File:Superpositieformule c7.png
U u n i e u w = U i ⋅ H 1 ⋅ H 2 ⋅ A + U u o u d ⋅ H 3 ⋅ H 2 ⋅ A − U u o u d ⋅ A s t e l : U u = U u o u d = U u n i e u w A → lim ∞ U u U i = H 1 ⋅ H 2 1 − H 2 ⋅ H 3 H = U u U i = Z 1 ⋅ Z 2 R 1 ⋅ ( R 2 + Z 1 ) + Z 1 ⋅ ( R 2 + Z 2 ) H ( ω ) = 1 C 1 ⋅ C 2 ⋅ R 1 ⋅ R 2 ⋅ ( j ω ) 2 + C 2 ⋅ ( R 1 + R 2 ) ⋅ j ω + 1 = − j C 2 ⋅ ( R 1 + R 2 ) ⋅ ω + j ⋅ ( C 1 ⋅ C 2 ⋅ R 1 ⋅ R 2 ⋅ ω 2 − 1 ) {\displaystyle {\begin{aligned}&Uu_{nieuw}=Ui\cdot H1\cdot H2\cdot A+Uu_{oud}\cdot H3\cdot H2\cdot A-Uu_{oud}\cdot A\\&stel\!\!:Uu=Uu_{oud}=Uu_{nieuw}\\&A{\xrightarrow {\lim }}\infty \;{\frac {Uu}{Ui}}={\frac {H1\cdot H2}{1-H2\cdot H3}}\\&H={\frac {Uu}{Ui}}={\frac {Z1\cdot Z2}{R1\cdot (R2+Z1)+Z1\cdot (R2+Z2)}}\\&H(\omega )={\frac {1}{C1\cdot C2\cdot R1\cdot R2\cdot (j\omega )^{2}+C2\cdot (R1+R2)\cdot j\omega +1}}\\&={\frac {-j}{C2\cdot (R1+R2)\cdot \omega +j\cdot (C1\cdot C2\cdot R1\cdot R2\cdot \omega ^{2}-1)}}\end{aligned}}}
