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Date: Tue, 9 Sep 2014 16:11:17 +0530
Subject: Subject: Changing all content and name of directory and file to
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Description: The content of file,name of directory and file has been
changed in the below format.

1. Oscad to FreeEDA
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-%$Header: /cvsroot/latex-beamer/latex-beamer/solutions/generic-talks/generic-ornate-15min-45min.en.tex,v 1.4 2004/10/07 20:53:08 tantau Exp $
-\documentclass{beamer}
-\mode<presentation>
-{
-  \usecolortheme{seahorse}
-  \usefonttheme{professionalfonts}
-  \useinnertheme{rounded}
-  \useoutertheme{shadow}
-%  \useoutertheme{smoothbars}
-}
-%\setbeamertemplate{background canvas}[vertical shading][bottom=white!10,top=blue!5]
-\usepackage{verbatim} 
-\usepackage[english]{babel}
-\usepackage[latin1]{inputenc}
-\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
-\usepackage{amsmath,amsfonts,amsthm,amssymb}
-\usepackage{times}
-\usepackage[T1]{fontenc}
-\usepackage{graphics}
-\usepackage{graphicx}
-%\usepackage{psfig}
-\usepackage{algorithmic}
-
-\title
-{Scilab based Mini Circuit Simulator for Academic Purpose}
-
-\author[]
-{Yogesh Dilip Save}
-\institute
-{
-  Indian Institute of Technology, Bombay
-}
-%\pgfdeclareimage[height=0.7cm]{university-logo}{iitblogo.eps}
-%\logo{\pgfuseimage{university-logo}}
-
-
-\date[seminar] % (optional)
-{\today}
-
-
-\begin{document}
-%***************************************************************************************
-\begin{frame}
-  \titlepage
-\end{frame}
-%***************************************************************************************
-\begin{frame}
-  \frametitle{Presentation Outline}
-  \tableofcontents
-\end{frame}
-%***************************************************************************************
-
-\section{Introduction}
-\begin{frame}
- \frametitle{Motivation}
-\begin{block}{Objective}
-To assist students in improving their knowledge in field of circuit simulation.
-\end{block}
-\begin{block}{Problem with commercial simulators}
-\begin{itemize}
-\item Generally software codes are not available.
-\item Software codes are written in higher level language (C Programming and Fortran....).
-\item Complex due to implementation of many features and complex modeling.
-\end{itemize}
-\end{block}
-\end{frame}
-
-\begin{frame}
- \frametitle{Motivation}
-\begin{block}{Objective}
-To assist students in improving their knowledge in field of circuit simulation.
-\end{block}
-\begin{block}{Mini simulator}
-\begin{itemize}
-\item used Scilab for coding.
-\item integrated least number of component.  
-\item different versions for add-on features. 
-\end{itemize} 
-\end{block}
-\end{frame}
-
-\begin{frame}
- \frametitle{Plan}
-\begin{block}{Display Symbolic Equations}
-\end{block}
-\begin{block}{Display Numerical Values}
-\end{block}
-\begin{block}{Complete Report Generation}
-\end{block}
-\begin{block}{GUI for circuit drawing}
-\end{block}
-\begin{block}{GUI for simulator option}
-\end{block}
-\begin{block}{Spoken Tutorial}
-\end{block}
-%\begin{block}
-%\begin{itemize}
-%\item Display Numerical Values  
-%\item Complete Report Generation
-%\item Graphical User Interface
-%\item Spoken Tutorial 
-%\end{itemize} 
-%\end{block}
-\end{frame}
-
-\begin{frame}
- \frametitle{Core of circuit simulator}
-\begin{itemize}
-\item Operating Point Analysis plays an important role in a circuit simulation. 
-\item DC Analysis is equivalent to performing OP Analysis at each voltages/currents. 
-\item Transient Analysis is equivalent to performing OP Analysis at each time step.  
-\item AC Analysis computes the small-signal behavior of a circuit about an operating point 
-\item Thus implementation of Operating Point Analysis affects overall performance of the circuit simulator.
-\end{itemize} 
-\end{frame}
-
-\section{Operating Point Analysis}
-\begin{frame}
-\begin{block}{Operating Point (OP) Analysis}
-\begin{itemize}
-\item OP Analysis is the central part of a circuit simulator.
-\item The equations that describe the electrical system are nonlinear and algebraic and their solution gives operating point.
-\item Systems of nonlinear equations are solved by iteratively formulating and solving systems of linear algebraic equations. 
