1. (2 points) - University of...

55:041 Electronic Circuits The University of Iowa Fall 2011

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Exam 1 Solution

Name: ___________________________ Score__________/60___

Question 1 Short Takes – 1 point each unless noted otherwise.

1. An engineer measures the (step response) rise time of an amplifier as . Estimate the

3-dB bandwidth of the amplifier. (2 points)

Solution

2. True or false: one can use an ordinary glass Si diode as a photodetector.

3. The abbreviation/term “ESR” is often encountered in data sheets of capacitors. What does ESR

stand for?

( ) ( )

( )

4. The output voltage of a three-terminal voltage regulator is 5 V @ 5 mA load, and 4.96 V @ 1.5 A

load. What is the regulator’s load regulation? (2 points)

5. True or false: the diffusion capacitance of a pn junction is negligible when the junction is

reverse-biased.

6. True or false: a diode, forward biased at ID = 1 mA, has a small-signal or incremental resistance

of about . (2 points)

Answer:


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7. True or false: the turn-on voltages of Schottky diodes are less than that of Si diodes. However,

their reverse leakage/saturation currents are also higher.

8. True or false: The turn-on voltage of red LEDs is larger than the turn-on voltage of blue LEDs.

9. Which of the following depicts the correct current direction? Circle one.

10. In the context of diodes, the term “PIV” means:

11. True or false: the diffusion capacitance of a pn junction is generally much larger than the

junction capacitance .

12. True or false: a silicon diode is biased so that at 25 oC. VD changes with 2 mV/

oC, so

that at 125 oC, will be 0.7 + 100×0.002 = 0.9 V

13. True or false: in the circuit below, even though the diode equation is nonlinear, the photocurrent

is essentially linear with photon flux density.


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Question 2 What is the voltage in the circuit below? Assume an ideal op-amp. (6 points)

Solution Call the voltage at the output of the op-amp , and note that the voltage at node is 5 V.

Then two KCL equations for node A and the output node are:

Solving yields and .

Question 3 Find the expression for for the differential amplifier circuit below. Assume ideal op-

amps. (6 points)

Solution Recognizing that op-amp is wired as an inverting amplifier with voltage gain ,it

immediately follows that the voltage at the output terminal of is . Note that is wired as a

noninverting summer, so that its output voltage is

( )

( )


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Question 4 For each of the circuits below, determine the output voltage . (2 points each)

( )( )

This is a current-to-voltage converter with

This is a follower where .

Thus

(

)

This is a noninverting summing amplifier where

Thus


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Question 5 The circuit below has input, output, and capacitors voltages that are zero at . It is

driven by the input signal shown below. The resistance and capacitance in the circuit are ,

and . Sketch and label the resulting output waveform. Assume an ideal op-amp. (8 points)

Solution

This circuit is an op-amp integrator. The input, output, and capacitor voltages are initially 0, so that

∫ ( )

( )( )∫ ( )

∫ ( )

For , we can write ( ) , so the output is

∫

That is, the voltage decreases linearly with time. At , the value is .

For , we can write ( ) , so the output is . That is, the voltage increases

linearly with time. At , the value is .

This pattern repeats. The output voltage is shown below.


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Problem 6 An engineer designs a power supply that consists of a transformer, a full-wave, 4-diode

bridge rectifier and a smoothing capacitor. The nominal load current is 1.2 A. By what percentage will

the ripple voltage increase/decrease if the supply is used with an actual load of A? Assume the

transformer and rectifier diodes are capable of handling the increase in load current. (4 points)

Solution The ripple voltage for a full-wave rectifier is:

(

)

The ⁄ term represents the peak current though the load resistance . Increasing the load from A

to A (a 25 % increase) will increase the ripple voltage by the same percentage, or 25 %.

Problem 7 Draw the schematic of a power supply that consists of a step-down transformer, full-wave

rectifier bridge, smoothing capacitor, and 7805 linear regulator. (5 points)


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Problem 8 An engineer designs a power supply that consists of a transformer, a full-wave, 4-diode

bridge rectifier and a smoothing capacitor. The transformer secondary voltage is 7.4 VAC at ,

and the load resistance is . The bridge rectifier diodes are silicon. Determine the value of the

smoothing capacitor if the output ripple voltage is to be less than 500 mV. (5 points)

Solution

( )(√ )

( )( )( )

Problem 9 An engineer measures the bandwidth of the simple low-pass filter below by driving it with a

sinusoidal signal and measuring the attenuation at various frequencies. She uses an oscilloscope with an

input impedance of along with a probe. What is the true bandwidth of the circuit? What will

the engineer measure? (6 points)

Solution

( )( )

( ‖ )

( )‖( )( )


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Question 10 Consider the current-to-voltage converter circuit shown. The current source has a finite

output resistance , and the op-amp is ideal except for a finite open-loop gain . Show that the input

resistance indicated in the figure is given by ( )⁄ . (6 points)

Solution Turn off independent sources add a test voltage and determine the resulting current . Then

⁄ . To turn off a current source, we remove it from the circuit. The circuit below indicates the

setup to determine .

The output voltage is , no current flows into the inverting input and applying Ohm’s law

yields

( )

Since ⁄ , it follows that ( )⁄ .


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Question 11 An amplifier is designed to provide a 12 V peak-to-peak swing across a load. Assume

sinusoidal signals. Assuming the amplifier has output resistance how much power will the

load dissipate? (4 points)

Solution

A 12 V peak-to-peak sinusoidal signal has an amplitude of 6 V and with , the signal amplitude

across the load is, using voltage division, ( ( )⁄ ) . The rms value is

√ ⁄ , and the power is ( ) ⁄

Problem 12 In the circuit shown, is a dc current and is a sinusoidal

voltage signal. Capacitors and are very large; their function is to

couple the signal to and from the diode but block dc current from flowing

into the signal source or the load (not shown). Ignore junction- and

diffusion capacitances. Use the diode small-signal model to show that the

signal component of the output is

(5 points)

Solution

The small-signal equivalent circuit is shown right. The small-signal

incremental resistance of the diode is given by ⁄ . Applying voltage

division gives

⁄

⁄


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Question 13 We would like to measure the voltage in the circuit below with a voltmeter.

What is the value of , and what is the common-mode voltage associated with ? What CMMR (in

dB) is required of the voltmeter if we are to measure to within 0.01%? (6 points)

Solution The current through the resistance is ( ) ⁄ . The voltage across the

resistor is therefore 3.75 V. Further, ( ) , and

The common-mode voltage is then

( )

The error must be less than or or 3.75 V, which is 0.375 mV. Thus, the multimeter must

suppress the 7.5 V common-mode voltage to less than 0.375 mV. In other words, the CMMR must be at

least

This is equivalent to 86 dB.

Question 14 Determine a value for in the circuit below such that mA. Assume .

The LED’s I-V plot is shown below. (4 points)

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