Name: ________________________________________________

DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Spring 2018 Quiz 6.101 Introductory Analog Electronics Laboratory

NOTE: SHOW ALL CALCULATIONS FOR ALL ANSWERS! [This will allow for partial credit for wrong answers.]

Please look through the whole quiz before beginning. There are lots of questions, but most of them are very easy. It’s always good test-taking procedure to look over the whole quiz before deciding where to start, and so you can plan your time. To receive full credit values must also include the correct sign and units eg; volts, mv, ma, uF, pF, sec, ms, ohm, mohm, mHz, etc.

Where numerical values are required, the answer must be a number and not an equation or ratio. 1 sheet double sided handwritten notes only.

If needed, you may use these values for constants

VT (thermal voltage at 25 deg C) = kT/q = 26mv pi = 3.14, sqrt(2) = 1.41

Problem 1 /18 Problem 2 /12 Problem 3 /10 Problem 4 /20 Problem 5 /4 Problem 6 /6 Problem 7 /8 Problem 8 /4 Problem 9 /18

Total

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? pF RPara 240 µHto radio first stage

EM radiation: 0.530 - 1.710 MHz

Problem 1 [18 points]

Most radios in the late 1930’s, and the 1940’s through 1960’s used loop antennas to receive the AM signal. These antennae were about 1/3 the size of the transmitting antenna we used in Lab 1, and were usually wound flat on the inside back panel of the radio. These coils respond primarily to the M part of the EM radiation, and thus a current is induced in the coil. To get the largest input voltage to the radio, we like to resonate the coil with a tunable variable capacitor, which is actually inside the radio.

1a. What should be the range [in pF] that the tuning capacitor must cover to tune the whole AM band [0.530-1.710MHz]?

From: pF

To: pF

1b. If we manipulate the bandwidth using this circuit, we can help to reduce interference from adjacent signals, just as we did in Lab 1 with tuning the ferrite loopstick. What total value of parallel resistance [Rpara] do we need to keep the bandwidth to 10 kHz at 1 MHz? [Rpara] includes resistance at the input to the 1st stage. At 1MHz, C = 105.5pf.

Rpara =

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1c. What will the bandwidth (Hz) be at the extremes of the AM band using the above resistance?

530 kHz

1.71 MHz

1d. What is the Q of this tank circuit at 1 MHz? Q =

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Problem 2 [12 points]

2a. Draw a schematic for a half-wave rectifier using one real diode with a VF = 0.6 volt, an ideal power transformer whose primary is designed for 120 V RMS 60 Hz input and whose secondary is designed to put out 18 VCT under any load conditions [zero source resistance]. Use a 1000 μF polarized electrolytic filter capacitor on the output, in parallel with a load resistor of value RL. Use the whole secondary.

Pri Sec

2b. To what exact value of voltage will the capacitor charge when there is no load current? 2c. How much load current can we draw from this power supply [through RL] without exceeding an output ripple current of 1 volt peak-to-peak?

2d. When the diode is not conducting, what is the peak inverse voltage across the diode?

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Problem 3 [10 points]

The following schematic represents a Zener diode regulator. It’s driven by a simple diode rectifier with capacitor filter, which have been replaced by an average DC voltage source in series with an AC ripple generator generating a sawtooth waveform (0 to 1.0V p-p). (The peak voltage to the 100 ohm resistor is 19 + 1 = 20V.)

R=100Ω ILOAD

VZ =12.0 V

1.0 V p-p

19.0 V Average

+

VLOAD

-

RL+

Assuming that we want to leave a minimum DC current of 1 mA through the (ideal) Zener to keep it in reverse breakdown, what is the maximum DC current that can pass through the load?

[8 point] Max current

[2 point] What is the color code for the 100 ohm resistor? ____________________________________

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Problem 4 [20 points]

0.1 Ω

2N3904

7.5 k

-

+

+vout

_100 k10 k

750

130 k

13 kAC

BFC3

BFC1

+15 V

1 Amp peak Sine @1000 Hz

BFC4

Class B PowerAmp

B

C

Rs =10 k BFC2

D

BFC5+

For the transistor: IC = 1 mA, βF = βo = 200, ro = infinity, rπ = 5.0 kΩ, gm = 40 mmho, Vbe = 0.6 volts. BFC = Big Farad Capacitor (assume a short for AC)

The 0.1Ω resistance represents the resistance of a long wire. The class B power amplifier is just like the one you designed in lab 5, and the op-amp used is an LF356. Assume heat dissipation is not an issue.

