Some noise, opamps, and preferred numbers

handbook.tex

@@ -1,6 +1,7 @@
 \documentclass[a6paper, fontsize=6pt, twosided]{scrreport}
 
 \usepackage[T1]{fontenc}
+\usepackage{tablefootnote}
 \usepackage{booktabs}
 \usepackage[svgnames]{xcolor}
 \usepackage{siunitx}
@@ -88,12 +89,15 @@ With color rings, read with outermost ring to the right
 With digits: 2 digits + exponent. The base units are \unit{\ohm}, \unit{\micro\henry} and \unit{\pico\farad}.
 
 \paragraph{Preferred numbers}
-\begin{fulltab}{lcccccccccccc}
+\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} \\
+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
@@ -102,7 +106,7 @@ E12 & \mc{1.0} & \mc{1.2} \\
 \paragraph{Complementary BJT pairs}
 \begin{fulltab}{lccccc}
 \toprule
-	Part n°  & $V_{\textrm{CEO}}$ (V) & $I_{C,\textrm{max}}$ (mA) & $\beta$@$I_C$  & $f_T$ (MHz) \\
+	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\\
@@ -113,13 +117,26 @@ BC327,'337 & 45 & 500 & 100..600 @ 100 & 100\\
 \paragraph{Power BJTs}
 \begin{fulltab}{lccccc}
 \toprule
-	Part n° & $V_{\textrm{CEO}}$ (V) & $I_{C,\textrm{max}}$ (A) & $\beta$@$I_C$  & $f_T$ (MHz)\\
+	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.
@@ -127,8 +144,19 @@ TIP41,'42 & 80 & 6  & 15..75 @ 3 & 3\\
 
 \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
-\(i_n = \sqrt{\kbT / R}\).
+\(i_n = \sqrt{\kbT / R}\). 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}
@@ -140,4 +168,7 @@ TIP41,'42 & 80 & 6  & 15..75 @ 3 & 3\\
 \section{Character encodings}
 \paragraph{7-bit ASCII}
 \paragraph{HD4480}
+
+\chapter{Fundamental constants}
+
 \end{document}