\usepackage[european resistors,american inductors, american voltages]{circuitikz}

\usepackage[utf8]{inputenc}

\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);

\subsection{Chain Matrix}

\frac{z_R + z_C}{z_R}&z_C \\

\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);

\subsection{Chain Matrix}

\frac{z_R + z_C}{z_C} & z_R \\

\section{Bandpass, second order}

\subsection{Highpass followed by Lowpass}

\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);

\subsubsection{Chain Matrix}

\frac{\left(z_{R_T} + z_{C_T} \right) \cdot \left(z_{C_H} + z_{R_H}\right)}{z_{R_H} \cdot z_{C_T}} +

\frac{z_{C_H}}{z_{C_T}} & \frac{z_{C_H} \cdot z_{R_T}}{z_{R_H}} + z_{R_T} + z_{C_H}\\

\frac{z_{R_H} + z_{R_T} + z_{C_T}}{z_{C_T} \cdot z_{R_H}} & \frac{z_{R_T}}{z_{R_H}} + 1

\subsection{Lowpass followed by Highpass}

\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);

\subsubsection{Chain Matrix}

\frac{\left(z_{R_T} + z_{C_T} \right) \cdot \left(z_{C_H} + z_{R_H}\right)}{z_{R_H} \cdot z_{C_T}} +

\frac{z_{R_T}}{z_{R_H}}& \frac{z_{C_H} \cdot z_{R_T}}{z_{C_T}} + z_{R_T} + z_{C_H}\\

\frac{z_{R_H} + z_{C_H} + z_{C_T}}{z_{C_T} \cdot z_{R_H}} & \frac{z_{C_H}}{z_{C_T}} + 1

\subsection{Frequency dependent voltage divider}

\draw (0,3) to [short, o- ,i=$I_1$] (1,3)

to [C, l_=$C_S$, -*](5,3)

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);

\subsubsection{Chain Matrix}

\frac{\left(z_{R_P} + z_{C_P} \right) \cdot \left(z_{C_S} +
</div></div>z</span>_{R_S}\right)}{z_{C_P} \cdot z_{R_P}} +1 & z_{C_S}+z_{R_S}\\

\frac{z_{C_P}+z_{R_P}}{z_{C_P} \cdot z_{R_P}} & 1

$$K_{TH} \neq K_{HT} \neq K_{ST}$$

</pre></div></figure>