-\item The overall efficiency of a circuit simulator is dependent upon the performance of the linear DC analyzer.
-%\item Thus, our work is towards improving the performance of linear DC Analyzers and handling convergence issues related to large size nonlinear circuits.
-\end{itemize}
-\end{block}
-\end{frame}
-
-\begin{frame}
-\begin{block}{Circuit with linear elements}
-\end{block}
-\end{frame}
-
-\begin{frame}
-\begin{block}{\small Nodal Analysis}
-\begin{itemize}
-\begin{small}
-\item Applicable when the network has only current sources and conductances type devices i.e., $i=g(v)$.
-\item Let, $\mathbf{A}_r$ be the reduced incidence matrix of $\cal{G}$ which is a representative matrix of $V_v(\cal{G})$. \\
-\end{small}
-\begin{tiny}
-The KCL constraints are
-$$\mathbf{A_ri}=\mathbf{0}$$
-$$\left[\begin{array}{cc}
-  \mathbf{A}_{rG} & \mathbf{A}_{rJ}
-\end{array}\right]
-\left[\begin{array}{c}
-  \mathbf{i}_{G} \\
-  \mathbf{i}_{J}
-\end{array}\right]
-=\mathbf{0}$$
-$$\mathbf{A}_{rG}\mathbf{i}_{G}=-\mathbf{A}_{rJ}\mathbf{i}_{J}$$
-
-$$\mathbf{A}_{rG}\mathbf{G}\mathbf{v}_{G}=-\mathbf{A}_{rJ}\mathbf{i}_{J}\ \ \ \ \ \ \ \ (As, \mathbf{i}_{G}=\mathbf{G}\mathbf{v}_{G})$$
-
-The KVE constraints are
-$$\left[\begin{array}{c}
-  \mathbf{v}_{G} \\
-  \mathbf{v}_{J}
-\end{array}\right]
-=
-\left[\begin{array}{c}
-  \mathbf{A}_{rG}^T \\
-  \mathbf{A}_{rJ}^T
-\end{array}\right]
-\mathbf{v}_n$$
-
-\begin{equation}
-\mathbf{A}_{rG}\mathbf{G}\mathbf{A}_{rG}^{T}\mathbf{v}_{n}=-\mathbf{A}_{rJ}\mathbf{i}_{J}
-\label{nodal_equation}
-\end{equation}
-\end{tiny}
-\end{itemize}
-\end{block}
-\end{frame}
-
-\begin{frame}[fragile]
-\begin{block}{Matrix Formulation}
-\begin{itemize}
-\item The diagonal entries of the matrix are the sum of conductances incident on the corresponding nodes.
-\item The off diagonal entries $(i,j)^{th}$ of the matrix is the negative of conductances between node $i$ and $j$.
-\item The $\mathbf{A}_{rJ}\mathbf{i}_{J}$ is the sum of current sources leaving the nodes.
-\end{itemize}
-\end{block}
-\begin{block}{Example}
-\end{block}
-\begin{minipage}[!b]{0.4\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.35]{../figures/nodal_figure.eps}
-\end{figure}
-\end{minipage}
-\begin{minipage}[!b]{0.55\linewidth} % A minipage that covers half the page
-\begin{tiny}
-$$\left[
-\begin{array}{ccc}
-\widehat{R}_{1}+\widehat{R}_{2} & -\widehat{R}_{2} & 0\\
--\widehat{R}_{2} & \widehat{R}_{2}+\widehat{R}_{3}+\widehat{R}_{4} & -\widehat{R}_{4}\\
-0 & -\widehat{R}_{4} & \widehat{R}_{4}+\widehat{R}_{5}
-\end{array}
-\right] \left[
-\begin{array}{c}
-v_{1}\\
-v_{2}\\
-v_{3}
-\end{array}
-\right]= \left[
-\begin{array}{c}
-I_{1}\\
-0\\
-I_{2}
-\end{array}
-\right]$$
-\end{tiny}
-\end{minipage}
-\tiny $$\mbox{Note that } \widehat{R}=1/R$$
-\tiny \href{run:../../LPCSim_1.0/ckt/nodalExample.ckt}{\color{red} Click here to see the example}
-\end{frame}
-
-
-\begin{frame}
-\begin{block}{Modified Nodal Analysis}
-\begin{small}
-\begin{itemize}
-\item applicable to all kinds of networks.
