Quiz III Fall 2015 - Rensselaer Polytechnic Institute Quiz 3... · K. A. Connor, - 1 - Revised: 1 May 2016 Rensselaer Polytechnic Institute Troy, New York, USA Quiz III Fall 2015

K. A. Connor, - 1 - Revised: 1 May 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz III Fall 2015

Part A (25 Points) Complete on Blackboard

A. (25 Pts) _________

Part B (75 Points)

1. (14 Pts) _________

2. (4 Pts) _________

3. (12 Pts) _________

4. (12 Pts) _________

5. (15 Pts) _________

6. (15 Pts) _________

7. (3 Pts) _________

Total __________________

Draw circuit diagrams for all problems, especially as you simplify the circuits.

Be sure to fully annotate plots, even when the problem does not ask you to do this.

Show all of your work

At least skim through the entire quiz before you begin and then start with the problems

you know best.

Note that some questions involve using things you have learned in new ways and some

involve some minor new information. Focusing on what you know will make the

problems easier to solve.

The proctor will only answer clarification questions where wording is unclear or where

there may be errors/typos. No other questions will be responded to.



Quiz III Fall 2015

Theme for 2015: Inclusion matters: access and empowerment for people of all abilities

The estimated one billion people living with disabilities worldwide face many barriers to inclusion in

many key aspects of society. As a result, people with disabilities do not enjoy access to society on an

equal basis with others, which includes areas of transportation, employment, and education as well as

social and political participation. The right to participate in public life is essential to create stable

democracies, active citizenship and reduce inequalities in society.

Persons with disabilities must be able to fulfil their role in society and participate on an equal basis with

others. It is important to focus on the ability and not on the disability of an individual. Often, the societal

image of persons with disabilities is impacted by attitudes based on stigma and discrimination, as well as

archaic ideas about disability and persons with disabilities that are often the greatest barrier to their full

and equal participation in society and development on an equal basis with others. It is important to note

that disability is part of the human condition, and that all of us either are or will become disabled to one

degree or another during the course of our lives.

By promoting empowerment, real opportunities for people are created. This enhances their own capacities

and supports them in setting their own priorities. Empowerment involves investing in people - in jobs,

health, nutrition, education, and social protection. When people are empowered they are better prepared to

take advantage of opportunities, they become agents of change and can more readily embrace their civic

responsibilities.

Source: UN.org



Quiz III Fall 2015

Op-Amp Specs (Excerpts)



Quiz III Fall 2015



Quiz III Fall 2015



Quiz III Fall 2015

Transformer Specs (Excerpts)

Note: This transformer is so good that its single piece price is over $70!



Quiz III Fall 2015

Part B (75 Points)

Problem 1 (14 Points) – Logic Gates This problem addresses building logic devices from a single type of

device, which is shown at the right.

a. (3 Pts) What kind of a logic gate is this and what is its truth

table? Name the device and fill out the table below.

Input A Input B Output

0 0 1

0 1 1

1 0 1

1 1 0

NAND gate

b. (3 Pts) Assume that the two inputs are tied together to

create a single input device, as shown. Name the device

and fill out its truth table below.

Input A Output

0 1

1 0

NOT gate or inverter

c. (4 Pts) Assume that two of the

configurations from part b are combined

with the device from part a, as shown.

Name the device that matches the

functionality of this combination and fill

out its truth table below. Note that, unlike

parts a and b, you are asked to find the

values at the intermediate points, not just

the inputs and output.

Input A Input B C D Output

0 0 1 1 0

0 1 1 0 1

1 0 0 1 1

1 1 0 0 1

OR

C

D



Quiz III Fall 2015

d. (4 Pts) Finally, add one more configuration from part b. Name the device this

combination produces and fill out its truth table. Again, you must find the values at

intermediate points, not just the inputs and output.

Input A Input B C D E Output Q

0 0 1 1 0 1

0 1 1 0 1 0

1 0 0 1 1 0

1 1 0 0 1 0

NOR

Problem 2 (4 Points) – Logical Function

What logic gate functionality is described by the following situations?

a. You can buy a new car only if both of your parents approve.

AND

b. You can buy a new car if at least one of your parents approve.

OR

C

D

E



Quiz III Fall 2015

Problem 3 (12 Points) – Operational Amplifiers

The two amplifier circuits below are configured with the same op-amp and resistors. Identify

which type of amplifier each is and its gain in

out

V

VG . For your calculations, assume that R1=

3kΩ and R2 = 12kΩ.

a. (4 Pts) The circuit a at the upper left:

Inverting amplifier, Gain = -4

b. (4 Pts) The circuit b at the upper right:

Non-inverting amplifier, Gain = 5

c. (2 Pts) If the op-amp is powered with two 9V batteries, which of the following input

voltages listed below will amplifier a (upper left) be able to amplify without distortion?

Circle all correct answers.

a. 1V

b. 2V

c. 3V

d. 4V

e. 5V

d. (2 Pts) If the op-amp is powered with two 9V batteries, which of the following input

voltages listed below will amplifier b (upper right) be able to amplify without distortion?

