# Exam Below are two schematics of current sources implemented with MOSFETs. Which current source has the best compliance voltage?

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1 Exam 2 Name: Score /90 Question 1 Short Takes 1 point each unless noted otherwise. 1. Below are two schematics of current sources implemented with MOSFETs. Which current source has the best compliance voltage? (Answer: (a)) (a) (b) 2. True or false: for a MOSFET, g m decreases with increasing temperature, which explains why MOSFETs are not prone to thermal runaway. (True) 3. The figure, extracted from a data sheet, indicates which type of transistor (circle one)? (a) n-channel MOSFET (b) p-channel MOSFET (c) n-channel JFET (d) p-channel JFET (e) Undetermined, need additional information Answer: (b), Since the body diode will normally be reverse-biased PMOS 4. Explain with one word/phrase what every letter in CMOS mean. Answer: Complementary Metal Oxide Semiconductor 1

2 5. True or false: the threshold voltage ( for a particular MOSFET is, as is the case with the cut-in voltage ( ) of diodes, well-defined and not subject to large variation between samples of the same part number. (False) 6. True or false: the MOSFET parameter (NMOS) or (PMOS) varies between samples of the same part number, but essentially constant for specific MOSFET. (False) 7. True or false: assuming that for the amplifiers below, then is larger than. However, also more sensitive to FET parameter variation than. (True) 8. True or false: in the following circuit, regardless the value of R, the FET always operates its saturation region. Answer: True 9. What does the + signify in n+ in the figure below? Answer: heavily-doped 2

3 55:041 Electronic Circuits 10. The University of Iowa Fall 2011 The figure below depicts a MOS capacitor. The thickness of the oxide insulator is on the order of (circle one). (a) (b) (c) (d) (e) None of above Answer: (c) or (b), but (c) would be a better answer. 11. Draw a diagram of a CMOS inverter for digital signals. Answer 12. Below are the characteristics for a MOSFET. What type of FET is this (circle one)? (a) Enhancement PMOS (b) Depletion PMOS (c) Enhancement NMOS (d) Depletion NMOS (e) Undetermined, need additional information Answer: PMOS since and will be zero when 3, and enhancement since

4 13. Write down the dc load line equation for the MOSFET in the circuit below. (2 points) 14. Briefly explain (1 2 sentences) what is ( as it pertains to MOSFETs. (2 points) Answer: This is parameter found in MOSFET data sheets and typically indicate the lowest resistance between Drain and Source when the FET is turned on hard That is, when (NMOS) or (PMOS) 15. 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. Answer: True 16. Annotate the diagram below, showing the MOSFET channel width (W) and length (L). Also indicate the body diode for this n-channel MOSFET. (2 points) 4

5 17. In the following circuit, is replaced with a resistor double its original value. The new is (circle one) (a) Unchanged (b) Undetermined, need additional information (c) Double the original (d) Half the original (e) Quadruple the original Answer: (a) Since no current flows into gate, voltage drop across 18. In the following circuits the MOSFETs are identical, except for the ratio as indicated. The unknown current is (circle one) (2 points): (a) Undetermined, need additional information (b) (c) (d) (e) Answer: (b), since, and 19. In the following circuits the MOSFETs are identical. The unknown current is (circle one) (2 points): (a) Undetermined, need additional information (b) (c) (d) (e) Answer: (b) Since the drain current of the MOSFETs on the right add (KCL) 5

6 20. A MOSFET is operating in saturation at and. If increases by 10 mv, the new is (circle one) (2 points): (a) Unchanged, because the MOSFET is in saturation and behaves line like current source (b) Undetermined, need additional information (c) (d) (e) ma Answer: (e) because the change in is ( ( and the new Q-value is 3 ma. 6

7 Question 2 Consider the following circuit. Assume that,, and. Sketch versus for. Label and add numerical values on each the axis. Calculate and indicate ( on the plot. Clearly indicate the saturation and Ohmic regions and the saturation current. (5 points) Solution ( In the saturation region, ( (. Plot see below. 7

8 Question 3 The small-signal parameters for the MOSFET below are and output resistance. (a) Draw a small-signal model for the amplifier. (6 points) (b) Using the small-signal model, determine an expression for the output resistance. (6 points) (c) Determine a numerical value for (2 points) R o Solution The small-signal model for the amplifier is shown in (a) and (b) below. (a) (b) To determine the output resistance, turn off independent sources, add a test voltage, and determine the current that flows. The resulting small-signal model is shown right. A KCL equation at the source, taking currents into the node as positive, is From the diagram follows that, so that ( ) Then ( ) 8

9 Question 4 Consider the ac equivalent of a CMOS amplifier. The transistor parameters for the NMOS are and. The transistor parameters for the PMOS are and. (a) Draw the equivalent small-signal model. (6 points) (b) Determine numerical values for model parameters. (3 points) (c) Using the model and numerical values, determine the smallsignal voltage gain. (4 points) Solution and the current source biases the NMOS transistor and presents a load resistance. The small-signal model is shown below. Calculating numerical values for model parameters: ( ( The voltage gain is ( ( ( ( ( 9

10 Question 5 Consider the amplifier shown. The transistor has an Early voltage analysis reveals that, and. A dc (a) Draw the corresponding small-signal circuit that incorporates the MOSFETs output resistance (6 points) (b) Determine numerical value for (1 point) (c) Determine the amplifier s voltage gain (8 points) Solution The small-signal model for the amplifier is shown right. The numerical values for all components are known, except for. However, we can calculate that from. We can lump and together as. Next, write a KCL equation at the output node From the small-signal model it is clear that so that the equation above becomes Some algebraic manipulation yields ( ( Substituting, and yields 10

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12 Question 6 An engineer uses the circuit shown to estimate both the input offset voltage and input bias current for the op-amp as follows. A she opens the switch and measures the output voltage at different times. The table shows her measurements for and. (a) Redraw the circuit showing and (2 points) (b) The op-amp, and form an amplifier. What is the gain of the amplifier? (2 points) (c) Use her data and estimate (3 points) (d) Use her data and estimate. (6 points) You may assume is constant (seconds) (V) Solution Part (a) Part (b) ( Part (c) When the switch is closed ( the op-amp amplifies the offset voltage which results in an output voltage (see table), so that. Part (d) After the switch opens, charges the capacitor the output voltage rises. From the differential equation for a capacitor ( it follows that From the table, is about V/s after the switch opens. Substituting values gives 12

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14 Question 7 For the circuit below, determine the saturation region. (5 points). You may assume the transistor is operating in Solution The gate current is zero, so Further ( Thus ( ( ( ( Solving using trial-and-error gives 2.55 V. 14

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