# Homework Assignment 07

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1 Homework Assignment 07 Question 1 (Short Takes). 2 points each unless otherwise noted. 1. A single-pole op-amp has an open-loop low-frequency gain of A = 10 5 and an open loop, 3-dB frequency of 4 Hz. If an inverting amplifier with closed-loop low-frequency gain of A f = 50 uses this op-amp, determine the closed-loop bandwidth. 2. A MOSFET is biased such that g m = 1.78 ma/v and I D = 1 ma. If v GS changes with 1 mv, by how much does the drain current change? 3. The units for the λ parameter for a MOSFET is 4. The op-amp in the circuit is ideal, and R 1 = 10K, R 2 = 100K, and R 3 = 10K. The input resistance that the source sees is (a) R 1 = 10K (b) R 1 + R 3 = 20K (virtual short between + and ) (c) (Ideal op-amp has R i = ) (d) R 1 R 2 R 3 = 4.72K (KCL at terminal) 5. What is frequency is 3 decades down from 220 Hz? (a) 22 mhz (b) 220 mhz (c) 6.4 mhz (d) 190 Hz 6. A signal with amplitude v = 4 V at 4 khz decreases as frequency increases at 2 db/octave. What is the amplitude in V at 13 khz? (3 points) 1

2 7. Below are two schematics of current sources implemented with MOSFETs. Which current source has the best compliance voltage? (a) (b) 8. True or false: in IC circuits, transistors are often used to replace resistors, because IC realestate is expensive, and resistors, especially large value resistors, require large surface area. 9. True or false: assuming that g m1 = g m2 for the amplifiers below, then A v1 is larger than A v2. However, A v1 also more sensitive to FET parameter variation than A v2. 2

3 10. Which one of the MOSFET circuits below behaves as a non-linear resistor? (1) (2) (3) (a) Only (1) (b) Only (2) (c) Only 3 (d) Both (1) and (3) (e) All (f) None 11. True or false: everything else being equal, MOSFETs the drain current is directly proportional to the width-to-length ratio. 12. Consider two MOSFETs A and B that are identical in all respects except that A s channel is twice as wide as channel B s channel: W A = 2W B. Under identical bias what is the relationship between the drain current of A and B? I DA = 13. Consider two MOSFETs A and B that are identical in all respects except that A s channel is twice as long as channel B s channel: L A = 2L B. Under identical bias what is the relationship between the drain current of A and B? I DA = 14. True or false: given the symmetrical construction of MOSFETs one can, in principle, at least, interchange the drain and the source terminals without affecting device behavior. 15. The output frequency of a full-wave rectifier is the input frequency. (a) one-half (b) double (c) same as (d) quarter 3

4 16. Write down the dc load line equation for the MOSFET in the circuit below. (3 points) 17. Write down the dc load line equation for the MOSFET in the circuit below. (3 points) 18. The R DS(on) for a small switching MOSFETs such as the 2N7000 is (circle one) (1 point) (a) 20 mω 200 mω (b) 200 mω 20 Ω (c) 20 Ω 200 Ω 19. Briefly explain (1 2 sentences) what is R DS(on) as it pertains to MOSFETs. (3 points) 4

5 20. Below is a depiction of an n-channel enhancement-mode MOSFET. Annotate the diagram with a p or n to show the type of substrate material, and then indicate the body diode. 21. What is the magnitude of the current phase angle for a 5.6 μf capacitor and a 50-Ω resistor in series with a 1.1 khz, 5 VAC source? (a) 72.9 (b) 62.7 (c) 27.3 (d) 17.1 Question 2 (Own, non-ideal op-amp) In the circuit the opamp is ideal, except for an input bias current I b = 10 na. Further, R F = 10K, R 1 = 100 Ω and C = 6.8 μf. The switch is opened at t = 0. What is the output voltage after 10 seconds? (3 points) 5

