Exam 03 Solution

55:041 Electronic Circuits The University of Iowa Fall 2011

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Exam 3

Name: ___________________________ Score__________/94___

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

1. Write down one phrase/sentence that describes the purpose of the diodes and constant

current source in the amplifier below.

Answer: Reduction of cross-over distortion

2. What is the maximum theoretical efficiency for a class-B amplifier?

Answer: 78%

3. Many BJT datasheets do not list explicitly, but list an equivalent h-parameter instead.

What is this parameter?

Answer:

4. Consider a frequency . How many octaves higher is the frequency ?

Answer: Each octave means a doubling in frequency. Thus, we have to find in

. Substituting values gives ( ⁄ ) ( ) ⁄ octaves.

5. Consider a frequency . How many decades higher is the frequency ?

Answer: Each decade means a frequency higher. Thus, we have to find in

. Substituting values gives ( ⁄ ) decades.


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6. The small-signal output resistance of a BJT biased at = 1 mA is100K. What is

when the transistor is biased at ?

Answer: is inversely-proportional to ( ⁄ ) so that will be smaller at

5 mA, or .

7. A MOSFET has rated power of 25 W at an ambient temperature and a

maximum specified junction temperature of 105oC. What is the thermal resistance

between the case and the junction?

Answer:

8. What does “SOA” in the context of power transistors stand for?

Answer: Safe Operating Area

9. True or false: if class-A amplifiers are not carefully biased, they will suffer from

crossover distortion.

Answer: False

10. Identify the false statement

(a) FETs do not suffer from thermal runaway, but BJTs do

(b) Everything else being equal, BJTs have an order of magnitude more gain than FETs

(c) BJT technology has superior performance in power application when compared to the

modern MOS technology, which explains why BJTs are still widely incorporated in

power designs.

Answer: (c) is false

11. An engineer designs a MOSFET-based class-AB amplifier to deliver 6.25 W

(sinusoidal) signal power to a resistive load. What is the required peak-to-peak

voltage swing across the load? (2 points)

Answer: ⁄ , so that , so that


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12. In the circuit below, what is the maximum current that can flow through ? Make

reasonable assumptions. (2 points)

Answer. Assume that for , ( ) . Thus, will turn on and starve

from additional base current when the current through (which is also the current

through ) is ⁄

13. Consider the current mirror below, and neglect base currents. What is ? (2 points)

Answer:

14. In the current mirrors below, neglect the base currents. What is ? (2 points)

Answer:


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15. In the circuit below . Estimate the midband gain ⁄ . (2 points)

(a)

(b)

(c)

(d) Need additional information

Answer: (b)

16. A BJT has rated power of 115 W at and maximum allowable junction

temperature . It is mounted on a heat sink with . It is

dissipating 5 W at an ambient temperature . What is the temperature of the

heat sink? (2 points)

(a) Need additional information

(b)

(c)

(d)

Answer: 5 W through the heat sink will elevate the sink’s temperature by

= above the ambient, so the answer is (c).

17. Estimate assuming and . (2 points)

(a)

(b) ‖ ‖

(c) ‖ ‖

(d) ‖ ‖

(e) Need additional information

Answer: Using BJT scaling the resistance looking into the transistors base is about

and assuming and this about 7.3K. This is in parallel with

the 82K and 22K resistors, so (d) is the correct answer.


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18. Consider a first-order RC low-pass filter with 3-dB frequency . What is the

phase shift in degrees at 50 Hz? (2 points)

Answer: The phase shift at 60 Hz is and increases at / decade. 50 Hz is

( ) ⁄ decades higher than 60 Hz. (The negative sign implies 50 Hz is

0.08 decades before 60 Hz.) Thus, the phase shift is .

An alternate and more accurate calculation is ( ⁄ ) .

19. The following circuit has a time-constant of . What is the attenuation (in

dB) at (3 points)

Answer. This is a 1st order low-pass network with a corner frequency of

( ) ⁄ . The attenuation is 20 dB/decade above and 30 kHz is 2

decades higher than 300 Hz. Thus, the network will attenuate at 40 dB at 30 kHz.

An alternate calculation is (√ ( ⁄ ) ) .

