# Simple Model

# Transmission line Model

# Parallel Model

# Extended Parallel Model

%Modeling of Supercapacitors (UltraCapacitors) % Author: Amir Ostadrahimi % for more information see: https://doi.org/10.1109/ACCESS.2023.3250965 --> ( New Parameter Identification Method for Supercapacitor Model ) \documentclass[border=3pt, tikz]{standalone} \usepackage[american,cuteinductors,smartlabels]{circuitikz} \ctikzset{bipoles/thickness=1.2} \ctikzset{bipoles/length=1.5cm} \tikzstyle{every node}=[font=\large] \tikzstyle{every path}=[line width=1 .1pt,line cap=round,line join=round] \begin{document} \begin{tikzpicture} %Simple models of SCs %First Model (left) \coordinate (SC0) at (0,0) ; \draw (SC0) to [short,o-]++(0.4,0) to [R, l=$ESR$]++(1.9,0) to [C, l_=$C$]++(1.9,0) to [short,-o] ++(0.4,0); %Second Model (right) \coordinate (SC1) at (6,0) ; \draw (SC1) to [short,o-]++(0.4,0) to [R, l=$ESR$]++(1.9,0) coordinate (E2) to [short] ++(0,1) to [R, l=$EPR$] ++(1.8,0) to [short] ++(0,-1) coordinate (C2) to [vC, invert,mirror, l=$C$](E2);% using "mirror" and "invert" one can change the direction of the arrow. \draw (C2) to [short, -o]++(0.8,0); \end{tikzpicture} % \begin{tikzpicture} %Transmission line Model \newcommand\gap{0.2} %short gap between elements \newcommand\Rlength{2.1} %length of resistors \newcommand\Clength{2.9} %length of Capacitors \coordinate (SC0) at (0,0) ; \draw (SC0) to [short,o-]++(\gap,0) to [R, l=$R_{1}$]++(\Rlength,0) to [short]++(\gap,0) coordinate (C1T); %% C1T is the point from which capacitor1 will be \draw (C1T) to [short]++(\gap,0) to [R, l=$R_{2}$]++(\Rlength,0) to[short]++(\gap,0) coordinate (C2T); %% C2T is the point from which capacitor1 will be \draw (C2T) --++(0.5,0) coordinate (dashedT1); %% dashed line in the top part of the circuit \draw [dashed] (dashedT1) --++ (1,0) coordinate (dashedT2); %% where dashed finishes in the top \draw (dashedT2) to [R, l=$R_{n-1}$]++(\Rlength,0) to [short]++(\gap,0) coordinate (CN1T) to[short]++(\gap,0) to [R, l=$R_{n}$]++(\Rlength,0) to [short]++(\gap,0) to [C, l=$C_{n}$]++(0,-\Clength) coordinate (CnB); %% CnB is the bottom of Cn %CAPACITORS \draw (C1T) to [C, l=$C_{1}$]++(0,-\Clength) coordinate (C1B); %% C1B is the bottom of C1 \draw (C2T) to [C, l=$C_{2}$]++(0,-\Clength) coordinate (C2B); %% C2B is the bottom of C2 \draw (CN1T) to [C, l=$C_{n-1}$]++(0,-\Clength) coordinate (CN1B); %% CN1B is the bottom of CN1 \draw (SC0) to [open,] ++(0,-\Clength) coordinate (SC0B) ; %% SC0B is the bottoom part of the input % Lines \draw (CnB) -- (CN1B); \draw [dashed] (CN1B) -- (C2B); \draw (C2B) -- (C1B) to [short,-o] (SC0B); %description \coordinate [label={[xshift=0, yshift=0] \large $R_{1}C_{1}<R_{2}C_{2} <...<R_{n-1}C_{n-1}<R_{n}C_{n}$ }] (des) at (6,-3.7) ; \end{tikzpicture} % \begin{tikzpicture} % Parallel model \newcommand\shortgap{0.9} %short gap between elements \newcommand\Rlength{2.1} %length of resistors \newcommand\Clength{2.9} %length of Capacitors \coordinate (SC0) at (0,0) ; \draw (SC0) to [R,l_=$R_{L}$] ++(0, 2*\Rlength) to [short] ++(3*\shortgap,0) coordinate (B2T); %% B2T is the top part of Branch 2 \draw (B2T) to [R,l=$R_{1}$] ++(0, -\Rlength) coordinate (R1B) to [short] ++(-\shortgap,0) to [C, l=$C_{1}$] ++(0, -\Rlength) coordinate (C1B); %%R1B is bottom of the R1 and C1B is the top part of capacitor 1 \draw (R1B) to [short]++(\shortgap,0) to [vC, invert, l=$C_{V}$] ++ (0,-\Rlength); \draw (B2T) to [short] ++(3*\shortgap,0) coordinate (B3T); %% B3T is the top part of Branch 3 \draw (B3T)to [R,l=$R_{2}$]++ (0, -\Rlength) coordinate (mid1) to [C,l=$C_{2}$] ++ (0, -\Rlength) coordinate (B3B); %% B3B is the top part of Branch 3 \draw (B3T) to [short] ++(0.5*\shortgap,0) coordinate (dashed1); %% dashed1 is the start of the dashed area \draw [dashed] (dashed1)--++(1.3,0) coordinate (dashed2); %% dashed 2 is the end of dashed area \draw (dashed2) to [short]++(0.3,0) to [R, l=$R_{n}$] ++(0, -\Rlength) coordinate (mid2) to [C, l=$C_{n}$]++(0,-\Rlength) coordinate (endd); %%endd is the end of the design \draw (endd) to [short]++(-0.3,0) coordinate (dashed2B); \draw [dashed] (dashed2B) -- ++(-1.3,0) coordinate (dashed1B); \draw (dashed1B) -- (SC0); \draw (mid1) to [open, l= \Large $...