-\item Let $\mathbf{A}_{r}$ be the reduced incidence matrix of ${\cal{G}}$
-By Tellegan's theorem,
-\begin{tiny}
-$$\mathbf{A_ri}=\mathbf{0}$$
-$$\left[\begin{array}{ccc}
-  \mathbf{A}_{rG} & \mathbf{A}_{rT} & \mathbf{A}_{rJ}
-\end{array}\right]
-\left[\begin{array}{c}
-  \mathbf{i}_{G} \\
-  \mathbf{i}_{T} \\
-  \mathbf{i}_{J}
-\end{array}\right]
-=\mathbf{0}$$
-
-$$\left[\begin{array}{cc}
-  \mathbf{A}_{rG}\mathbf{G} & \mathbf{A}_{rT}
-\end{array}\right]
-\left[\begin{array}{c}
-  \mathbf{v}_{G} \\
-  \mathbf{i}_{T}
-\end{array}\right]
-=-\mathbf{A}_{rJ}\mathbf{i}_{J}$$
-
-\begin{equation}
-\label{mna_eq1}
-\left[\begin{array}{cc}
-  \mathbf{A}_{rG}\mathbf{G}\mathbf{A}_{rG}^{T} & \mathbf{A}_{rT}
-\end{array}\right]
-\left[\begin{array}{c}
-  \mathbf{v}_{n} \\
-  \mathbf{i}_{T}
-\end{array}\right]
-=-\mathbf{A}_{rJ}\mathbf{i}_{J}
-\end{equation}
-
-Device characteristics of the branches in $T$ be
-$$\left[\begin{array}{cc}
-  \mathbf{M} & \mathbf{N}
-\end{array}\right]
-\left[\begin{array}{c}
-  \mathbf{i}_{T} \\
-  \mathbf{v}_{T}
-\end{array}\right]
-=\mathbf{S}_{T}$$
-
-\begin{equation}
-\label{mna_eq2}
-\left[\begin{array}{cc}
-  \mathbf{NA}_{rT}^{T} & \mathbf{M}
-\end{array}\right]
-\left[\begin{array}{c}
-  \mathbf{v}_{n} \\
-  \mathbf{i}_{T}
-\end{array}\right]
-=\mathbf{S}_{T}
-\end{equation}
-\end{tiny}
-\end{itemize}
-\end{small}
-\end{block}
-\end{frame}
-
-\begin{frame}
-\begin{block}{Example}
-\begin{figure}[!ht]
-\begin{center}
-\includegraphics[scale=0.35]{../figures/modified_figure.eps}
-\caption{ Example for MNA } \label{modifiedfig}
-\end{center}
-\end{figure}
-\begin{tiny}
-$$\left[
-\begin{array}{cccccc}
-\widehat{R}_{1}+\widehat{R}_{4} & -\widehat{R}_{1} & -\widehat{R}_{4} & 1 & 0 \\
--\widehat{R}_{1} & \widehat{R}_{1}+\widehat{R}_{2}+\widehat{R}_{3} & -\widehat{R}_{3} & 0 & 0 \\
--\widehat{R}_{4} & -\widehat{R}_{3} & \widehat{R}_{3}+\widehat{R}_{4} & 0 & 1  \\
-1 & 0 & 0 & 0 & 0 \\
-0 & 0 & 1 & 0 & 0
-\end{array}
-\right] \left[
-\begin{array}{c}
-v_{1}\\
-v_{2}\\
-v_{3}\\
-i_{V_1}\\
-i_{V_2}\\
-\end{array}
-\right]= \left[
-\begin{array}{c}
-0\\
-0\\
-0\\
-V_{1}\\
-V_{2}
-\end{array}
-\right]$$
-\end{tiny}
-\tiny $$\mbox{Note that } \widehat{R}=1/R$$
-\tiny \href{run:../../LPCSim_1.0/ckt/modifiedNodalExample.ckt}{\color{red} Click here to see the example}
-\end{block}
-\end{frame}
-
-\begin{frame}
-\frametitle{Controlled Sources}
-\begin{minipage}[!b]{0.47\linewidth} % A minipage that covers half the page
-  \begin{figure}[!ht]
-      \centering
-      \includegraphics[scale=0.6]{../figures/VCCS.eps}
-      \caption{\scriptsize Voltage Controlled Current Source (VCCS)}
-      \label{vccs}
-  \end{figure}
-\end{minipage}
-%\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.47\linewidth}
-  \begin{figure}[!ht]
-     \centering
-      \includegraphics[scale=0.6]{../figures/VCVS.eps}
-      \caption{\scriptsize Voltage Controlled Voltage Source (VCVS) }
-      \label{vcvs}
-  \end{figure}
-    \end{minipage}
-\begin{minipage}[!b]{0.47\linewidth} % A minipage that covers half the page
-  \begin{figure}[!ht]
-      \centering
-      \includegraphics[scale=0.6]{../figures/CCCS.eps}
-      \caption{\scriptsize Current Controlled Current Source (CCCS)}
-      \label{cccs}
-  \end{figure}
-\end{minipage}
-%\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.47\linewidth}
-  \begin{figure}[!ht]
-     \centering
-      \includegraphics[scale=0.6]{../figures/CCVS.eps}
-      \caption{\scriptsize Current Controlled Voltage Source (CCVS) }
-      \label{ccvs}
-  \end{figure}
-    \end{minipage}
-\begin{scriptsize}
-\begin{itemize}
-\item In voltage controlled devices, we have added a $0A$ current source as controlling branch
-%without disturbing the incidence relationship of existing edges (i.e., the addition is 'soldering type') and its voltage is used for calculating the value of the devices.