20. In the circuit below and all the capacitors are large enough to be considered

shorts. Estimate the midband gain ⁄ (3 points)

(a)

(b)

(c)

(d) ( ) ( )

Answer: (d)


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21. In the circuit below and all the capacitors are large enough to be considered

shorts. Estimate the midband gain ⁄ (3 points)

(a)

(b)

(c)

(d) ( )

Answer: ( ) ⁄⁄ , so (b) is the answer.


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Question 2 For the BJT amplifier below, determine and . For the Si transistor,

, and assume the transistor is operating in the forward active mode. (6 points)

Solution

Replace the base bias network with its Thevenin equivalent network as shown below. For a Si

transistor, .

Now

However, ( ) so that

( )

( ) ( )( )( )

Solving yields . From this follows

( )


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Question 3 Consider the amplifier shown. Neglect the

BJTs internal capacitances. Estimate the 3-dB

frequency and the midband gain and then make a plot

of the frequency response. You can assume

and that . Further, . (15 points)

Hint: using BJT scaling concepts will greatly simplify

your work.

Solution

Note that ( ) ( ) ⁄⁄⁄ . Turn off the input voltage and use

BJT scaling to determine the resistance looking back into the emitter:

( )⁄

sees ‖ ( )‖ and the circuit time constant is

( )( ) ( )( ) = 10 ms, so that ( ) ⁄ .

Using BJT scaling, the resistance looking into the base at midband frequencies is

( )( ) ( )( )

The parallel combination of and is much larger than so the amplifier does not load the

input. Since this is a CC amplifier, . The Bode plot is shown below.


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Question 4 Consider a BJT with a rated power of 115 W at , and a maximum

allowable junction temperature . The transistor is mounted on a heat sink with

parameters , and . Determine how much power the

BJT can safely dissipate at an ambient temperature of . (12 points)

Solution

The thermal resistance from the device/junction to the case is not given explicitly, so we need to

determine it before proceeding. The BJT is rated at 115 W at and a thermal

model and the calculation of is then

( )

( ) ⁄

(3 points)

Now we can determine the maximum allowable power dissipation when the BJT is mounted on a

heat skink with the given parameters. A thermal model for the problem is shown below.

( )

( )

(9 points)


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Question 5 Consider the circuit below. The duty cycle and frequency of the 555 astable is 60%

and 10 kHz respectively.

(a) Specify a value for to ensure that the average current through the IR diode does not

exceed 30 mA (4 points)

(b) Explain (2 sentences maximum) the purpose of the decoupling capacitor (1 point)

(c) Give a reasonable value for the decoupling capacitor (1 point)

Solution

Part (a) The peak current must be ( ) ⁄ . This value will give an

average of 30 mA with a 60% “on” time. Assuming the ( ) for the BJT, then

⁄ . Choose the closest standard value of .

Part (b) When the FET switches, large current spikes may appear on the supply rail, which can

propagate into the IC and disturb its operation. The decoupling capacitor provides a local

reservoir of energy, and ensures a clean power supply rail.

Part (c) A good first try would be .


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Question 6 In the following circuit, the three transistors are matched and in the same thermal

environment. Determine the values for and to produce an output current of 0.4 mA. You

may ignore base currents and make reasonable assumptions about VBE. (6 points)

Solution

The voltage across the diode-strapped transistors is and we ignore base currents, so the

voltage drop across the base-emitter of the output transistor is , and the voltage drop across

is . Assume VBE = 0.7 V, so that

( )⁄

and


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Question 7 For the amplifier below, . Determine , and estimate .

(8 points)

Hint, use BJT scaling.

Solution

Since is large, . Then ⁄ and ⁄

.

Using BJT scaling:

and

( ) ( )( )

This is an Emitter Follower, so


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Question 8 Consider the amplifier shown. The maximum

power the transistor may dissipate is , and

.

(a) Determine a load resistance so maximum power is

delivered it.

(b) For , determine the signal power dissipated

in the load

For the power calculations, neglect the base currents

(8 points)

Solution

Part (a) The transistor will dissipate the maximum power (25 W) when ⁄ .

From this follows that ⁄ and ⁄ .

Part (b) The gain of the amplifier is ( )( )( )

, so that the amplitude of the signal output voltage is .

The signal power dissipated in the resistor is

( ) ( ) ⁄⁄⁄

Exam 03 Solution

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