EE 4312
Fall 2022
Homework 3
Fig. 1
1. [12pts] Review the circuit in Fig. 1; the nodes are labeled with numbers, please use these node numbers in your analysis to facilitate the grading. You can assume an ideal opamp with very large gain, no offset and powered with symmetric supplies +2.5/-2.5. The output of this circuit is at node 4. R1 = 1K; R2 = 9K; R3 = 9K.
a. Assume Rs = 90.
i. What is the function of this circuit? [2pts]
ii. Find an expression for V4/Vin. [3pts]
iii. Plot the DC input-output transfer characteristic of this circuit when Vin varies from -2.5 to 2.5. [3pts]
b. Assume Rs = 3K.
i. Does the circuit have the same or a different function? [2pts]
ii. Do sufficient analysis to motivate your answer, but you are not required to find the full DC input-output characteristic to answer this part. [2pts]
Hint: Derive an expression for (V2-V3) as a function of V4.
(a) Circuit to be analyzed
(b) Model for opamp operating in linear region Fig. 2
2. [19pts] For the circuit of Fig. 2 (a) with a voltage input and a voltage output at node 4; assume an ideal opamp with a gain a, as shown in the model. Assume R1 = 10K, R2 = 90K, R3 = 10K, R4 = 90K
a. First, assume that the gain a is infinite so that you can assume that V1=V2 given that there is negative feedback. Now analyze the circuit and find an expression for the ideal closed-loop gain. You can make the appropriate approximations. [3pts]
b. Now, analyze the circuit as a feedback system assuming finite a;
i. What type of feedback configuration is present? [1pts]
ii. Find the expressions for the closed-loop gain, the open-loop gain and the feedback factor. [4pts / expression]
c. Compare the results of the two analyses. [2pts]
d. Do you see any advantages or disadvantages to this resistor arrangement compared to using a single resistor to replace R2, R3, and R4.[1pts]
Fig. 3
3. [19pts] The circuit in Fig. 3 has a current input and a voltage input at node 4. Assume R2 = 90K, R3 = 10K, R4 = 90K. Repeat the analyses a, b, c, and d in problem 2 for this circuit.