251 lines
8.2 KiB
TeX
251 lines
8.2 KiB
TeX
\documentclass[a6paper, fontsize=6pt, twosided]{scrreport}
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\usepackage[T1]{fontenc}
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\usepackage{tablefootnote}
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\usepackage{booktabs}
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\usepackage[svgnames]{xcolor}
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\usepackage{siunitx}
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\usepackage[french]{babel}
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\usepackage{graphicx}
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\usepackage{tikz}
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\newenvironment{fulltab}[1]{\begin{center}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}} #1}}
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{\end{tabular*}\end{center}}
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\def\N{\mathrm N}
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\let\epsilon\relax
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\def\epsilon{\varepsilon}
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\def\Vt{V_{\mathrm T}}
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\def\kbT{k_{\mathrm B}T}
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\setlength\tabcolsep{0pt}
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\setlength\parindent{0pt}
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\newcounter{colw}
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\newcommand{\mc}[1]{\multicolumn{\thecolw}{l}{#1}}
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\title{Incomplete handbook of all things useful}
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\author{Sélène Corbineau}
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\begin{document}
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\maketitle
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\tableofcontents
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\pagebreak
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\chapter{Mechanics}
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\section{Metric machine bolts}
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%\paragraph{Threads}
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\begin{fulltab}{lccccc}
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\toprule
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Thread & Pitch & Tapping dia. & \multicolumn{3}{c}{Clearance dia.}\\
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\cmidrule{4-6}
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& & & Close & Medium & Loose\\
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\midrule
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M1.6 & 0.35 & 1.25 & 1.7 & 1.8 & 2.0\\
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M2 & 0.4 & 1.6 & 2.2 & 2.4 & 2.6\\
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M2.5 & 0.45 & 2.05 & 2.7 & 2.9 & 3.1\\
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M3 & 0.5 & 2.5 & 3.2 & 3.4 & 3.6\\
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M4 & 0.7 & 3.3 & 4.3 & 4.5 & 4.8\\
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M5 & 0.8 & 4.2 & 5.3 & 5.5 & 5.8\\
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M6 & 1 & 5 & 6.4 & 6.6 & 7.0\\
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M8 & 1.25 & 6.8 & 8.4 & 9.0 & 10.0\\
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M10 & 1.5 & 8.5 & 10.5 & 11.0 & 12.0\\
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\bottomrule
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\end{fulltab}
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\begin{minipage}[c]{\linewidth}
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\paragraph{Socket head cap screws (ISO 4762)}
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\begin{center}
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\includegraphics[width=\linewidth]{sockhead.jpg}
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\end{center}
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\begin{fulltab}{lccc}
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\toprule
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Thread & s (nom.) & dk (max) & k (max)\\
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\midrule
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M1.6 & 1.5 & 3.14 & 1.6\\
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M2 & 1.5 & 3.98 & 2\\
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M2.5 & 2 & 4.68 & 2.5\\
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M3 & 2.5 & 5.68 & 3\\
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M4 & 3 & 7.22 & 4\\
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M5 & 4 & 8.72 & 5\\
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M6 & 5 & 10.22 & 6\\
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M8 & 6 & 13.27 & 8\\
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M10 & 8 & 16.27 & 10\\
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\bottomrule
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\end{fulltab}
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\end{minipage}
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\begin{minipage}[c]{\linewidth}
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\paragraph{Hex heads, nuts (ISO 4014, 4032)}
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\begin{center}
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\includegraphics[width=\linewidth]{hexcap.png}
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\end{center}
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\begin{fulltab}{lccccc}
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\toprule
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Thread & s & e (min.) & k (nom.) & m (max.) & m'\\
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\midrule
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M1.6 & 3.2 & 3.28 & 1.1 & 1.3\\
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M2 & 4.0 & 4.18 & 1.4 & 1.6 & 0.95\\
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M2.5 & 5.0 & 5.31 & 1.7 & 2 & 1.35\\
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M3 & 5.5 & 5.88 & 2 & 2.4 & 1.55\\
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M4 & 7 & 7.50 & 2.8 & 3.2 & 1.95\\
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M5 & 8 & 8.63 & 3.5 & 4 & 2.45\\
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M6 & 10 & 10.89 & 4 & 5 & 2.90\\
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M8 & 13 & 14.20 & 5.3 & 6.5 & 3.70\\
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M10 & 16 & 17.59 & 6.4 & 8 & 4.70\\
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\bottomrule
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\end{fulltab}
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m and m' are analogous to k for nuts (resp. jam nuts).
