Tex work

Doc/main.tex

@@ -4,7 +4,13 @@
 \usepackage[a4paper, total={7in, 10in}]{geometry}
 \usepackage{multicol}
 \usepackage{lipsum}
+\usepackage{caption}
 \usepackage{graphicx}
+\usepackage{enumitem}
+
+\newenvironment{Figure}
+  {\par\medskip\noindent\minipage{\linewidth}}
+  {\endminipage\par\medskip}
 
 \graphicspath{{images/}}
 
@@ -24,26 +30,125 @@
   \section{Introduction}
     \lipsum[1-2]
 
+
   \section{Circuit Description}
+    % Filler image, don't get attached
+    \begin{Figure}
+      \centering
+      \includegraphics[scale=0.38]{SCHEMATIC_FULL.png}
+      \captionof{figure}{WIP}
+      \label{fig:schematic_full}
+    \end{Figure}
     \lipsum[3-4]
 
+
   \section{Methodology}
     To characterize the system, several tests have been performed. The 
     characteristics of interest are the following:
-    \begin{enumerate}
+    \begin{enumerate}[nosep]
         \item Efficiency
         \item Noise
         \item Ripple characteristics
         \item Transients
     \end{enumerate}
+    In this section a test or measurement will be described for each of the above 
+    characteristics.
 
-  Each of these characteristics have been tested at two different output voltages
+    Each of the characteristics have been tested at two different output voltages
-  and load currents. The different voltages are $7V$ and $3.3V$. The chosen load
+    and various load currents. The different voltages are $7V$ and $3.3V$. The 
-  currents are $10$, $20$, $30$, $40$ and $50 mA$. These values were chosen to 
+    chosen load currents are $10$, $20$, $30$, $40$ and $50 mA$. These values 
-  give characterize the circuit over a broad range of conditions. 
+    were chosen to give characterize the circuit over a broad range of conditions.
+
+
+  \subsection{Efficiency}
+    \begin{Figure}
+      \centering
+      \includegraphics[scale=0.34]{SCHEMATIC_EFFICIENCY.png}
+      \captionof{figure}{WIP}
+      \label{fig:schematic_efficiency}
+    \end{Figure}
+    To measure the efficiency of the circuit, four measurements were taken.
+    A current and a voltage measurement were taken at the supply and load
+    respectively. The measurements were taken as shown in figure 
+    \ref{fig:schematic_efficiency}. The energy used by the supply and the load 
+    can be calculated using the equation \ref{eq:power}. Then, using equation
+    \ref{eq:efficiency}, efficiency can be calculated.
+    \begin{equation}
+      \label{eq:power}
+      P [W] = U[V] \cdot I[A]
+    \end{equation} 
+    \begin{equation}
+      \label{eq:efficiency}
+      \eta[\%] = \frac{P_{load}[W]}{P_{supply}[W]} \cdot 100\%
+    \end{equation}
+  
+
+  \subsection{Noise}
+    To measure the noice of the circuit an oscilloscope probe was placed on the
+    variable resistor in figure \ref{fig:schematic_full}. Over the period of 1 
+    millisecond, 20,000 points were measured. 
+
+    Noise has several metrics in which it can be quantized. Two metrics were
+    calculated, the standard devation (SD) and the peak to peak noise. 
+
+
+  \subsubsection{Peak to peak}\label{section:peak_to_peak}
+    Peak to peak is the simplest way to look at noise. The signal has a stationary
+    mean over the period of 1 millisecond. Thus the highest measured value can be
+    subtracted from the lowest measured value.
+
+
+  \subsubsection{Standard Deviation}
+    The second metric used to measure noise was the standard deviation. 
+    Unlike, peak to peak it givesa better impression of the noise over a longer 
+    signal. SD can be calculated using equation \ref{eq:sd}.
+
+    \begin{equation}
+      \label{eq:sd}
+      \sigma = \sqrt{\frac{1}{N}\sum^{N-1}_{i=0}(x[i] - \mu)^2}
+    \end{equation}
+
+    Where $x[i]$ is each voltage measurement, $\mu$ is the mean of the signal and
+    $N$ is the total amount of samples.
+
+    \subsection{Ripple characteristics}
+    \begin{Figure}
+      \centering
+      \includegraphics[scale=0.5]{RIPPLE.png}
+      \captionof{figure}{WIP}
+      \label{fig:ripple}
+    \end{Figure}
+    A significant source of the noise was caused by a specific ripple, shown in
+    figure \ref{fig:ripple}. 
+    This ripple coincided with the MOSFETs opening or closing.
+    
+    To further characterize this behaviour a close up measurement was taken.
+    The oscilloscope was set to AC-coupling and the settigns were adjusted
+    for the ripple to be full screen. Then, two additional characteristics can 
+    be calculated. The ripple's peak to peak voltage and the ripple's (most prevalent) 
+    frequency. The peak to peak value can be calculated using the method described in 
+    section \ref{section:peak_to_peak}.
+
+    To measure the frequency of the signal using an FFT, it had to be pre-processed 
+    first using a Hamming window this eliminates sharp edges at the edge of the 
+    measurement, causing unwanted frequencies to appear in the frequency domain. 
+    \begin{equation} 
+      \label{eq:hamming}
+      % 0.54 - 0.46 * cos(2*np.pi*(n/N))
+      w(i) = 0.54 - 0.46 \cdot cos \left(2 \pi \frac{i}{N} \right)
+    \end{equation}
+    Where $i$ is the current sample and $N$ is the total amount of samples. Each
+    sample in the signal can be multiplied by the corresponding value in the window,
+    preparing the signal for the FFT.
+
+    \subsection{Transients}
+    The last measurements were hocus pocus
 
   \section{Results}
+  \lipsum[1-2]
+
 
   \section{Conclusion}
+  \lipsum[3-4]
 \end{multicols}
 \end{document}

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