4a. Given IC = 1 mA, what is the DC input voltage at the positive terminal of the power amp [node C] with no input? 4b. What is the DC voltage at the output of the power amp with no input [Vout] ?

4c. What is the DC voltage gain of the power amplifier stage [ahead of BFC5] ?

4d. What is the DC voltage at the + terminal of BFC5?

4e. What is the AC voltage gain of the power amplifier stage?

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[same circuit from previous page]

For the transistor: IC = 1 mA, βF = βo = 200, ro = infinity, rπ = 5.0 kΩ, gm = 40 mmho, Vbe = 0.6 volts. BFC = Big Farad Capacitor (assume a short for AC)

4f. What is the voltage drop across the 0.1Ω wire resistance due to the 1A peak current drain from the power amp? [Ignore any current drain from the transistor.]

4g. What component could be added and where, to prevent/reduce this voltage from being generated and thus coupled into the transistor at its input and output?

4h. Ignoring BFC5, what value do we need for BFC4 to produce a –3dB point at 10Hz, for the power amp only?

4i. [Re: question 4h] The gain below 10 Hz will roll off at 20dB per decade, but at some lower frequency it will stop dropping. Why?

4j. What is the approximate lower frequency and what is the gain that we end up with?

0.1 Ω

2N3904

7.5 k

-

+

+vout

_100 k10 k

750

130 k

13 kAC

BFC3

BFC1

+15 V

1 Amp peak Sine @1000 Hz

BFC4

Class B PowerAmp

B

C

Rs =10 k BFC2

D

BFC5+

Name: ________________________________________________

Problem 5 [4 points]

The 2N5459 JFET is used as a current source in for a differential amplifier. If the current through this JFET is to be 2.6 mA, find the value of R to create this current, assuming that the voltage drop across the JFET is approximately 15 volts.

R = _____________________________________

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Problem 6 [6 points]

-

++15

LF356

3

24

7

6

vout-15

To output ofprevious stage.

Non-Inv

Inv

200 kΩ

200 kΩ

The circuit above (not complete) is a switch selectable amplifier with a gain or +1 or -1. Add the necessary parts so that when the switch is in the position shown, it will become a non-inverting amplifier with a gain of +1 and an input impedance of 200 kΩ. You may not change or remove the 2-200 kΩ resistors.

FYI - this type of circuit with a programmable gain of +1 and -1 is used as a synchronous demodulator and not just a quiz question.

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Problem 7 [8 points]

This circuit is used to estimate the gate capacitance of a 2N7000 n-channel MOSFET with Vgs=2.0V (threshold voltage). The gate current is assumed to be negligible. The switch is normally closed, i.e. the gate voltage is at 5V with the LED on. At T=0, the switch is opened. The LED goes off in 5 microseconds. What is the gate capacitance?

The log table is for your convenience.

ln(5) = 1.609

ln(4) = 1.386

ln(3) = 1.099

ln(2) = 0.693

ln(1) = 0.000

Question 8 [4 points]

-

+

+15

IDEAL

2

3 4

7

6 vout

-15

I–

I+

Give the following ac characteristics for the op-amp shown at left: ROUT = RIN = AVOL = I+ = I- =

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Question 9 [18 points]

You are building a lantern/flashlight with a 6V rechargeable battery. Initially it was designed for a +12V DC input. Unfortunately, the unit was fried when the charging wires were attached backwards. Design a circuit that will accept 12VAC or 12V DC and charge the battery with a 50ma current source. You have available diodes (VF = 0.6V), resistors, bypass caps, 7805 (see datasheet), general purpose 2N2222 NPN transistor (see datasheet) and a 1,000uF 50V capacitor. The light bulb and switch attached to the battery are not shown in the diagram below. You may assume with a fully drained battery, when charging, the battery voltage reaches 6V quickly enough so that power dissipation is not an issue. When not charging, there must be no leakage current from the battery. [In addition to the design are additional questions on the design]

Work sheet; show design on next sheet

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Design [12 points] _________________

What is the efficiency of your design when charging the battery @50ma with an input of 12 VDC? [3 points] _________________________

What is the ripple voltage across the capacitor with an input of 12VAC? You may make simplifying assumptions. [3 points] __________________________