6 Question 3 An engineer uses the circuit shown in (a) below to measure the input offset voltage V OS and input bias current I B for an op-amp. In the circuit, R 1 = 98 Ω, R F = 9.9K, and C = 13 μf. In (b) is the output voltage for various values of R T. Plot her data and use the plot to estimate V OS and I B. (10 points) (a) R T (Ω) V O (V) K K K K K K (b) 6

7 Question 4 (Own) Consider the following circuit. Assume that V TN = 1 V, K n = 1.5 ma V 2, and λ = 0. Sketch I D versus V DS for 0 V DS 5 V. Label and add numerical values on each the axis. Calculate and indicate V DS (sat) on the plot. Clearly indicate the saturation and Ohmic regions and the saturation current. (5 points) 7

8 Question 5 The transistor characteristics for an NMOS FET are shown below. (a) Is this an enhancement- or depletion-mode device? (1 points) (b) Estimate a value for V TN. (5 points) (Hint: consider using the supplied graph paper) 8

9 Question 6 The graph and table below summarize the output characteristics for the 2N7000 MOSFET. Use this information and estimate a value for K n. (8 points) 9

10 Problem 7 The transistor in the circuit shown has K n = 0.5 ma V 2, V TN = 2 V, and λ = 0. Determine I DQ, assuming the MOSFET operates in the saturation region. (6 points) Question 8 The circuit shown uses an NMOS transistor to implement a current source. For the transistor, V TN = 1 V and K n = 12.5 μa V 2. What is the required value op V GS so that I dc = 25 μa? (3 points) What is the compliance voltage? (2 points) 10

11 Problem 9 The so-called diode-connected transistor is sub circuit that appears in many other circuits. Of interest is the output resistance. Draw the small-signal model and determine R o. Be sure to include the transistor s own output resistance r o. What is a simplified expression for R O when r O is very large? (10 points) 11

12 Problem 10 Using the results from the previous problem, determine R O for the circuits below if I D = 0.5 ma, and λ = 0.02 V 1 and K n = 0.1 ma/v 2 and K p = 0.06 ma/v 2, and R g = 1M. (6 points) (a) (b) (c) 12

13 Question 11 A MOEFET amplifier along with the FET and circuit parameters are shown below. C C1, C C2 are coupling capacitors. Determine R 1, R 2 such that R in = 200K, and I DQ = 3 ma. (10 points) K n = 2 ma V 2 V TN = 2 V λ = 0 V DD = 15 V R S = 0.5K R D = 2K R in = 200K R 1 =? R 2 =? R L = 5K I DQ = 3 ma 13

14 Question 12 The parameters of the transistor are K n = 0.5 ma V 2, V TN = 1.2 V and λ = 0. Further, the bias current is I Q = 50 μa. Determine v GS (5 points) and v DS (2 points) for the circuit. 14

15 Question 13 An op-amp has a voltage gain of 100 db at dc and a unity-gain frequency of 5 MHz. (a) What is f B, the low frequency 3-dB cutoff frequency? (2 points) (b) Write an expression for the transfer function A(f) for the open loop gain of the op amp (2 points) (c) The op-amp is used in a non-inverting configuration with a gain of 40 db. What is the bandwidth of the feedback amplifier? (2 points) (d) Write an expression for the transfer function A(f) for the feedback gain of the op amp. (2 points) (e) By how much (i.e., how many microseconds) does the amplifier delay a 10 khz sine wave? (3 points) Assume that the op-amp has a single-pole frequency response. 15

16 Question 14 Consider the amplifier shown. The transistor has an Early voltage V A = 50 V. A dc analysis reveals that I D = 1.06 ma, and g m = ma V. Assume that the coupling capacitors are large enough so that they are shorts at the operating frequency. Draw the corresponding small-signal circuit. Incorporate the MOSFETs output resistance r o. Next, determine the amplifier s voltage gain. Finally, determine the amplifier s input and output resistances. (25 points) C C = Coupling Capacitors R G = 10M R D = 10K R L = 10K 16

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