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\end{minipage}
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\chapter{Electronics}
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\section{Labelling}
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\paragraph{Color code}
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\newcommand{\cbox}[1]{\colorbox{#1}{\phantom{Cor}}}
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\begin{fulltab}{lcccccccccccc}
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\toprule
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& \cbox{black} & \cbox{brown} & \cbox{red} & \cbox{orange} & \cbox{yellow} & \cbox{green} & \cbox{blue}
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& \cbox{violet} & \cbox{gray} & \cbox{white} & \cbox{Gold} & \cbox{Silver}\\
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\midrule
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Digit& 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & -1 & -2\\
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Tol. & & 1\% & 2\% & & & 0.5\% & 0.25\% & 0.1\% & & & 5\% & 10\%\\
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\bottomrule
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\end{fulltab}
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\og Ne Mangez Rien Ou Je Vous Battrai Violemment, Grand Boa. \fg{} Gold and Silver cannot occur in the mantissa.
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\paragraph{Marking schemes}
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With color rings, read with outermost ring to the right
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\begin{itemize}
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\item 2 digits + exponent + tolerance
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\item 3 digits + exponent + tolerance
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\end{itemize}
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With digits: 2 digits + exponent. The base units are \unit{\ohm}, \unit{\micro\henry} and \unit{\pico\farad}.
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\paragraph{Preferred numbers}
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\begin{fulltab}{l lll lll lll lll lll lll lll lll}
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\toprule
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\setcounter{colw}{4}
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E3 & \mc{1.0} & \mc{2.2} & \mc{4.7}\\
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\setcounter{colw}{2}
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E6 & \mc{1.0} & \mc{1.5} & \mc{2.2} & \mc{3.3} & \mc{4.7} & \mc{6.8}\\
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\setcounter{colw}{1}
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E12 & \mc{1.0} & \mc{1.2} & \mc{1.5} & \mc{1.8} & \mc{2.2} & \mc{2.7}
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& \mc{3.3} & \mc{3.9} & \mc{4.7} & \mc{5.6} & \mc{6.8} & \mc{8.2} \\
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\bottomrule
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\end{fulltab}
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% Recall E6/E12/E24
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\section{Common components}
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\paragraph{Complementary BJT pairs}
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\begin{fulltab}{lccccc}
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\toprule
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Part n° & $V_{\textrm{CEO}}$ (V) & $I_{C,\textrm{max}}$ (mA) & $\beta$@$I_C$ & $f_T$ (\unit{\mega\hertz}) \\
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\midrule
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BC547C,'557 & 45 & 100 & 420..800 @ 10 & 300\\
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2N3904,'06 & 40 & 200 & 100..300 @ 10 & 300\\
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BC327,'337 & 45 & 500 & 100..600 @ 100 & 100\\
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\bottomrule
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\end{fulltab}
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\paragraph{Power BJTs}
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\begin{fulltab}{lccccc}
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\toprule
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Part n° & $V_{\textrm{CEO}}$ (V) & $I_{C,\textrm{max}}$ (A) & $\beta$@$I_C$ & $f_T$ (\unit{\mega\hertz})\\
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\midrule
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D44H11,'45 & 80 & 10 & 60 @ 1 & 50\\
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TIP41,'42 & 80 & 6 & 15..75 @ 3 & 3\\
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\bottomrule
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\end{fulltab}
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\paragraph{Operational amplifiers}
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\begin{fulltab}{lccccc}
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\toprule
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Part n° & Technology & $V_{\textrm{sup}}$ (\unit\volt) & RRI/O? & GBW (\unit{\mega\hertz}) & Slew (\unit{\volt\per\micro\second})\\
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\midrule
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TL081,'2,'4 & FET & 4.5\dots40 & +/ & 5.25 & 20\\
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RC4558,'9 & BJT & 10\dots30 & / & 3 & 1.7\\
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NE5532,'4\tablefootnote{Specified for noise} & BJT & 10\dots40 & / & 10 & 13\\
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LM2904 & BJT & 3\dots 36 & -/ & 1.2 & 0.5\\
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\bottomrule
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\end{fulltab}
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\section{Topologies}
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\paragraph{Differential gain of diff-pair} $U_d$ is the \emph{one-legged} bias drop.
