q1 hw4

Solving the circuit. Let's consider Vcc = 14V, Vee = -14V. - Initially, assume that there is no saturation on OpAmps - Check if there is negative feedback. Yes, there is negative feedback on U2 (R2). Considering the inverting amplifier formed by U2 as a black box we can assume negative feedback via R4. - if there is neg. feedback on U1, the voltage at inverting input will be the same as non-inverting input (V1). With this is possible to calculate the current through R3. This current will be the same through R4. - Now it's possible to calculate Vo = VR3 + Vr4 = 6.667V. If this voltage is present Vo2, Vo1 = Vo2/gain2 = 6,667/0,25 = -26,67V. This value is impossible because the maximum voltage at Vo1 is +-14V. This lets us conclude that U1 is not in the linear region of operation. - Now let consider Vo1 = -14V, because the last step shows a negative saturation. This voltage times the gain2 will lead to Vo2 = 3.5V. - R4 and R3 form a voltage divider and the voltage on inverting input of U1 is 2.625V. - As the voltages on the inputs are different we know that the opamp is not in the linear region. - +5V is greater than 2.625V, saturating Vo1 to the positive rail, and this contradicts the initial assumption (Vo1 = -14). - Finally, we need to do the same analysis considering Vo1 = 14V. In this case, Vo2 = -3.5V and the voltage at the inverting input of U1will be -2.625V. - +5V is greater than -2.625V, saturating Vo1 to the positive rail, validating our analysis. Based on: https://youtu.be/5U1xtY8t2oo