6.3 時定数が3段の場合の周波数特性

A_L	=	A_M $\displaystyle {\frac{{1}}{{1+\frac{1}{j\omega T_{L1}}}}}$ ^. $\displaystyle {\frac{{1}}{{1+\frac{1}{j\omega T_{L2}}}}}$ ^. $\displaystyle {\frac{{1}}{{1+\frac{1}{j\omega T_{L3}}}}}$
	=	A_M $\displaystyle {\frac{{1}}{{1-j\frac{1}{\omega T_{L1}}}}}$ ^. $\displaystyle {\frac{{1}}{{1-j\frac{1}{\omega T_{L2}}}}}$ $\displaystyle {\frac{{1}}{{1-j\frac{1}{\omega T_{L3}}}}}$

A_L	=	A_M $\displaystyle {\frac{{1}}{{1-jx}}}$ ^. $\displaystyle {\frac{{1}}{{1-jx/n}}}$ ^. $\displaystyle {\frac{{1}}{{1-jx/m}}}$
	=	A_M $\displaystyle {\frac{{1}}{{1-x^2(\frac{1}{n}+\frac{1}{m}+\frac{1}{nm}) - jx(1+\frac{1}{n}+\frac{1}{m}-\frac{x^2}{nm})}}}$

A'_L	=	$\displaystyle {\frac{{A_L}}{{1+A_L\beta}}}$
	=	$\displaystyle {\frac{{A_M}}{{1-x^2(\frac{1}{n}+\frac{1}{m}+\frac{1}{nm}) - jx(1+\frac{1}{n}+\frac{1}{m}-\frac{x^2}{nm})+A_M\beta}}}$
	=	$\displaystyle {\frac{{A_M}}{{1+A_M\beta-x^2(\frac{1}{n}+\frac{1}{m}+\frac{1}{nm}) - jx(1+\frac{1}{n}+\frac{1}{m}-\frac{x^2}{nm})}}}$

A'_L = $\displaystyle {\frac{{A_M}}{{F_M-x^2(\frac{1}{n}+\frac{1}{m}+\frac{1}{nm}) - jx(1+\frac{1}{n}+\frac{1}{m}-\frac{x^2}{nm})}}}$

(6.26)

| A'_L| = A_M $\displaystyle {\frac{{1}}{{ \sqrt{\bigl\{F_M-x^2(\frac{1}{n}+\frac{1}{m}+\frac{1}{nm})\bigr\}^2 + x^2(1+\frac{1}{n}+\frac{1}{m}-\frac{x^2}{nm})^2}}}}$

(6.27)

$\displaystyle \Bigl\{$ F_M-X $\displaystyle \Bigl($ $\displaystyle {\frac{{1}}{{n}}}$ + $\displaystyle {\frac{{1}}{{m}}}$ + $\displaystyle {\frac{{1}}{{nm}}}$ $\displaystyle \Bigr)$ $\displaystyle \Bigr\}^{2}_{}$ +X $\displaystyle \Bigl($ 1+ $\displaystyle {\frac{{1}}{{n}}}$ + $\displaystyle {\frac{{1}}{{m}}}$ - $\displaystyle {\frac{{X}}{{nm}}}$ $\displaystyle \Bigr)^{2}_{}$
	=	$\displaystyle {\frac{{X^3}}{{n^2m^2}}}$ + $\displaystyle \Bigl\{$ $\displaystyle \Bigl($ $\displaystyle {\frac{{1}}{{n}}}$ + $\displaystyle {\frac{{1}}{{m}}}$ + $\displaystyle {\frac{{1}}{{nm}}}$ $\displaystyle \Bigr)^{2}_{}$ -2 $\displaystyle \Bigl($ 1 + $\displaystyle {\frac{{1}}{{n}}}$ + $\displaystyle {\frac{{1}}{{m}}}$ $\displaystyle \Bigr)$ $\displaystyle {\frac{{1}}{{nm}}}$ $\displaystyle \Bigr\}$ X²
		+ $\displaystyle \Bigl\{$ $\displaystyle \Bigl($ 1 + $\displaystyle {\frac{{1}}{{n}}}$ + $\displaystyle {\frac{{1}}{{m}}}$ $\displaystyle \Bigr)^{2}_{}$ -2F_M $\displaystyle \Bigl($ $\displaystyle {\frac{{1}}{{n}}}$ + $\displaystyle {\frac{{1}}{{m}}}$ + $\displaystyle {\frac{{1}}{{nm}}}$ $\displaystyle \Bigr)$ $\displaystyle \Bigr\}$ X + F_M²
	=	$\displaystyle {\frac{{1}}{{n^2m^2}}}$ [X³ + (n² + m² +1)X² + {(nm + n + m)² -2F_Mnm(n + m + 1)}X + n²m²F_M²]	(6.28)

- a + $\displaystyle \sqrt{{a^2-3b}}$	>	0
- b	>	0
2F_Mnm(n + m + 1) - (nm + n + m)²	>	0
F_M	>	$\displaystyle {\frac{{(nm+n+m)^2}}{{2nm(n+m+1)}}}$

x² = X = $\displaystyle {\frac{{-a+\sqrt{a^2-3b}}}{{3}}}$ = $\displaystyle {\frac{{-a+\sqrt{D}}}{{3}}}$

(6.30)

\| A'_Lp\|	=	A_M $\displaystyle {\frac{{nm}}{{\sqrt{\frac{2}{27}D(a-\sqrt{D}) - \frac{1}{9}ab + c}}}}$
	=	A_M $\displaystyle {\frac{{nm}}{{\sqrt{-\frac{2}{9}DX - \frac{1}{9}ab + c}}}}$