Circle all correct answers.

a. 1V

b. 2V

c. 3V

d. 4V

e. 5V

Output cannot exceed ±9V and 9/4 = 2.25 and for

part d 9/5 = 1.8



Quiz III Fall 2015

Problem 4 (12 Points) – Complex Impedance

Earlier this semester, we analyzed circuits using complex impedances, where the impedance of

resistors is real and the impedances of inductors and capacitors are imaginary. The ability to

analyze circuits like the ones shown above will be useful in a following problem involving an

audio amplifier. To be prepared for the audio problem, you are to evaluate the net impedance of

the two circuits at the bottom end (50Hz) and the top end (8.5kHz) of the practical audio range of

frequencies. (See Problem 6 for more information.)

a. (4 Pts) Evaluate the impedances for both L and C at these two frequencies and fill in the

table below. That is, find ZC and ZL.

Frequency 50Hz 8.5kHz

ZC -j(1.8e6) -j(1e4)

ZL j(.3) j53

CjZC

1 LjZC Answers above within 10% are OK

b. (3 Pts) Find the parallel combination of R and C for both frequencies.

1.0e+03 *(1.1000 - 0.0007i) 1.0e+03 *(1.0878 - 0.1150i)

c. (3 Pts) Find the series combination of R and L for both frequencies.

1.0e+03 *(1.1000 + 0.0003i) 1.0e+03 *(1.1000 + 0.0534i)

d. (2 Pts) Simplify your answers to parts b and c by dropping the smaller term, if it is less

than 20% of the larger term.

Drop all imaginary terms and we are left with R = 1100

Anything within 10% is acceptable, but the value should be real

a) b)



Quiz III Fall 2015

Problem 5 (15 Points) – Transformers Transformers also play a role in an interesting circuit you

are to analyze in a following problem. Shown at the right is

the symbol for an iron core transformer, like the one you

built by winding magnet wires on a toroidal ferrite core.

Unlike the one you made, this transformer does not have the

same number of turns on the primary and the secondary.

Rather it has more secondary turns than primary. Assume

that the transformer has the load resistor shown (colors are

brown-green-yellow).

a. (1 Pt) What is the value of the load resistor?

150kΩ (also confirmed in a later problem)

b. (2 Pts) What is the ratio of in

out

V

V?

10

c. (2 Pts) What is the ratio of in

out

I

I?

0.1

d. (3 Pts) What is the input impedance of the loaded transformer inZ ? That is, what is in

in

I

V?

150k/100 = 1.5kΩ

e. (3 Pts) If the RMS sinusoidal input voltage is 1V, how much power is delivered to the

load resistor?

V*I = 102/150 mW = 0.67 mW

f. (4 Pts) The transformer addressed in this problem, is and ideal model of the Jensen audio

transformer whose datasheet is provided on page 6 of this quiz. Identify two terms from

the datasheet that correspond to the answers to parts b, c or d above. Because this

transformer is not ideal (e.g. coupling is not equal to 1), the agreement will not be perfect.

However, the values given for the real transformer will be close.

Voltage gain is 19.75dB which converts to a little less than the 10 found here. The input

impedance is 1.4kΩ rather than the 1.5kΩ here. Very close.

1:10 Primary Secondary



Quiz III Fall 2015

Problem 6 (15 Points) – High Quality Microphone Preamplifier

The circuit above is an application found in the datasheet for the OP27 op-amp. This figure has

been slightly modified to indicate that the 150Ω source is the output impedance of the

microphone, which is, otherwise, not shown. This is the practical circuit that the analysis in

problems 4 and 5 was done to understand its operation. The typical audio spectra shown below

indicate why we chose to analyze the circuits at 50Hz and 8.5kHz, since they nicely cover the

useful range of frequencies that a microphone must be sensitive to.

Output Impedance of

Microphone

AMP-IN INPUT

150kΩ



Quiz III Fall 2015

a. (4 Pts) For the audio range of frequencies that you considered in problem 4, you should

be able to simplify this circuit by eliminating one component. Identify this component by

describing it below and drawing a circle around it in the circuit diagram above.

Capacitor C2 can be neglected.

b. (4 Pts) Now that you have simplified the circuit, identify the type of op-amp-based

amplifier it is and determine its gain INAMP

OUT

V

V

.

Non-inverting op-amp so gain is 1 + 1100/121 = 10.1

c. (4 Pts) From the gain of the amplifier that you just determined and your answer to

problem 7, determine the overall gain of the complete circuit IN

OUT

V

V.

The transformer steps up the voltage by another factor of 10 so gain = 101

d. (3 Pts) In the OP27 datasheet, the gain of the overall circuit is given in dB, so covert your

answer to part c to decibels.

100 is 40dB and 101 is 40.1dB … anything close is fine



Quiz III Fall 2015

Problem 7 (3 Points) – Nest Thermostat Transformer Issue

Thermostats with no C-Wire (above) and with C-Wire (below)

Problem continues on the next page …



Quiz III Fall 2015

One of the great new devices we have to make our

homes smart is the Nest thermostat or similar

smart devices from other manufacturers.

Unfortunately, it is not usually straight-forward to

install because the transformers we use to power

the thermostats in most of our homes are missing

what is called the C-Wire. The two circuit

diagrams on the previous page show traditional

transformers (above) and transformers for smart

thermostats (below). The ‘Bells and Whistles’ represent the hardware that allows the thermostat

to be smart.

(3 Pts) Describe what the C-Wire provides for the ‘Bells and Whistles.’ Any reasonable response

is acceptable. Guess if you have to.

Always on power because the smart thermostat needs power to run.

Documents

Quiz III Fall 2015 - Rensselaer Polytechnic Institute Quiz 3... · K. A. Connor, - 1 - Revised: 1 May 2016 Rensselaer Polytechnic Institute Troy, New York, USA Quiz III Fall 2015