-\item In current controlled devices, we have added a $0V$ voltage source as controlling branch
-%by splitting a node (i.e., plier type entry) and the current through it is used for calculating the value of the devices.
-\end{itemize}
-\end{scriptsize}
-\end{frame}
-
-\begin{frame}
-\begin{block}{Example with controlled sources}
-\begin{figure}[!ht]
-\begin{center}
-\includegraphics[scale=0.6]{../figures/linearckt.eps}
-\caption{ \scriptsize Example with controlled source (MNA)} \label{modifiedfig}
-\end{center}
-\end{figure}
-\begin{tiny}
-$$\left[
-\begin{array}{ccccccc}
-\widehat{R}_{1} & -\widehat{R}_{1} & 0 & 0 & 0 & 1 & 0 \\
--\widehat{R}_{1} & \widehat{R}_{1}+\widehat{R}_{2} & 0 & 0 & 0 & 0 &1\\
-0 & 0& \widehat{R}_{4} & -\widehat{R}_{4}-g_1 & 0 & 0 & -1  \\
-0 & 0& -\widehat{R}_{4} & \widehat{R}_{3}+ \widehat{R}_{4}+\widehat{R}_{5} &-\widehat{R}_{5}  & 0 & 0  \\
-0 & 0& 0 &g_1-\widehat{R}_{5} & \widehat{R}_{5}+\widehat{R}_{6} & 0 & 0   \\
-1 & 0 & 0 & 0 & 0 &0 &0\\
-0 & 1 & -1 &-e1 &e1 &0 & 0
-\end{array}
-\right] \left[
-\begin{array}{c}
-v_{1}\\
-v_{2}\\
-v_{3}\\
-v_{4}\\
-v_{5}\\
-i_{V_1}\\
-i_{E_1}\\
-\end{array}
-\right]= \left[
-\begin{array}{c}
-0\\
-0\\
-I_1\\
-0\\
-0\\
-V_{1}\\
-0
-\end{array}
-\right]$$
-\end{tiny}
-\tiny $$\mbox{Note that } \widehat{R}=1/R$$
-\tiny \href{run:../../LPCSim_1.0/ckt/linear1.ckt}{\color{red} Click here to see the example}
-\end{block}
-\end{frame}
-
-\begin{frame}
-\begin{block}{Example with controlled sources-2}
-\begin{figure}[!ht]
-\begin{center}
-\includegraphics[scale=0.6]{../figures/linearckt2.eps}
-\caption{ \scriptsize Example2 with controlled source (MNA)} \label{modifiedfig}
-\end{center}
-\end{figure}
-\begin{tiny}
-$$\left[
-\begin{array}{cccccc}
-\widehat{R}_{1}+\widehat{R}_{2} & -\widehat{R}_{2} & 0 & 0 & 0 &0\\
--\widehat{R}_{2} &\widehat{R}_{2}+\widehat{R}_{4} &0& -\widehat{R}_{4} & 1 & 0  \\
-0 & -\widehat{R}_{4} & 0 & \widehat{R}_{4} & 0  & 1  \\
-0 & 1& -1 &0 & 0 & 0   \\
-0 & 0 & 0 & 1 & -h_1 &0 
-\end{array}
-\right] \left[
-\begin{array}{c}
-v_{1}\\
-v_{2}\\
-v_{3}\\
-v_{4}\\
-i_{V_1}\\
-i_{H_1}\\
-\end{array}
-\right]= \left[
-\begin{array}{c}
-I_1\\
-0\\
-0\\
-0\\
-V_{1}\\
-0
-\end{array}
-\right]$$
-\end{tiny}
-\tiny $$\mbox{Note that } \widehat{R}=1/R$$
-\tiny \href{run:../../LPCSim_1.0/ckt/linear2.ckt}{\color{red} Click here to see the example}
-\end{block}
-\end{frame}
-
-\begin{frame}
-\frametitle{Circuit with nonlinear elements}
-Simulation of circuit with nonlinear element is done in two steps:
-\begin{itemize}
-\item Formulating the nonlinear equilibrium equations using topological constraints (i.e., KCE, KVE).
