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eehelp150
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Homework Statement
Homework Equations
The Attempt at a Solution
Nodal Equations
By property of OpAmp, V2=Vo
eq1:[tex]\frac{V_{1}-V_{in}}{R_1}+\frac{V_{1}-V_{o}}{R_2}+C_2*(\dot{V_1}-\dot{Vo})[/tex]
eq2: [tex]V_1=C_1R_2\dot{V_o}+V_o[/tex]
eq3:[tex] \dot{V_1}=C_1R_2\ddot{V_o}+\dot{V_o}[/tex]
Sub 2 & 3 into 1
[tex]\frac{C_1R_2\dot{V_o}+V_o-V_{in}}{R_1}+\frac{C_1R_2\dot{V_o}+V_o-V_o}{R_2}+C_2(C_1R_2\ddot{V_o}+\dot{V_o}-\dot{V_o})[/tex]
Simplify
[tex]\frac{C_1R_2\dot{V_o}+V_o-V_{in}}{R_1}+ C_1\dot{V_o}+C_2(C_1R_2\ddot{V_o})[/tex]
[tex]\frac{C_1R_2\dot{V_o}}{R_1}+\frac{V_o}{R_1}-\frac{V_{in}}{R_1}+C_1\dot{V_o}+C_1C_2R_2\ddot{V_o}[/tex]
[tex]\frac{C_1R_2\dot{V_o}}{R_1}+\frac{V_o}{R_1}+C_1\dot{V_o}+C_1C_2R_2\ddot{V_o}=\frac{V_{in}}{R_1}[/tex]
Divide everything by C1C2R2 to single out Vo''
[tex]\frac{C_1R_2\dot{V_o}}{C_1C_2R_1R_2}+\frac{V_o}{C_1C_2R_1R_2}+\frac{C_1\dot{V_o}}{C_1C_2R_2}+\frac{C_1C_2R_2\ddot{V_o}}{C_1C_2R_2}=\frac{V_{in}}{R_1C_1C_2R_2}[/tex]
Simplify
[tex]\frac{\dot{V_o}}{R_1C_2}+\frac{V_o}{C_1C_2R_1R_2}+\frac{\dot{V_o}}{C_2R_2}+\ddot{V_o}=\frac{V_{in}}{R_1C_1C_2R_2}[/tex]
Rearrange
[tex]\ddot{V_o}+\frac{\dot{V_o}}{R_1C_2}+\frac{\dot{V_o}}{C_2R_2}+\frac{V_o}{C_1C_2R_1R_2}=\frac{V_{in}}{R_1C_1C_2R_2}
[/tex]
This is the correct solution:
[tex]\ddot{V_o}+\frac{\dot{V_o}}{R_1R_2}+\frac{V_o}{R_1R_2C_1C_2}=\frac{V_{in}}{R_1}[/tex]
What am I doing wrong?