\documentclass[a6paper, fontsize=6pt, twosided]{scrreport}

\usepackage[T1]{fontenc}
\usepackage{tablefootnote}
\usepackage{booktabs}
\usepackage[svgnames]{xcolor}
\usepackage{siunitx}
\usepackage[french]{babel}
\usepackage{graphicx}
\usepackage{tikz}

\newenvironment{fulltab}[1]{\begin{center}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}} #1}}
{\end{tabular*}\end{center}}
\def\N{\mathrm N}
\let\epsilon\relax
\def\epsilon{\varepsilon}

\def\Vt{V_{\mathrm T}}
\def\kbT{k_{\mathrm B}T}
\setlength\tabcolsep{0pt}
\setlength\parindent{0pt}

\newcounter{colw}
\newcommand{\mc}[1]{\multicolumn{\thecolw}{l}{#1}}
\title{Incomplete handbook of all things useful}
\author{Sélène Corbineau}
\begin{document}
\maketitle
\tableofcontents
\pagebreak

\chapter{Mechanics}
\section{Metric machine bolts}

%\paragraph{Threads}
\begin{fulltab}{lccccc}
\toprule
Thread & Pitch & Tapping dia. & \multicolumn{3}{c}{Clearance dia.}\\
\cmidrule{4-6}
 & & & Close & Medium & Loose\\
\midrule
M1.6 & 0.35 & 1.25 & 1.7 & 1.8 & 2.0\\
M2 & 0.4 & 1.6 & 2.2 & 2.4 & 2.6\\
M2.5 & 0.45 & 2.05 & 2.7 & 2.9 & 3.1\\
M3 & 0.5 & 2.5 & 3.2 & 3.4 & 3.6\\
M4 & 0.7 & 3.3 & 4.3 & 4.5 & 4.8\\
M5 & 0.8 & 4.2 & 5.3 & 5.5 & 5.8\\
M6 & 1 & 5 & 6.4 & 6.6 & 7.0\\
M8 & 1.25 & 6.8 & 8.4 & 9.0 & 10.0\\
M10 & 1.5 & 8.5 & 10.5 & 11.0 & 12.0\\
\bottomrule
\end{fulltab}

\begin{minipage}[c]{\linewidth}
\paragraph{Socket head cap screws (ISO 4762)}
\begin{center}
\includegraphics[width=\linewidth]{sockhead.jpg}
\end{center}
\begin{fulltab}{lccc}
\toprule
Thread & s (nom.) & dk (max) & k (max)\\
\midrule
M1.6 & 1.5 & 3.14 & 1.6\\
M2   & 1.5 & 3.98 & 2\\
M2.5 & 2 & 4.68 & 2.5\\
M3 & 2.5 & 5.68 & 3\\
M4 & 3 & 7.22 & 4\\
M5 & 4 & 8.72 & 5\\
M6 & 5 & 10.22 & 6\\
M8 & 6 & 13.27 & 8\\
M10 & 8 & 16.27 & 10\\
\bottomrule
\end{fulltab}
\end{minipage}

\begin{minipage}[c]{\linewidth}
\paragraph{Hex heads, nuts (ISO 4014, 4032)}

\begin{center}
\includegraphics[width=\linewidth]{hexcap.png}
\end{center}
\begin{fulltab}{lccccc}
\toprule
	Thread & s   & e (min.)   & k (nom.) & m (max.) & m'\\
\midrule
M1.6   & 3.2 & 3.28       & 1.1 & 1.3\\
M2     & 4.0 & 4.18       & 1.4 & 1.6 & 0.95\\
M2.5   & 5.0 & 5.31       & 1.7 & 2 & 1.35\\
M3     & 5.5 & 5.88       & 2 & 2.4 & 1.55\\
M4     & 7   & 7.50       & 2.8 & 3.2 & 1.95\\
M5     & 8   & 8.63       & 3.5 & 4 & 2.45\\
M6     & 10  & 10.89      & 4 & 5 & 2.90\\
M8     & 13  & 14.20      & 5.3 & 6.5 & 3.70\\
M10    & 16  & 17.59      & 6.4 & 8 & 4.70\\
\bottomrule
\end{fulltab}
m and m' are analogous to k for nuts (resp. jam nuts).
\end{minipage}
\chapter{Electronics}
\section{Labelling}
\paragraph{Color code}

\newcommand{\cbox}[1]{\colorbox{#1}{\phantom{Cor}}}

\begin{fulltab}{lcccccccccccc}
\toprule
& \cbox{black} & \cbox{brown} & \cbox{red} & \cbox{orange} & \cbox{yellow} & \cbox{green} & \cbox{blue}
	& \cbox{violet} & \cbox{gray} & \cbox{white} & \cbox{Gold} & \cbox{Silver}\\
\midrule
Digit& 0 & 1   & 2   & 3 & 4 & 5     & 6      & 7     & 8 & 9 & -1  & -2\\
Tol. &   & 1\% & 2\% &   &   & 0.5\% & 0.25\% & 0.1\% &   &   & 5\% & 10\%\\
\bottomrule
\end{fulltab}
\og Ne Mangez Rien Ou Je Vous Battrai Violemment, Grand Boa. \fg{} Gold and Silver cannot occur in the mantissa.

\paragraph{Marking schemes}
With color rings, read with outermost ring to the right
\begin{itemize}
\item 2 digits + exponent + tolerance
\item 3 digits + exponent + tolerance
\end{itemize}
With digits: 2 digits + exponent. The base units are \unit{\ohm}, \unit{\micro\henry} and \unit{\pico\farad}.