$] (mid2); \end{tikzpicture} % \begin{tikzpicture} % Extended parallel model \newcommand\shgap{1} %short gap between elements \newcommand\Lgap{4} %large gap between elements \newcommand\Reslength{1.7} %length of resistors \newcommand\CapLength{1.7} %length of Capacitors \coordinate (SC0) at (0,0); %reference point %Rectangle1 \draw (SC0) ++ (-0.7,0.5) coordinate (RE1LB); %RE1LB= Rectangle 1 left bottom \draw (SC0) ++ (12.5, 0.5) coordinate (RE1RB); %RE1LB= Rectangle 1 Right bottom \draw (RE1LB) ++ (0,1.5* \Lgap) coordinate (RE1LT); %RE1LB= Rectangle 1 left top \draw (RE1RB) ++ (0, 1.5* \Lgap) coordinate (RE1RT); %RE1LB= Rectangle 1 Right top \draw [ dotted, fill=cyan!10] (RE1LB)-- (RE1RB)-- (RE1RT) --(RE1LT) -- cycle; % Rectangle2 \draw (SC0) ++ (-0.7,7) coordinate (RE1LB); %RE1LB= Rectangle 1 left bottom \draw (SC0) ++ (12.5, 7) coordinate (RE1RB); %RE1LB= Rectangle 1 Right bottom \draw (RE1LB) ++ (0, 1.2* \Lgap) coordinate (RE1LT); %RE1LB= Rectangle 1 left top \draw (RE1RB) ++ (0, 1.2* \Lgap) coordinate (RE1RT); %RE1LB= Rectangle 1 Right top \draw [ dotted, fill=gray!10] (RE1LB)-- (RE1RB)-- (RE1RT) --(RE1LT) -- cycle; %First Branch \draw (SC0) --++(0,\Lgap) coordinate (B1L); %% B1L is the left side of the branch 1 \draw (B1L) to [short]++(\shgap,0) to [R, l=$R_{1}$]++(\Reslength,0) to [C, l=$C(V)$] ++(\CapLength,0) to [short]++(\shgap,0) coordinate (P1L); % P1L is the left side of the first parallel branch. \draw (P1L) to [short] ++ (0,1) to [C, l= \Large $\frac{C(V)}{2}$] ++(\CapLength,0) to [short] ++ (0,-1) coordinate (P1R); %% P1R is the right side of the parallel branch \draw (P1L) to [short] ++ (0,-1) to [R, l_= \Large $\frac{2\tau (V)}{l^{2} \pi ^{2} C(V)}$] ++(\CapLength,0) to [short] ++ (0,1); \draw [dashed] (P1R) --++(2,0) coordinate (P2L); % P1L is the left side of the first parallel branch. \draw (P2L) to [short] ++ (0,1) to [C, l= \Large $\frac{C(V)}{2}$] ++(\CapLength,0) to [short] ++ (0,-1) coordinate (P2R); %P2R is the right side of the second parallel branch \draw (P2L) to [short] ++ (0,-1) to [R, l_= \Large $\frac{2\tau (V)}{n^{2} \pi ^{2} C(V)}$] ++(\CapLength,0) to [short] ++ (0,1) to [short]++(1,0) coordinate (B1R); % B1R is the right side of the branch \draw (B1R) -- ++(0,-\Lgap) coordinate (SC1); \draw (SC0) to [open, o-o] (SC1); % Second Branch \draw (B1L)--++(0,\Lgap) coordinate (B2L); % B2L is the left side of the second branch \draw (B1R)--++(0,\Lgap) coordinate (B2R); % B2R is the right side of the second branch \draw (B2L) to [short] ++(3*\shgap,0) to [R, l=$R_{2}$]++(\Reslength,0) to [C, l=$C_{2}$] (B2R); %Third Branch \draw (B2L)--++(0,\Lgap/2) coordinate (B3L); % B3L is the left side of the third branch \draw (B2R)--++(0,\Lgap/2) coordinate (B3R); % B3R is the right side of the third branch \draw (B3L) to [short] ++(3*\shgap,0) to [R, l=$R_{3}$]++(\Reslength,0) to [C, l=$C_{3}$] (B3R); %Fourth Branch \draw [loosely dashed] (B3L)--++(0,\Lgap/1.5) coordinate (B4L); % B4L is the left side of the fourth branch \draw [loosely dashed] (B3R)--++(0,\Lgap/1.5) coordinate (B4R); % B4R is the right side of the fourth branch \draw (B4L) to [R, l=$R_{leak}$] (B4R); %Descriptions \coordinate [ label={ \Large First Branch}] (DES1) at (6.3,0.7); \coordinate [ label={ \Large Parallel Branches }] (DES1) at (6.3,11); \end{tikzpicture} \end{document}