A. 等価回路

**図 19:** 電圧源モデルによるSRPPの等価回路
$\begin{figure}\input{figs/srpp_eqv} \end{figure}$

- μ₂i₁R_k2	=	(i₂ - i₁)R_L + i₂r_p2
(- μ₂R_k2 + R_L)i₁	=	(R_L + r_p2)i₂	(58)

μ₁e_i = {r_p1 + (μ₁ +1)R_k1 + R_k2 + R_L}i₁ - R_Li₂

(59)

e_o	=	R_Li₂ - R_Li₁
i₂	=	$\displaystyle {\frac{{e_o + R_L i_1}}{{R_L}}}$ = $\displaystyle {\frac{{e_o}}{{R_L}}}$ + i₁	(60)

(- μ₂R_k2 + R_L)i₁	=	(R_L + r_p2)( $\displaystyle {\frac{{e_o}}{{R_L}}}$ + i₁)
(- μ₂R_k2 - r_p2)i₁	=	e_o $\displaystyle {\frac{{R_L+r_{p2}}}{{R_L}}}$
i₁	=	- $\displaystyle {\frac{{r_{p2}+R_L}}{{(r_{p2}+\micro_2 R_{k2})R_L}}}$ e_o	(61)

μ₁e_i	=	{r_p1 + (μ₁ +1)R_k1 + R_k2 + R_L}i₁ - R_L( $\displaystyle {\frac{{e_o}}{{R_L}}}$ + i₁)
μ₁e_i + e_o	=	{r_p1 + (μ₁ +1)R_k1 + R_k2}i₁

μ₁e_i + e_o	=	- $\displaystyle {\frac{{\{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}\}(r_{p2}+R_L)}}{{(r_{p2}+\micro_2 R_{k2})R_L}}}$ e_o
- μ₁e_i	=	$\displaystyle {\frac{{\{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}\}(r_{p2}+R_L)+(r_{p2}+\micro_2 R_{k2})R_L}}{{(r_{p2}+\micro_2 R_{k2})R_L}}}$ e_o
e_o	=	- μ₁e_i $\displaystyle {\frac{{(r_{p2}+\micro_2 R_{k2})R_L}}{{\{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}\}(r_{p2}+R_L)+(r_{p2}+\micro_2 R_{k2})R_L}}}$
	=	- μ₁e_i $\displaystyle {\frac{{(1+\frac{\micro_2}{r_{p2}}R_{k2})R_L}}{{\{r_{p1}+(\micro_... ..._{k1}+R_{k2}\}\frac{r_{p2}+R_L}{r_{p2}}+(1+\frac{\micro_2}{r_{p2}}R_{k2})R_L}}}$
	=	- μ₁e_i $\displaystyle {\frac{{(1+g_{m2}R_{k2})R_L}}{{\{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}\}\frac{r_{p2}+R_L}{r_{p2}}+(1+g_{m2}R_{k2})R_L}}}$
	=	- μ₁e_i $\displaystyle {\frac{{R_L}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}\cdot\frac{r_{p2}+R_L}{r_{p2}}+R_L}}}$
	=	- μ₁e_i $\displaystyle {\frac{{\frac{r_{p2}R_L}{r_{p2}+R_L}}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}+\frac{r_{p2}R_L}{r_{p2}+R_L}}}}$
	=	- μ₁e_i $\displaystyle {\frac{{r_{p2}//R_L}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}+r_{p2}//R_L}}}$

A = - μ₁ $\displaystyle {\frac{{r_{p2}//R_L}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}+r_{p2}//R_L}}}$

(62)

**図 20:** 電流源モデルによるSRPPの等価回路
$\begin{figure}\input{figs/srpp_eqi} \end{figure}$

i₁R_k1	=	e_p1 - i₁R_k2 + e_o
e_p1	=	(R_k1 + R_k2)i₁ - e_o	(69)

i₁	=	g_m1(e_i - i₁R_k1) - $\displaystyle {\frac{{e_{p1}}}{{r_{p1}}}}$
	=	g_m1(e_i - i₁R_k1) - $\displaystyle {\frac{{(R_{k1}+R_{k2})i_1-e_o}}{{r_{p1}}}}$
(1 + g_m1R_k1 + $\displaystyle {\frac{{R_{k1}+R_{k2}}}{{r_{p1}}}}$ )i₁	=	g_m1e_i + $\displaystyle {\frac{{e_o}}{{r_{p1}}}}$
{(1 + g_m1R_k1)r_p1 + R_k1 + R_k2}i₁	=	g_m1r_p1e_i + e_o
(r_p1 + μ₁R_k1 + R_k1 + R_k2)i₁	=	μ₁e_i + e_o
i₁	=	$\displaystyle {\frac{{\micro_1 e_i + e_o}}{{r_{p1} + (\micro_1+1)R_{k1}+R_{k2}}}}$	(70)

i₂

- g_m2i₁R_k2 - $\displaystyle {\frac{{e_o}}{{r_{p2}}}}$

(71)

e_o	=	(- g_m2i₁R_k2 - $\displaystyle {\frac{{e_o}}{{r_{p2}}}}$ - i₁)R_L
	=	- (1 + g_m2R_k2)R_Li₁ - $\displaystyle {\frac{{R_L}}{{r_{p2}}}}$ e_o	(72)

e_o	=	- $\displaystyle {\frac{{(1 + g_{m2}R_{k2})R_L(\micro_1 e_i + e_o)}}{{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}}}$ - $\displaystyle {\frac{{R_L}}{{r_{p2}}}}$ e_o
(1 + $\displaystyle {\frac{{R_L}}{{r_{p2}}}}$ + $\displaystyle {\frac{{(1+g_{m2}R_{k2})R_L}}{{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}}}$ )e_o	=	- μ₁e_i $\displaystyle {\frac{{(1+g_{m2}R_{k2})R_L}}{{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}}}$
e_o	=	- μ₁e_i $\displaystyle {\frac{{\frac{(1+g_{m2}R_{k2})R_L}{r_{p1}+(\micro_1+1)R_{k1}+R_{k... ...{R_L}{r_{p2}} + \frac{(1+g_{m2}R_{k2})R_L}{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}}}}$
	=	- μ₁e_i $\displaystyle {\frac{{R_L}}{{\frac{r_{p2}+R_L}{r_{p2}}\cdot\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}} + R_L}}}$
	=	- μ₁e_i $\displaystyle {\frac{{\frac{r_{p2}R_L}{r_{p2}+R_L}}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}+\frac{r_{p2}R_L}{r_{p2}+R_L}}}}$
	=	- μ₁e_i $\displaystyle {\frac{{r_{p2}//R_L}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}+r_{p2}//R_L}}}$

A = - μ₁ $\displaystyle {\frac{{r_{p2}//R_L}}{{\frac{r_{p1}+(\micro_1+1)R_{k1}+R_{k2}}{1+g_{m2}R_{k2}}+r_{p2}//R_L}}}$

(73)

A..1 電圧源モデル