-\item Solving these equations using appropriate numerical technique.
-\end{itemize} 
-Newton-Raphson method -- Numerical technique to solve nonlinear equations
-\begin{itemize}
-\item fast convergence rate
-\item needs good initial guess
-\item does not guaranteed to converge
-\item slower when multiple solution
-\end{itemize}
-\end{frame}
-
-\begin{frame}
-\frametitle{Linearization of Nonlinear Elements}
-\begin{minipage}[!b]{0.5\linewidth}
-Diode characteristics,
-$$I_D=I_S(e^{qV/kT}-1)$$
-$$I_D=I_D|_{V=V_0} + (V-V_0)\frac{I_D}{V}|_{V=V_0}$$
-$$I_D=I_{D0}+(V-V_0)G_{D0}$$
-\begin{figure}[h]
-\begin{center}
-\includegraphics[scale=0.4]{../figures/diodeI.eps}
-\begin{small}Modeling of Diode\end{small}
-\label{diodeI}
-\end{center}
-\end{figure}
-\end{minipage}
-\begin{minipage}[!b]{0.4\linewidth}
-\begin{figure}[h]
-\begin{center}
-\includegraphics[scale=0.3]{../figures/diodechar1.eps}
-\begin{small}Linearized approximation of diode model\end{small}
-\begin{tiny}$$I_{DN0}=I_{D0}-V_0G_{D0}$$\end{tiny}
-\end{center}
-\end{figure}
-\end{minipage}
-\end{frame}
-
-
-\begin{frame}
-{\bf Procedure:}{Operating Point Analysis}
-\small
-\begin{algorithmic}[1]
-\STATE Find Node Potential and Current through devices whose device characteristic can not be expressed in terms of voltage.
-\STATE Find branch voltage and node potential.
-\STATE Find branch current from branch voltage using device characteristics.
-\IF{Non-linear component}
-\STATE {\bf NR:} Check  device characteristics of non-linear devices.
-\IF {Device characteristics is not satisfied}
-\STATE Call Newton Raphson procedure
-\STATE Find Node Potential and Current through devices whose device characteristic can not be expressed in terms of voltage.
-\STATE Find branch current from branch voltage using device characteristics.
-\STATE Go to {\bf NR}
-\ENDIF
-\STATE Check for KCL
-\ENDIF
-\end{algorithmic}
-\normalsize
-\end{frame}
-
-\begin{frame}
-\frametitle{Full Wave Bridge Rectifier}
-\begin{minipage}[!b]{0.4\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.5]{../figures/bridge.eps}
-\end{figure}
-\end{minipage}
-\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.5\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.3]{../figures/bridgeOutput.eps}
-\end{figure}
-\end{minipage}
-\end{frame}
-
-\section{DC Analysis}
-\begin{frame}
-\frametitle{DC Analysis}
-{\bf Procedure:}{DC Analysis}
-\small
-\begin{algorithmic}[1]
-\STATE Modify the value of the sweep source and update Modified Nodal matrix.
-\STATE Do Operating Point Analysis.
