Hi,

for my electronics workshop, I compiled a short summary on low- and highpass filters and how they function once they are combined to a bandpass.

Special care was taken in regards to how they are combined (Low + High vs High + Low).

At the end of this document, you will find the complete code to compile the summary for yourself.

## Chain Matrix Highpass

Failed to render the following block of LaTeX:

\documentclass[standalone]{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}

\begin{circuitikz}
\draw (1,2) to [C, l_=$C$, -*] (3,2);
\draw (3,2) to[R=$R$] (3,0);
\draw (0,0) to[short, o-*] (3,0) to[short, -o] (4,0);
\draw (0,0) to [open, v^>=$U_1$] (0,2);
\draw (0,2) to [short, o- ,i=$I_1$] (1,2);
\draw (4,0) to [open, v>=$U_2$] (4,2);
\draw (3,2) to [short, -o ,i=$I_2$] (4,2);
\end{circuitikz}
\end{document}

## Chain Matrix Lowpass

Failed to render the following block of LaTeX:

\documentclass[standalone]{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}

\begin{circuitikz}
\draw (1,2) to [R, l_=$R$, -*] (3,2);
\draw (3,2) to[C=$C$] (3,0);
\draw (0,0) to[short, o-*] (3,0) to[short, -o] (4,0);
\draw (0,0) to [open, v^>=$U_1$] (0,2);
\draw (0,2) to [short, o- ,i=$I_1$] (1,2);
\draw (4,0) to [open, v>=$U_2$] (4,2);
\draw (3,2) to [short, -o ,i=$I_2$] (4,2);
\end{circuitikz}
\end{document}

## Bandpasses

### Chain Matrix of Highpass followed by Lowpass

Failed to render the following block of LaTeX:

\documentclass[standalone]{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}

\begin{circuitikz}
\draw (0,0) to [short, o-*] (3,0) to [short, -*] (5,0) to [short, -o] (6,0);
\draw (0,3) to [short, o-] (1,3) to [C, l_=$C_H$, -*] (3,3) to [R, l_=$R_T$, -*] (5,3) to [short] (5,3);
\draw (3,3) to [R, l_=$R_H$] (3,0);
\draw (5,3) to [C, l_=$C_T$] (5,0);
\draw (0,0) to [open, v^>=$U_1$] (0,3);
\draw (0,3) to [short, o- ,i=$I_1$] (1,3);
\draw (6,0) to [open, v>=$U_2$] (6,3);
\draw (5,3) to [short, -o ,i=$I_2$] (6,3);
\end{circuitikz}
\end{document}

### Chain Matrix of Lowpass followed by Highpass

Failed to render the following block of LaTeX:

\documentclass[standalone]{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}

\begin{circuitikz}
\draw (0,0) to [short, o-*] (3,0) to [short, -*] (5,0) to [short, -o] (6,0);
\draw (0,3) to [short, o-] (1,3) to [R, l_=$R_T$, -*] (3,3) to [C, l_=$C_H$, -*] (5,3) to [short] (5,3);
\draw (3,3) to [C, l_=$C_T$] (3,0);
\draw (5,3) to [R, l_=$R_H$] (5,0);
\draw (0,0) to [open, v^>=$U_1$] (0,3);
\draw (0,3) to [short, o- ,i=$I_1$] (1,3);
\draw (6,0) to [open, v>=$U_2$] (6,3);
\draw (5,3) to [short, -o ,i=$I_2$] (6,3);
\end{circuitikz}
\end{document}

### Chain Matrix of frequency dependent voltage divider

Failed to render the following block of LaTeX:

\documentclass[standalone]{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}

\begin{circuitikz}
\draw (0,3) to [short, o- ,i=$I_1$] (1,3) to [R, l_=$R_S$](3,3) to [C, l_=$C_S$, -*](5,3) to [short, -*](7,3) to [short, -o, i=$I_2$] (8,3);
\draw (0,0) to [short, o-*](5,0) to [short, -*] (7,0) to [short, -o](8,0);
\draw (7,3) to [R, l_=$R_P$] (7,0);
\draw (5,3) to [C, l_=$C_P$] (5,0);
\draw (0,0) to [open, v^>=$U_1$] (0,3);
\draw (8,0) to [open, v>=$U_2$] (8,3);
\end{circuitikz}
\end{document}

## \LaTeX

This includes pictures of the circuits based on circuitikz.

summary_filters.tex