$\displaystyle\frac{ a_o }{ a_{lc} }=\displaystyle\frac{ s_o }{ s_{lc} }$

a_o / a_lc = s_o / s_lc

$\displaystyle\frac{1}{ f_{lc} }=\displaystyle\frac{1}{ s_o }+\displaystyle\frac{1}{ s_{lc} }$

1/ f_lc =1/ s_o +1/ s_lc

$\displaystyle\frac{1}{ f_{vvd} }=( n -1)\left(\displaystyle\frac{1}{ R_1 }+\displaystyle\frac{1}{ R_2 }-\displaystyle\frac{( n -1)d}{ n R_1 R_2 }\right)$

1/ f_vvd =( n -1)*(1/ R_1 + 1/ R_2 -( n -1)* d /( n * R_1 * R_2 ))

$\displaystyle\frac{1}{ f_{ccd} }=-( n -1)\left(\displaystyle\frac{1}{ R_1 }+\displaystyle\frac{1}{ R_2 }+\displaystyle\frac{( n -1)d}{ n R_1 R_2 }\right)$

1/ f_ccd =-( n -1)*(1/ R_1 +1/ R_2 +( n -1)* d /( n * R_1 * R_2 ))

$\displaystyle\frac{1}{ f_{vcs} }=( n -1)\left(\displaystyle\frac{1}{ R_1 }-\displaystyle\frac{1}{ R_2 }+\displaystyle\frac{( n -1) d }{ n R_1 R_2 }\right)$

1/ f_vcs =( n -1)(1/ R_1 -1/ R_2 +( n -1)* d /(n * R_1 * R_2 ))

$\displaystyle\frac{1}{ f_{lv} }=\displaystyle\frac{1}{ s_o }+\displaystyle\frac{1}{ s_i }$

1/ f_lv =1/ s_o + 1/ s_i

$\displaystyle\frac{1}{ f_c }=\displaystyle\frac{1}{ D - s_i }+ \displaystyle\frac{1}{ s_b }$

1/ f_c =1/( D - s_i ) + 1/ s_b

$\displaystyle\frac{1}{ s_o }+\displaystyle\frac{1}{ D -\displaystyle\frac{1}{\displaystyle\frac{1}{ f_{lv} }-\displaystyle\frac{1}{ s_b }}}=\displaystyle\frac{1}{ f_c }$

1/ s_o + 1/( D -1/(1/ f_lv -1/ s_b ))=1/ f_c

$\displaystyle\frac{1}{ f_{cvs} }=\displaystyle\frac{( n -1)^2 d }{ n R ^2}$

1/ f_cvs =( n -1)^2* d /( n * R ^2)

$\displaystyle\frac{1}{ f_{vcs} }=\displaystyle\frac{( n -1)^2 d }{ n R ^2}$

1/ f_vcs =( n -1)^2* d /( n * R ^2)

$\displaystyle\frac{1}{ f_{csd} }=-( n -1)\left(\displaystyle\frac{2}{ R } +\displaystyle\frac{( n -1) d }{ n R ^2}\right)$

1/ f_csd =-( n -1)*(2/ R + ( n -1)* d /( n * R ^2))

$\displaystyle\frac{1}{ f_{vsd} }=( n -1)\left(\displaystyle\frac{2}{ R }-\displaystyle\frac{( n -1) d }{ n R ^2}\right)$

1/ f_vsd =( n -1)*(2/ R -( n -1)* d /( n * R ^2))

$D=\displaystyle\frac{1}{f}$

D =1/ f