20.309:Recitation 092107: Difference between revisions
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(New page: <math> \frac{V_i-V_x}{R_1} + \frac{V_o-V_x}{R_2} + C_1 s (V_o - V_x) = 0 </math> <math> R_2(V_i-V_x) + R_1(V_o-V_x) + R_1 R_2C_1 s (V_o - V_x) = 0 </math>) |
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<div style="padding: 10px; width: 774px; border: 3px solid #000000;"> | |||
<center><big>'''20.309 Fall Semester 2007'''</big></center> | |||
<center><big>Recitation Notes for 9/21/2007'''</big></center> | |||
<br/> | |||
===Apply KCL at the <math>V_x</math> node and multiply by <math>R_1 R_2</math>=== | |||
<math> | <math> | ||
(V_i-V_x)/{R_1} + (V_o-V_x)/R_2 + C_1 s (V_o - V_x) = 0 | |||
</math> | </math> | ||
<br/> | |||
<math> | <math> | ||
R_2(V_i-V_x) + R_1(V_o-V_x) + R_1 R_2C_1 s (V_o - V_x) = 0 | R_2(V_i-V_x) + R_1(V_o-V_x) + R_1 R_2C_1 s (V_o - V_x) = 0 | ||
</math> | </math> | ||
<br/> | |||
===Apply KCL at the noninverting op amp input and multiply by <math>R_2</math>=== | |||
<math> | |||
(V_x-V_o)/R_2 - V_o C_2 s = 0 | |||
</math> | |||
<br/> | |||
<math> | |||
V_x=V_o (1 + R_2 C_2 s) | |||
</math> | |||
===Substitute expression for <math>V_x</math> inte=== | |||
</div> | |||
Revision as of 12:30, 21 September 2007
Apply KCL at the [math]\displaystyle{ V_x }[/math] node and multiply by [math]\displaystyle{ R_1 R_2 }[/math]
[math]\displaystyle{ (V_i-V_x)/{R_1} + (V_o-V_x)/R_2 + C_1 s (V_o - V_x) = 0 }[/math]
[math]\displaystyle{
R_2(V_i-V_x) + R_1(V_o-V_x) + R_1 R_2C_1 s (V_o - V_x) = 0
}[/math]
Apply KCL at the noninverting op amp input and multiply by [math]\displaystyle{ R_2 }[/math]
[math]\displaystyle{ (V_x-V_o)/R_2 - V_o C_2 s = 0 }[/math]
[math]\displaystyle{ V_x=V_o (1 + R_2 C_2 s) }[/math]