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\[H_{D\rightarrow D} = \frac{U_d}{\Vt}\]
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\section{Noise models}
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At room temperature, $\kbT = q\Vt = 4\cdot 10^{-21} \unit\joule.$
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\paragraph{Johnson noise} Typical power density is $4\kbT$, therefore \(e_n = \sqrt{4\kbT R}\) and
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\(i_n = \sqrt{\kbT / R}\). At 1 \unit{\kilo\ohm}, we have \(e_n = 4 \unit{\nano\volt\per\sqrt{\hertz}}\)
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or, equivalently, \(i_n = 4 \unit{\pico\ampere\per\sqrt{\hertz}}\).
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\paragraph{BJT noise} We have $i_{n,B} = \sqrt{2qI_C/\beta_{\mathrm{DC}}}$ at high frequencies. Below
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a few hundred \unit\hertz, there is flicker noise. The collector's "shot noise" is caused by an equivalent
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voltage noise in series with $r_\pi$, \[e_{n, BE} = \sqrt{2qI_C}/g_m = \Vt \sqrt{2q/I_C}.\]
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At \(I_C = 1 \unit{\milli\ampere}\) we have \(e_{n,BE} = 0.44 \unit{\nano\volt\per\sqrt{\hertz}}\).
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At high $I_C$ one needs to take into account a base-spreading resistance in
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series with the base $r_{bb'}$. It is typically a few hundred ohm, and is smaller
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for larger transistors.
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\chapter{Telecommunications}
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\section{Amateur radio}
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\paragraph{HF frequency allocations (Mainland France)}
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\begin{fulltab}{lll}
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\toprule
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Name & Range & Comments\\
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\midrule
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80\unit{\meter} & 3.500 - 3.800 \unit{\mega\hertz} & Shared \\
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60\unit{\meter} & 5.3515 - 5.3665 \unit{\mega\hertz} & Secondary \\
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40\unit{\meter} & 7.000 - 7.200 \unit{\mega\hertz} & \\
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30\unit{\meter} & 10.100 - 10.150 \unit{\mega\hertz} & Secondary, 15W EIRP \\
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20\unit{\meter} & 14.000 - 14.350 \unit{\mega\hertz} & \\
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17\unit{\meter} & 18.068 - 18.168 \unit{\mega\hertz} & \\
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15\unit{\meter} & 21.000 - 21.450 \unit{\mega\hertz} & \\
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12\unit{\meter} & 24.890 - 24.990 \unit{\mega\hertz} & \\
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10\unit{\meter} & 28.000 - 29.700 \unit{\mega\hertz} & \\
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\bottomrule
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\end{fulltab}
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\paragraph{Purity limits}
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HF and below: -50dBc if >5W carrier, otherwise -43dBW.\\
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VHF and above: -43dBW.
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\paragraph{Ambient radio noise}
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With $F$ the ratio between the effective temperature due to radio noise and
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ambient, $F_m$ the minimal value expected,
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\begin{fulltab}{lll}
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\toprule
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Frequency & $F_m$ & $e_n$ in 50\unit{\ohm}, 3\unit{\kilo\hertz}\\
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\midrule
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500\unit{\kilo\hertz} & 60dB & 49\unit{\micro\volt}\\
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3\unit{\mega\hertz} & 40dB & 4.9\unit{\micro\volt}\\
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30\unit{\mega\hertz} & 20dB & 490\unit{\nano\volt}\\
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\bottomrule
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\end{fulltab}
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\section{Character encodings}
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\paragraph{7-bit ASCII}
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\paragraph{HD4480}
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\chapter{Fundamental constants}
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\begin{fulltab}{lccc}
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\toprule
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& Symbol & Value & Unit\\
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\midrule
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Speed of light & $c$ & $3.0\cdot 10^9$ & \unit{\meter\per\second}\\
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Unit charge & $q$ & $1.6\cdot 10^{-19}$ & \unit{\coulomb}\\
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Boltzmann's constant & $k_B$ & $1.38\cdot 10^{-23}$ & \unit{\joule\per\kelvin}\\
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Permittivity of free space & $\epsilon_0$ & $8.86\cdot 10^{-12}$ & \unit{\farad\meter}\\
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Permeability of free space & $\mu_0$ & $1.26\cdot 10^{-6} \approx 4\pi\cdot 10^{-7}$ & \unit{\henry\per\meter}\\
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Faraday constant & $F$ & $9.65\cdot 10^{4}$ & \unit{\coulomb\per\mole}\\
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Electron mass & $m_{\mathrm e}$ & $9.1\cdot 10^{-31}$ & \unit{\kilogram}\\
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Proton/Neutron mass & $m_{\mathrm p}, m_{\mathrm n}$ & $1.67\cdot 10^{-27}$ & \unit{\kilogram}\\
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\bottomrule
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\end{fulltab}
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\end{document}
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