\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}
\usepackage{makecell}

\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{Fuse markings}
\begin{enumerate}
\item First character group is the speed, going from "TT" through "M" to "FF".
\item This is followed by the current in amperes.
\item The following character indicates either "H"igh or "L"ow breaking capacity.
\item Finally the voltage rating is given.
\end{enumerate}

\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 (Mainland France)}
\begin{fulltab}{llll}
\toprule
Name & Range & Center/deviation & Comments\\
\midrule
80\unit{\meter} & 3.500 - 3.800 \unit{\mega\hertz} & 3.646 \unit{\mega\hertz} $\pm$ 4\% & Shared \\
60\unit{\meter} & 5.3515 - 5.3665 \unit{\mega\hertz} & 5.359 \unit{\mega\hertz}$\pm$ 1\% & Secondary \\
40\unit{\meter} & 7.000 - 7.200 \unit{\mega\hertz} & 7.099 \unit{\mega\hertz} $\pm$ 1\% & \\
30\unit{\meter} & 10.100 - 10.150 \unit{\mega\hertz} & 1.125 \unit{\mega\hertz} $\pm$ 2\% & \makecell{Secondary\\ 15W EIRP} \\
20\unit{\meter} & 14.000 - 14.350 \unit{\mega\hertz} & 14.174 \unit{\mega\hertz} $\pm$ 1\% & \\
17\unit{\meter} & 18.068 - 18.168 \unit{\mega\hertz} & 18.118 \unit{\mega\hertz} $\pm$ .2\% & \\
15\unit{\meter} & 21.000 - 21.450 \unit{\mega\hertz} & 21.224 \unit{\mega\hertz} $\pm$ 1\% & \\
12\unit{\meter} & 24.890 - 24.990 \unit{\mega\hertz} & 24.940 \unit{\mega\hertz} $\pm$ .2\% & \\
10\unit{\meter} & 28.000 - 29.700 \unit{\mega\hertz} & 28.837 \unit{\mega\hertz} $\pm$ 3\% & \\
\bottomrule
\end{fulltab}

\paragraph{Purity limits}
HF and below: -50dBc if >5W carrier, otherwise -43dBW.\\
VHF and above: -43dBW.

\paragraph{Ambient radio noise}
With $F$ the ratio between the effective temperature due to radio noise and
ambient, $F_m$ the minimal value expected,
\begin{fulltab}{lll}
\toprule
Frequency & $F_m$ & $e_n$ in 50\unit{\ohm}, 3\unit{\kilo\hertz}\\
\midrule
500\unit{\kilo\hertz} & 60dB & 49\unit{\micro\volt}\\
3\unit{\mega\hertz} & 40dB & 4.9\unit{\micro\volt}\\
30\unit{\mega\hertz} & 20dB & 490\unit{\nano\volt}\\

\bottomrule
\end{fulltab}

\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}
