Question

3. For the circuit below in ouut assume that at t-0, Vin 0V and that there is no charge on either of the capacitors Show that for all later times and derive an expression for G in terms of Ci and C2 We'll discuss in class the circumstances in which it might make sense to design a circuit like this using capacitors instead of resistors.

Answer 1

CONCEPT USED Kirchhoff's current low = Net current entering a node is equal to net current leaving the node. In an ideal op - amp V_in = V_out Step - by - step solution Based on the diagram, we find: - V_p = V_n (Assuming ideal op - amp) Now because V_p = 0 therefore V_N = 0 Now, at node V_N: - KCL given: - V_N - V_in/1/SC_1 + V_N - V_0/1/SC_2 = 0 because V_N = V_P = 0 therefore get rightarrow - V_in/1/SC_1 - V_0/1/SC_2 = 0 rightarrow V_in/1/SC_1 = -V_0/1/SC_2 rightarrow V_0/V_in = -1/SC_2/1/SC_1 rightarrow V_0/V_in = -CS_1/SC_2 raV_0 = -C_1/C_2 V_in therefore C_1 = -C_1/C_2 rightarrow Required Answer