- #1
trickae
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Homework Statement
Find a transfer function: [tex]\frac{V_o(s)}{V_i(s)} = \frac{Z_2 (s)}{-Z_1(s)}[/tex]
Homework Equations
[tex]Z_1(s) = R_1 + \frac{1}{C_1s}[/tex]
[tex]Z_2(s) = \frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}[/tex]final solution should be:
[tex]G(s) = \frac{V_o(s)}{V_i(s)} = \frac{C_1C_2R_1R_2s^2 + (C_2R_2 + C_1R_2 + C_1R_1)s + 1}{C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1}[/tex]
The Attempt at a Solution
- Give me a second I'm still typing up the latex commands
[tex]G(s) = \frac{V_o(s)}{V_i(s)}= \frac{-\frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}}{R_1 + \frac{1}{C_1s}}[/tex]
[tex] = -\frac {\frac{R_2}{C_2s}}{(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s}) }[/tex]
[tex] = \frac{-R_2}{(C_2s)(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s})} [/tex]
[tex]= \frac{-R_2(C_1C_2s)}{(C_2s)(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}[/tex]
[tex]=\frac{-R_2(C_1)}{(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}[/tex]
which is no where near the solution.
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