-\end{algorithmic}
-\normalsize
-\end{frame}
-
-\begin{frame}
-\frametitle{Voltage Sweep}
-\begin{minipage}[!b]{0.4\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.8]{../figures/V_Sweep.eps}
-\caption{Example of DC Analysis (Vsweep.ckt)}
-\end{figure}
-\end{minipage}
-\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.5\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.3]{../figures/V_SweepOutput.eps}
-\end{figure}
-\end{minipage}
-\end{frame}
-
-\begin{frame}
-\frametitle{User defined Components}
-Consider, a non-linear resistance,
-$$I=\frac{1}{R}V^3$$
-
-\begin{itemize}
-\item Create  a file \$CompName.sci
-\item Define
-\begin{itemize}
-\item Function in the $i=g(v)$ form
-\item Jacobian of the function
-\end{itemize}
-\end{itemize}
-
-%{\bf Syntax:-}
-%\newline
-%function I=\$CompName\_func(voltage,parameter)
-%\$par\_2=parameter(2)
-%\$par\_3=parameter(3)
-\end{frame}
-
-\begin{frame}
-\frametitle{Non-linear Resistance}
-\begin{minipage}[!b]{0.43\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.7]{../figures/myR.eps}
-\end{figure}
-\begin{tiny}
-function I=myR\_func(voltage,parameter)
-\begin{center}
-        R=parameter(2); \newline
-        I=1/R*(voltage\^3);
-\end{center}
-endfunction \newline
-
-
-function Gj=myR\_Jacobian(voltage,parameter) 
-\begin{center}
-        R=parameter(2); \newline
-        Gj=3/R*(voltage\^2);
-\end{center}
-endfunction
-\end{tiny}
-\end{minipage}
-\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.5\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.3]{../figures/myROutput.eps}
-\end{figure}
-\end{minipage}
-\end{frame}
-
-\section{Transient Analysis}
-\begin{frame}
-  \begin{block}{What is Transient Analysis?}
-     \begin{itemize}
-       \item Computes the response of a circuit as function of time.
-       \item Time is discretized and the solution is computed piecewise.
-     \end{itemize}
-   \end{block}
-  \begin{block}{Important factors}
-    \begin{itemize}
-      \item Proper time Stepping.
-      \item Integration methods.
-    \end{itemize}
-  \end{block}
-\end{frame}
-
-\begin{frame}
-\frametitle{Discreatization}
-Consider, a capacitor
-\begin{tiny}
-$$I_C(t_n)=C\frac{\partial{V}_C(t_n)}{\partial{t}}$$
-Using Backward Euler's method,
-$$I_C(t_n)=C\frac{V(t_n)-V(t_{n-1})}{t_n-t_{n-1}}$$
-$$I_C(t_n)=\frac{C}{h}V(t_n)-\frac{C}{h}V(t_{n-1})$$
-$$I_C(t_n)=G_C^{(k)}V(t_n)-I_C^{(k)}$$
-\end{tiny}
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.8]{../figures/Ceq.eps}
-\end{figure}
-\end{frame}
-
-\begin{frame}
-\frametitle{RC Circuit}
-\begin{minipage}[!b]{0.4\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.8]{../figures/RC.eps}
-\end{figure}
-\end{minipage}
-\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.5\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.3]{../figures/RCOutput.eps}
-\end{figure}
-\end{minipage}
-\end{frame}
-
-\begin{frame}
-\frametitle{Full Wave Bridge Rectifier with Filter}
-\begin{minipage}[!b]{0.4\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.4]{../figures/bridgeFilter.eps}
-\end{figure}
-\end{minipage}
-\hspace{0.5cm} % To get a little bit of space between the figures
-\begin{minipage}[!b]{0.5\linewidth} % A minipage that covers half the page
-\begin{figure}[h]
-\centering
-\includegraphics[scale=0.3]{../figures/bridgeFilterOutput.eps}
-\end{figure}
-\end{minipage}
-\end{frame}
-
-\begin{frame}
-\frametitle{PseudoCode}
-{\bf Procedure:}{Transient Analysis}
-\small
-\begin{algorithmic}[1]
-\STATE Discretize time dependent Component and Update Modified Nodal matrix.
-\STATE Do Operating Point Analysis.
-\end{algorithmic}
-\normalsize
-
-{\bf Procedure:}{Discretization}
-\small
-\begin{algorithmic}[1]
-\STATE Compute time dependent source value at time t.
-\STATE Compute the values of static model of dynamic component at time t.
-\STATE Update Modified Nodal matrix.
-\end{algorithmic}
-\normalsize
-\end{frame}
-
-%\begin{frame}
-%\frametitle{CMOS Inverter}
-%\begin{minipage}[!b]{0.4\linewidth} % A minipage that covers half the page
-%\begin{figure}[h]
-%\centering
-%\includegraphics[scale=0.4]{../figures/inverter.eps}
-%\end{figure}
-%\end{minipage}
-%\hspace{0.5cm} % To get a little bit of space between the figures
-%\begin{minipage}[!b]{0.5\linewidth} % A minipage that covers half the page
-%\begin{figure}[h]
-%\centering
-%\includegraphics[scale=0.3]{../figures/inverterOutput.eps}
-%\end{figure}
-%\end{minipage}
-%\end{frame}
-
-\end{document}
-
-- 
cgit 

