Correction of doujinshi distributed at C101

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• P12

Impedance \(Z \) is the Euclidean distance of \(\dot{Z} \)

\begin{align}
\dot{Z}&=(ESR)+j\left ( 2 \pi f_R L+ \frac{1}{2 \pi f_R C}\right )\\
Z&=\sqrt{(ESR)^2+\left ( 2 \pi f_R L + \frac{1}{2 \pi f_R C}\right )^2}
\end{align}

Next,this explanation is for regulatory inductance. The value of parasitic inductance ESL symbol is L, unit is [H].

Therefore,quation 3 is

\begin{align}
ESL=L \mathrm{[H]}
\end{align}

• P13

The equations 9 and 10 are expressions for the capacitor, \(\frac{1}{2 \pi f L} \) is incorrect.

Correct equation is

\begin{align}
\lim_{f_R \to 0}&=\frac{1}{2 \pi f C} = \infty \mathrm{[\Omega]}\\
\lim_{f_R \to \infty}&=\frac{1}{2 \pi f C} = 0 \mathrm{[\Omega]}
\end{align}

• P14

The self-resonant frequency is the frequency when the imaginary part is zero.

The correct value is

\begin{align}
f_R =\frac{1}{2 \pi \sqrt{L C}} \mathrm{[Hz]}
\end{align}

Proof.

From definition of resonance circuit

\begin{align}
X_L &= X_C \\
2 \pi f L &= \frac{1}{2 \pi f C} \\
\end{align}

Dividely the both sides of the equation by \(L\),and maltiply the both sides of the equation the \(2 \pi f\) both sides

\begin{align}
(2 \pi f)^2 =\frac{1}{LC} \\
\end{align}

Dividely the both sides of the equation by \((2 \pi)^2 \)

\begin{align}
f^2 =\frac{1}{(2 \pi)^2 LC} \\
\end{align}

Finally,take the square root of both sides(note \(f\geq 0\))

\begin{align}
f =\frac{1}{2 \pi \sqrt{LC}} \\
\end{align}