\paragraph{Preferred numbers}
\begin{fulltab}{l lll lll lll lll lll lll lll lll}
\toprule
\setcounter{colw}{4}
E3 & \mc{1.0} & \mc{2.2} & \mc{4.7}\\
\setcounter{colw}{2}
E6 & \mc{1.0} & \mc{1.5} & \mc{2.2} & \mc{3.3} & \mc{4.7} & \mc{6.8}\\
\setcounter{colw}{1}
E12 & \mc{1.0} & \mc{1.2} & \mc{1.5} & \mc{1.8} & \mc{2.2} & \mc{2.7}
& \mc{3.3} & \mc{3.9} & \mc{4.7} & \mc{5.6} & \mc{6.8} & \mc{8.2} \\
\bottomrule
\end{fulltab}
% Recall E6/E12/E24

\section{Common components}
\paragraph{Complementary BJT pairs}
\begin{fulltab}{lccccc}
\toprule
	Part n°  & $V_{\textrm{CEO}}$ (V) & $I_{C,\textrm{max}}$ (mA) & $\beta$@$I_C$  & $f_T$ (\unit{\mega\hertz}) \\
\midrule
BC547C,'557 & 45 & 100 & 420..800 @ 10 & 300\\
2N3904,'06 & 40 & 200 & 100..300 @ 10 & 300\\
BC327,'337 & 45 & 500 & 100..600 @ 100 & 100\\
\bottomrule
\end{fulltab}

\paragraph{Power BJTs}
\begin{fulltab}{lccccc}
\toprule
	Part n° & $V_{\textrm{CEO}}$ (V) & $I_{C,\textrm{max}}$ (A) & $\beta$@$I_C$  & $f_T$ (\unit{\mega\hertz})\\
\midrule
D44H11,'45  & 80 & 10  & 60 @ 1 & 50\\
TIP41,'42 & 80 & 6  & 15..75 @ 3 & 3\\
\bottomrule
\end{fulltab}

\paragraph{Operational amplifiers}

\begin{fulltab}{lccccc}
\toprule
Part n° & Technology & $V_{\textrm{sup}}$ (\unit\volt) & RRI/O? & GBW (\unit{\mega\hertz}) & Slew (\unit{\volt\per\micro\second})\\
\midrule
TL081,'2,'4 & FET & 4.5\dots40 & +/ & 5.25 & 20\\
RC4558,'9 & BJT & 10\dots30 & / & 3 & 1.7\\
NE5532,'4\tablefootnote{Specified for noise} & BJT & 10\dots40 & / & 10 & 13\\
LM2904 & BJT & 3\dots 36 & -/ & 1.2 & 0.5\\
\bottomrule
\end{fulltab}

\section{Topologies}

\paragraph{Differential gain of diff-pair} $U_d$ is the \emph{one-legged} bias drop.
\[H_{D\rightarrow D} = \frac{U_d}{\Vt}\]

\section{Noise models}

At room temperature, $\kbT = q\Vt = 4\cdot 10^{-21} \unit\joule.$

\paragraph{Johnson noise} Typical power density is $4\kbT$, therefore \(e_n = \sqrt{4\kbT R}\) and
\(i_n = \sqrt{\kbT / R}\). At 1 \unit{\kilo\ohm}, we have \(e_n = 4 \unit{\nano\volt\per\sqrt{\hertz}}\)
or, equivalently, \(i_n = 4 \unit{\pico\ampere\per\sqrt{\hertz}}\).

\paragraph{BJT noise} We have $i_{n,B} = \sqrt{2qI_C/\beta_{\mathrm{DC}}}$ at high frequencies. Below
a few hundred \unit\hertz, there is flicker noise. The collector's "shot noise" is caused by an equivalent
voltage noise in series with $r_\pi$, \[e_{n, BE} = \sqrt{2qI_C}/g_m = \Vt \sqrt{2q/I_C}.\]
At \(I_C = 1 \unit{\milli\ampere}\) we have \(e_{n,BE} = 0.44 \unit{\nano\volt\per\sqrt{\hertz}}\).
At high $I_C$ one needs to take into account a base-spreading resistance in
series with the base $r_{bb'}$. It is typically a few hundred ohm, and is smaller
for larger transistors.

\chapter{Telecommunications}
\section{Amateur radio}
\paragraph{HF frequency allocations (region I)}

\paragraph{Q-code}
\paragraph{Purity limits}

\section{Character encodings}
\paragraph{7-bit ASCII}
\paragraph{HD4480}

\chapter{Fundamental constants}

\begin{fulltab}{lccc}
\toprule
 & Symbol & Value & Unit\\
\midrule
Speed of light & $c$ & $3.0\cdot 10^9$ & \unit{\meter\per\second}\\
Unit charge & $q$ & $1.6\cdot 10^{-19}$ & \unit{\coulomb}\\
Boltzmann's constant & $k_B$ & $1.38\cdot 10^{-23}$ & \unit{\joule\per\kelvin}\\
Permittivity of free space & $\epsilon_0$ & $8.86\cdot 10^{-12}$ & \unit{\farad\meter}\\
Permeability of free space & $\mu_0$ & $1.26\cdot 10^{-6} \approx 4\pi\cdot 10^{-7}$ & \unit{\henry\per\meter}\\
Faraday constant & $F$ & $9.65\cdot 10^{4}$ & \unit{\coulomb\per\mole}\\
Electron mass & $m_{\mathrm e}$ & $9.1\cdot 10^{-31}$ & \unit{\kilogram}\\
Proton/Neutron mass & $m_{\mathrm p}, m_{\mathrm n}$ & $1.67\cdot 10^{-27}$ & \unit{\kilogram}\\
\bottomrule
\end{fulltab}
\end{document}