Biquad Filter Topologie nach Tow-Thomas

Ein Tow-Thomas Filter ist eine schaltungstechnische Realisierung eines Integratorfilters.

Dieser Filter kombiniert einen aktiven Tiefpass und Bandpass 2. Ordnung.

\usepackage[european, straightvoltages]{circuitikz}
\usepackage{amsmath}

\begin{document}
\begin{circuitikz}[thick, scale=1, font=\Large]
\ctikzset{bipole voltage style/.style={color=green}, bipole current style/.style={color=red}}
% Begin Schematic

\newcommand{\gndlvl}{-3}

\draw (0,0) node[op amp] (opvA) {$A$};
\draw (opvA.out -| 4, 0) node[op amp, anchor=-] (opvB) {$B$};
\draw (opvB.out -| 9, 0) node[op amp, anchor=-] (opvC) {$C$};

% Umkehrsummierer
\draw (opvA.+) to[short] (opvA.+ |- 0, \gndlvl) node[tlground] {};
\draw (opvA.-)
    to [vR, l_=$R_2$, *-o] (opvA.- -| -3, 0)
    to[open, v=$U_E$] (-3, \gndlvl + 0.5)
    to[short, o-] (-3, \gndlvl) node[tlground] {};
\draw (opvA.-)
    to[short, -*] (opvA.- |- 0, 2.5)
    to[R=$R_1$] (opvA.out |- 0, 2.5)
    to[short, -o] (opvA.out);
\draw (opvA.out)
    to[open, v=$U_1$] (opvA.out |- 0, \gndlvl+0.5)
    to[short, o-] (opvA.out |- 0, \gndlvl) node[tlground] {};

% Mitkopplungszweig
\draw (opvA.- |- 0, 2)
    to[short] (opvA.- |- 0, 4)
    to[R, l=$R_1$] (opvA.out |- 0, 4)
    to[short] (opvC.out |- 0, 4)
    to[short, -o] (opvC.out);

% Integrator 1
\draw (opvA.out)
    to[vR=$R$, -*] (opvB.-)
    to[short] (opvB.- |- 0, 1)
    to[C, l=$C$] (opvB.out |- 0, 1)
    to[short, -o] (opvB.out)
    to[vR=$R$] (opvC.-);
\draw (opvB.- |- 0, 1)
    to[short, *-] (opvB.- |- 0, 2.5)
    to[vR, l=$R_3$] (opvB.out |- 0, 2.5)
    to[short, -*] (opvB.out |- 0, 1);
\draw (opvB.+) to[short] (opvB.+ |- 0, \gndlvl) node[tlground] {};
\draw (opvB.out)
    to[open, v=$U_{BP}$] (opvB.out |- 0, \gndlvl+0.5)
    to[short, o-] (opvB.out |- 0, \gndlvl) node[tlground] {};

% Integrator 2
\draw (opvC.-)
    to[short, *-] (opvC.- |- 0, 1)
    to[C, l=$C$, -*] (opvC.out |- 0, 1);
\draw (opvC.out)
    to[open, v=$U_{TP}$] (opvC.out |- 0, \gndlvl+0.5)
    to[short, o-] (opvC.out |- 0, \gndlvl) node[tlground] {};
    
\end{circuitikz}
\end{document}

Übertragungsfunktion

Durch Koeffizientenvergleich mit der Allgemeinen Übertragungsfunktion von Band- und Tiefpässen 2. Ordnung ergibt sich:

Bodediagramm und Ortskurve

mit den Parametern:

Bode Diagramm	Ortskurve

• 📈Mathematica Notebook

Funktionsweise

Zwischenspannungen können durch die einzelne Betrachtung jeder OPV Stufe ermittelt werden.

\usepackage[european, straightvoltages]{circuitikz}
\usepackage{amsmath}

\begin{document}
\begin{circuitikz}[thick, scale=1, font=\Large]
% Begin Schematic

\draw (0,0) node[op amp] (opv) {};
\draw (opv.+) to[short] ++(0,-0.5) node[tlground] {};
\draw (opv.-)
    to [R, l_=$R_2$, *-o] (opv.- -| -3,0)
    node[left] {$U_{E}$};
\draw (opv.-)
    to[short, *-*] (opv.- |- 0, 2)
    to[R, l_=$R_1$, -o] (-3, 2)
    node[left] {$U_{TP}$};
\draw (opv.- |- 0, 2)
    to[R=$R_1$] (opv.out |- 0, 2)
    to[short, -*] (opv.out)
    to[short, -o] ++(1,0) node[right] {$U_1$};

\end{circuitikz}
\end{document}

\usepackage[european, straightvoltages]{circuitikz}
\usepackage{amsmath}

\begin{document}
\begin{circuitikz}[thick, scale=1, font=\Large]
% Begin Schematic
% Begin Schematic
\draw (0,0) node[op amp] (opv) {};
\draw (opv.+)
    to[short] ++(0,-0.5)
    node[tlground] {};
\draw (opv.-)
    to [R, l_=$R$, *-o] ++(-2,0)
    node[left] {$U_1$};
\draw (opv.-)
    to[short, -*] (opv.- |- 0, 1.5)
    to[C=$C$] (opv.out |- 0, 1.5)
    to[short, *-] ++(0,-1.5)
    to[short] (opv.out);
\draw (opv.-)
    to[short] (opv.- |- 0, 3)
    to[R, l=$R_3$] (opv.out |- 0, 3)
    to[short] ++(0,-2)
    to[short, -*](opv.out);
\draw (opv.out)
    to[short, -o] ++(1, 0)
    node[right] {$U_{BP}$};

\end{circuitikz}
\end{document}

\usepackage[european, straightvoltages]{circuitikz}
\usepackage{amsmath}

\begin{document}
\begin{circuitikz}[very thick, scale=1, font=\Large]
% Begin Schematic

\draw (0,0) node[op amp] (opv) {};

\draw (opv.+) to[short] ++(0,-0.5) node[tlground] {};
\draw (opv.-)
    to[short, *-] (opv.- |- 0, 2)
    to[C=$C$] (opv.out |- 0, 2)
    to[short, -*] (opv.out);

\draw (opv.-)
    to[R, l_=$R$, -o] (opv.- -| -3,0)
    node[left] {$U_{BP}$};

\draw (opv.out)
    to[short, -o] ++(1,0)
    node[right] {$U_{TP}$};

\end{circuitikz}
\end{document}