Question

1. You want a gain of -8/5 V/V-1.6 VN on the input ac signal labeled Vi. (I know it's a strange value for gain, but just go with it.) (By the way, Vi has a zero DC offset.) Find R1 and R2 if the smaller of the two should be 500 k-ohms. (HINT: Use superposition by grounding VDC to figure this out. You can probably do this in your head.) 2. Now, you also want the output to have a DC offset of 1.3 V. What value should you make VDC? (HINT: Again, use superposition by grounding Vi to figure this out.)

Answer 1

First I apply super position principle to find out the output of circuit with vi and v_dc let output v_0 due to v_i be v_15 let output v_0 due v_dc be v_2 therefore total output v_0 due to v_dc be V_2 (superposition theorem)1 v_0 due to v_i with v_dc = 0 the above circuit a inverting amp therefore v_1 = (-R_2/R_1) V_i v_0 due to V_dc with v_i = 0 the above is an non - inverting amp v_2 = (1 + R_2/R_1) V_dc total output v_0 = (R_2/R_1) v_i + (1 + R_2/R_1) V_dc \r\n \ According to question we want gain of - 1.6 on vi and vdc = 0 therefore V_0 = R_2/R_1 v_i + v_dc (1 + R_2/R_1) becomes v_0 = -(R_2/R_1) vi gain = R_2/R)1 = 1.6 Let R_1 = 500 k therefore R_2 = 800 k according to question d we want an output DC offset of 1.3v from equation 1 the output Dc offset voltage is