EEC 210 Practice Final Problems
December 2, 2024
1 Transimpedance Amplifier
Figure 1 shows a transimpedance amplifier. Source iin is a small-signal current source only. For this problem, use the transistor parameters in Table 1, and IBIAS = 100 µA, RL = 10 kΩ, RS = 625 Ω, and CL = 100 fF.
Table 1: Problem 1 Transistor Parameters.
Problem 1.1 (3 points) Find the width W of M1 such that the large-signal output voltage VO = 2 V. You may ignore channel- length modulation for this part.
Figure 1: Transimpedance amplifier.
Problem 1.1 (cont.)
Problem 1.2 (4 points) Draw and label the small-signal model for the amplifier assum- ing M1 is active and ignoring all junction and overlap capacitances (i.e., consider intrinsic capacitance only).
Problem 1.3 (5 points) Find the small-signal transimpedance DC gain ZDC = i in/vo.
Problem 1.4 (6 points) Estimate the -3dB frequency (in Hz) using the method of zero- value time constants (open circuit time constants).
Problem 1.5 (2 points) Suppose the transfer function of the amplifier is modeled as:
where ZDC and ω−3dB = 2πf−3dB are as you found above. Find the location of the second pole ω2 = 2πf2 > ω−3dB such that the phase margin is 45◦ when the amplifier is placed in unity gain feedback.
Problem 1.6 (2 points) Is your answer for Problem 1.5 realistic? Why or why not?
Figure 2: Operational amplifier.
2 Operational Amplifier
Figure 2 shows the circuit schematic for an operational amplifier. For this problem, use the transistor parameters in Table 2. Assume that all transistors are biased in saturation and the following circuit parameters: VS ≈ 0V, IB1 = IB2 = 2 mA, RB1 = 500 kΩ, R1 = R2 = 20kΩ, (W/L)1 = (W/L)2 = (W/L)3 = (W/L)4 = 200, (W/L)5 = (W/L)6 = 20.
Table 2: Problem 2 Transistor Parameters.
Problem 2.1 (5 points) Find the differential-mode gain, v id/vo, where vid = v+ − v− .
Problem 2.2 (4 points) Assume the second stage common-mode gain Acm = −60 dB. Find the common-mode rejection ratio (CMRR) for the op amp expressed in dB.
Problem 2.3 (3 points) Suppose resistors R1 and R2 can each deviate from its nominal value by ±5%. Assuming there is no other mismatch, find the approximate worst case magnitude input-referred offset VOS .
Problem 2.4 (2 points) Do you expect mismatch in transistors M3-M6 to make a signifi- cant contribution to the input-referred offset? Why or why not?
Figure 3: Current source.
3 Current Source
Figure 3 shows a current source. For this problem, use the transistor parameters in Table 3.
Table 3: Problem 3 Transistor Parameters.
Problem 3.1 (9 points) Find the smallest (W/L)1 , (W/L)2 , and (W/L)3 which simulta- neously set the output current IOUT = 400µA, VO,MIN = 100 mV, M1 and M2 in the active (saturation) regime, and M3 in the triode (linear) regime. You may neglect channel length modulation for this first part.
Problem 3.2 (2 point) Find the output resistance RO of the current source given the dimensions you found in Problem 3.1.
Figure 4: Bias voltage generator.
4 Bias Voltage Generator
Figure 4 shows a proposed bias voltage generator circuit. For this problem, use the transistor parameters and constants in Table 4. Assume that a startup circuit (not shown) forces the branch currents to be nonzero.
Table 4: Problem 4 Parameters.
Problem 4.1 (8 points) Find (W/L)1 = (W/L)2 and (W/L)3 = (W/L)4 such that VBIAS = 1.75 V at T = 300 K.
Problem 4.2 (8 points) Find the RMS output noise voltage due to the shot noise of diode D2 over a bandwidth of 100 MHz for the transistor sizes you found and the operating point in Problem 4.1.