exam 2 name: score /90 question 1 short takes 1 point each...

55:041 Electronic Circuits The University of Iowa Fall 2011

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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, gm 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


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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


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10. 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 enhancement since | | | | and will be zero when | |


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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)


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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)


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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) 2.0283 mA

Answer: (e) because the change in is ( ( and the

new Q-value is 3 mA.


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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.


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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)

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

(

|| )

|| || ⁄

Ro


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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 small-

signal 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 ( ‖


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Question 5 Consider the amplifier shown. The transistor has an Early voltage A dc

analysis reveals that , and ⁄ .

(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


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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)

0 5.05

20 5.27

40 6.40

60 7.08

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


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Question 7 For the circuit below, determine . You may assume the transistor is operating in

the saturation region. (5 points)

Solution

The gate current is zero, so

Further

(

Thus

( (

( (

Solving using trial-and-error gives 2.55 V.

exam 2 name: score /90 question 1 short takes 1 point each...

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