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\\
V_{OUT}&=&V_{IN}-V_{REG}
\end{eqnarray}
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V_{OUT}&=&V_Z-V_{BE}{\;}{\approx}{\;}V_Z-0.6\\
\\
I_{IN}&=&I_{OUT}
\end{eqnarray}
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\begin{eqnarray}
I_{R1}=\frac{V_{IN}-V_{Z}}{R_1}
\end{eqnarray}
ãã®é»æµ\(I_{R1}\)ã¯ãã§ããŒãã€ãªãŒã\(D_Z\)ã®ãã§ããŒé»å§\(V_Z\)ãä¿ã€ã®ã«å¿ èŠãªãã§ããŒé»æµ\(I_Z\)ãšNPNãã©ã³ãžã¹ã¿\(Q_1\)ã®ããŒã¹é»æµ\(I_B\)ã®äž¡æ¹ãååã«æµãããããªå€ã«ããŸãã
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V_{OUT}&=&V_{REF}\left(1+\frac{R_1}{R_2}\right)+I_{BIAS}R_1\\
\\
I_{IN}&=&I_{OUT}
\end{eqnarray}
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åºåé»å§\(V_{OUT}\)ã¯äžèšã®ããã«å°åºããŠããŸãã
\begin{eqnarray}
V_{OUT}&=&V_{REF}+R_1ã®é»å§éäž\\
\\
&=&V_{REF}+R_1\left(\frac{V_{REF}}{R_2}+I_{BIAS}\right)\\
\\
&=&V_{REF}\left(1+\frac{R_1}{R_2}\right)+I_{BIAS}R_1
\end{eqnarray}
ããã§ããªãã¢ã³ãã®åè»¢å ¥å端åã«æµããé»æµ\(I_{BIAS}\)ã¯éåžžã«å°ããã®ã§ã\(I_{BIAS}R_1\)ãçç¥ãããšãåºåé»å§\(V_{OUT}\)ã¯æ¬¡åŒãšãªããŸãã
\begin{eqnarray}
V_{OUT}&=&V_{REF}\left(1+\frac{R_1}{R_2}\right)
\end{eqnarray}
äžåŒã¯äžèšã®ããã«åå§ãçšããŠãæ±ããããšãã§ããŸãã
\begin{eqnarray}
&&V_{OUT}ïŒV_{REF}=R_1+R_2ïŒR_2\\
\\
{\Leftrightarrow}&&V_{OUT}=V_{REF}\left(1+\frac{R_1}{R_2}\right)
\end{eqnarray}
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V_{OUT}&=&V_{REF}\left(1+\frac{R_1}{R_2}\right)+I_{REF}R_1\\
\\
I_{IN}&=&I_{OUT}
\end{eqnarray}
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åºåé»å§\(V_{OUT}\)ã¯äžèšã®ããã«å°åºããŠããŸãã
\begin{eqnarray}
V_{OUT}&=&V_{REF}+R_1ã®é»å§éäž\\
\\
&=&V_{REF}+R_1\left(\frac{V_{REF}}{R_2}+I_{REF}\right)\\
\\
&=&V_{REF}\left(1+\frac{R_1}{R_2}\right)+I_{REF}R_1
\end{eqnarray}
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\begin{eqnarray}
V_{OUT}&=&V_{REF}\left(1+\frac{R_1}{R_2}\right)
\end{eqnarray}
äžåŒã¯äžèšã®ããã«åå§ãçšããŠãæ±ããããšãã§ããŸãã
\begin{eqnarray}
&&V_{OUT}ïŒV_{REF}=R_1+R_2ïŒR_2\\
\\
{\Leftrightarrow}&&V_{OUT}=V_{REF}\left(1+\frac{R_1}{R_2}\right)
\end{eqnarray}
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