mm} + +{\bf Results:} \\ +\begin{figure}[h] +\centering +\includegraphics[scale=0.5]{output.eps} +\caption{plot} +\end{figure} + + +\end{document} + |