Simple transfer function - algebra giving me problems

Homework Statement

Find a transfer function: $$\frac{V_o(s)}{V_i(s)} = \frac{Z_2 (s)}{-Z_1(s)}$$

Homework Equations

$$Z_1(s) = R_1 + \frac{1}{C_1s}$$
$$Z_2(s) = \frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}$$

final solution should be:
$$G(s) = \frac{V_o(s)}{V_i(s)} = \frac{C_1C_2R_1R_2s^2 + (C_2R_2 + C_1R_2 + C_1R_1)s + 1}{C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1}$$

The Attempt at a Solution

- Give me a second i'm still typing up the latex commands

$$G(s) = \frac{V_o(s)}{V_i(s)}= \frac{-\frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}}{R_1 + \frac{1}{C_1s}}$$

$$= -\frac {\frac{R_2}{C_2s}}{(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s}) }$$

$$= \frac{-R_2}{(C_2s)(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s})}$$

$$= \frac{-R_2(C_1C_2s)}{(C_2s)(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}$$

$$=\frac{-R_2(C_1)}{(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}$$
which is no where near the solution.

Last edited:

$$\frac{Z_1(s) + Z_2(s)}{Z_1(s)}$$ - now i get the right answer
$$\frac{Z_1(s) + Z_2(s)}{Z_1(s)}$$ - now i get the right answer