121 lines
3.7 KiB
TeX
121 lines
3.7 KiB
TeX
\documentclass{article}
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\usepackage[margin=1in]{geometry}
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\usepackage{graphicx}
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\usepackage{minted}
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\usepackage{amsmath}
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\newcommand{\RE}[1]{\mathrm{Re} \left \{ #1 \right \}}
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\newcommand{\IM}[1]{\mathrm{Im} \left \{ #1 \right \}}
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\usepackage{longtable,booktabs,array}
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\usepackage{siunitx}
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\usepackage{commath}
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\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}}
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\usepackage{amsfonts}
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\usepackage{cancel}
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\usepackage[T1]{fontenc}
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\usepackage{framed}
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\usepackage{caption}
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\usepackage{gensymb}
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\title{Lab 3, EE3150}
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\author{Martin Kennedy and DJ}
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\begin{document}
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\maketitle
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\section{Introduction}
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In this lab, we investigate the response of a circuit (seen in figure
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\ref{img:circuit_diagram}) to different sinusoidal signals. We apply
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both symbolic analysis and numeric analysis (simulation) to affirm
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that this causal LTI system will always generate a sinusoidal response
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of the same frequency as that provided to it.
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\begin{figure}[h]
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\caption{A diagram of our two-stage RC circuit, with a fixed-gain amplifier between the two stages to act as a buffer}
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\label{img:circuit_diagram}
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\centering
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\includegraphics[width=0.8\textwidth]{circuit_diagram}
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\end{figure}
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\section{Discussion}
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A number of different sinusoidal input signals are considered.
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From the Lab3 description, we have:
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\subsubsection{Lab3 section 2.2.a.}
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$x(t) = A \sin(\omega t)$, for $A = 1 V_{pp}, f \in \left \{1, 5, 10, 100 \right \} \SI{}{\hertz}$.
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\subsubsection{Lab3 section 2.2.b.}
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$x_1(t) + x_2(t)$, with $x_1(t) = A_1 \sin(\omega_1 t)$,
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$x_2(t) = A_2 \sin(\omega_2 t)$, and $(f_1, f_2, A_1, A_2)$ with such
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values as
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$(\SI{50}{\hertz}, \SI{100}{\hertz}, \SI{1}{V}, \SI{0.5}{V})$ and
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$(\SI{50}{\hertz}, \SI{100}{\hertz}, \SI{2}{V}, \SI{4}{V})$.
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\subsubsection{Lab3 section 2.2.c.}
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As with 2.2.a, but with $x(t) = A \sin(\omega t - 0.025)$, for
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$A = 1 V_{pp}, f = \SI{10}{\hertz}$ (i.e., a 0.025 second delay).
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\section{Measurement data and/or Results}
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\subsubsection{Lab3 section 2.2.a.}
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Figures \ref{img:1hz_show}, \ref{img:5hz_show}, \ref{img:10hz_show}
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and \ref{img:100hz_show} depict a theoretical $1V_{pp}$ input at
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$f \in \left \{1, 5, 10, 100 \right \} \SI{}{\hertz}$, with output
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calculated first by convolution with the impulse response, then by
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solution of the representative ODE, and finally our experimentally
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measured input and output.
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\begin{figure}[h]
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\caption{A $1V_{pp}$ @ $\SI{1}{\hertz}$ input to our circuit, in theory and in practice, and respective outputs}
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\label{img:1hz_show}
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\centering
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\includegraphics[width=0.8\textwidth]{img/1hz_show}
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\end{figure}
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\begin{figure}[h]
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\caption{A $1V_{pp}$ @ $\SI{5}{\hertz}$ input to our circuit, in theory and in practice, and respective outputs}
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\label{img:5hz_show}
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\centering
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\includegraphics[width=0.8\textwidth]{img/5hz_show}
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\end{figure}
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\begin{figure}[h]
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\caption{A $1V_{pp}$ @ $\SI{10}{\hertz}$ input to our circuit, in theory and in practice, and respective outputs}
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\label{img:10hz_show}
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\centering
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\includegraphics[width=0.8\textwidth]{img/10hz_show}
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\end{figure}
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\begin{figure}[h]
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\caption{A $1V_{pp}$ @ $\SI{100}{\hertz}$ input to our circuit, in theory and in practice, and respective outputs}
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\label{img:100hz_show}
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\centering
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\includegraphics[width=0.8\textwidth]{img/100hz_show}
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\end{figure}
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\subsubsection{Lab3 section 2.2.b.}
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$x_1(t) + x_2(t)$, with $x_1(t) = A_1 \sin(\omega_1 t)$,
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$x_2(t) = A_2 \sin(\omega_2 t)$, and $(f_1, f_2, A_1, A_2)$ with such
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values as
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$(\SI{50}{\hertz}, \SI{100}{\hertz}, \SI{1}{V}, \SI{0.5}{V})$ and
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$(\SI{50}{\hertz}, \SI{100}{\hertz}, \SI{2}{V}, \SI{4}{V})$.
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\subsubsection{Lab3 section 2.2.c.}
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\section{Discusison of Measurements, experiments and/or simulations}
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\section{Summary and Conclusions}
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\end{document}
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