# Accurate Constant Phase Elements Dedicated for Audio Signal Processing
## 3 Approximation of CPE in Frequency Domain and Numerical Results
Numerical values associated with this CPE are specified in Tables 34 and 35, pseudo-capacitance is 1.33 \(\mu\)F/s\({}^{1/5}\) (type I) and 665 nF/s\({}^{1/5}\) (type II). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**R/Cp** & **R\({}_{1}\)/C\({}_{1}\)** & **R\({}_{2}\)/C\({}_{2}\)** & **R\({}_{3}\)/C\({}_{3}\)** & **R\({}_{4}\)/C\({}_{4}\)** & **R\({}_{5}\)/C\({}_{5}\)** & **R\({}_{6}\)/C\({}_{6}\)** & **R\({}_{7}\)/C\({}_{7}\)** \\ \hline
**30 kf**\(\Omega\) & **13 k\(\Omega\)** & **4 k\(\Omega\)** & **1.2 k\(\Omega\)** & **374 \(\Omega\)** & **115 \(\Omega\)** & **35 \(\Omega\)** & **13.3 \(\Omega\)** \\
15 kf\(\Omega\) \(\angle\) & 12 k\(\Omega\) \(\angle\) & 3.9 k\(\Omega\) \(\parallel\) & 1.2 k\(\Omega\) & 330 \(\Omega\) \(\angle\) & 100 \(\Omega\) \(\angle\) & 33 \(\Omega\) \(\angle\) & 10 \(\Omega\) \(\angle\) \\
15 kf\(\Omega\) & 1 k\(\Omega\) & 100 \(\Omega\) & & 47 \(\Omega\) & 15 \(\Omega\) & 2.2 \(\Omega\) & 3.3 \(\Omega\) \\ \hline
**500 nF** & **1.5**\(\mu\)F & **1.1**\(\mu\)F & **779 nF** & **556 nF** & **396 nF** & **283 nF** & **200 nF** \\
1 \(\mu\)F \(\angle\) & 1.5 \(\mu\)F & 1 \(\mu\)F & 560 nF & 330 nF & 330 nF \(\parallel\) & 270 nF \(\parallel\) & 100 nF \(\parallel\) \\
1 \(\mu\)F & & 100 nF & 220 nF & 220 nF & 68 nF & 12 nF & 100 nF \\ \hline \hline \end{tabular}
\end{table} 
Table 32: CPE with math order \(\alpha\) = 7/9; fully passive RC series-parallel topology of fractal capacitor. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**R/Cp** & **R\({}_{1}\)/C\({}_{1}\)** & **R\({}_{2}\)/C\({}_{2}\)** & **R\({}_{3}\)/C\({}_{3}\)** & **R\({}_{4}\)/C\({}_{4}\)** & **R\({}_{5}\)/C\({}_{5}\)** & **R\({}_{6}\)/C\({}_{6}\)** & **R\({}_{7}\)/C\({}_{7}\)** \\ \hline
**18 k\(\Omega\)** & **8.4** k\(\Omega\)** & **2.66** k\(\Omega\)** & **850 \(\Omega\)** & **271 \(\Omega\)** & **86.6**\(\Omega\)** & **27.7**\(\Omega\)** & **10 \(\Omega\)** \\
18 k\(\Omega\) & 8.2 k\(\Omega\) \(\angle\) & 2.2 k\(\Omega\) \(\parallel\) & 820 \(\Omega\) \(\angle\) & 270 \(\Omega\) & 82 \(\Omega\) \(\angle\) & 27 \(\Omega\) & 10 \(\Omega\) \\  & 220 \(\Omega\) & 470 \(\Omega\) & 33 \(\Omega\) & & 4.7 \(\Omega\) & & \\ \hline
**260 nF** & **1.1**\(\mu\)F & **820 nF** & **560 nF** & **383 nF** & **262 nF** & **179 nF** & **120 nF** \\
220 nF \(\parallel\) & 1 \(\mu\)F \(\parallel\) & 820 nF & 560 nF & 1.2 \(\mu\)F \(\angle\) & 220 nF \(\parallel\) & 180 nF & 120 nF \\
39 nF & 100 nF & & & 560 nF & 39 nF & & \\ \hline \hline \end{tabular}
\end{table} 
Table 30: CPE with math order \(\alpha\) = 3/4; fully passive RC series-parallel topology of fractal capacitor. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**R/Cp** & **R\({}_{1}\)/C\({}_{1}\)** & **R\({}_{2}\)/C\({}_{2}\)** & **R\({}_{3}\)/C\({}_{3}\)** & **R\({}_{4}\)/C\({}_{4}\)** & **R\({}_{5}\)/C\({}_{5}\)** & **R\({}_{6}\)/C\({}_{6}\)** & **R\({}_{7}\)/C\({}_{7}\)** \\ \hline
**30 kf**\(\Omega\) & **13 k\(\Omega\)** & **4 k\(\Omega\)** & **1.2 k\(\Omega\)** & **374 \(\Omega\)** & **115 \(\Omega\)** & **35 \(\Omega\)** & **13.3**\(\Omega\)** \\
15 kf\(\Omega\) \(\angle\) & 12 k\(\Omega\) \(\angle\) & 3.9 k\(\Omega\) \(\parallel\) & 1.2 k\(\Omega\) \(\angle\) & 330 \(\Omega\) \(\angle\) & 100 \(\Omega\) \(\angle\) & 33 \(\Omega\) \(\angle\) & 10 \(\Omega\) \(\angle\) \\
15 kf\(\Omega\) & 1 \(\Omega\) \(\Omega\) & 100 \(\Omega\) & & 47 \(\Omega\) & 15 \(\Omega\) \(\Omega\) & 2.2 \(\Omega\) & 3.3 \(\Omega\) \\ \hline
**500 nF** & **1.5**\(\mu\)F & **1.1**\(\mu\)F & **779 nF** & **556 nF** & **396 nF** & **283 nF** & **200 nF** \\
1 \(\mu\)F \(\angle\) & 1.5 \(\mu\)F & 1 \(\mu\)F \(\parallel\) & 560 nF \(\parallel\) & 330 nF \(\parallel\) & 330 nF \(\parallel\) & 270 nF \(\parallel\) & 100 nF \(\parallel\) \\
1 \(\mu\)F & & 100 nF & 220 nF & 220 nF & 68 nF & 12 nF & 100 nF \\ \hline \hline \end{tabular}
\end{table} 
Table 33: CPE with math order \(\alpha\) = 7/9; fully passive RC parallel-series topology of fractal capacitor.