CS计算机代考程序代写 EECS 16A Designing Information Devices and Systems I

EECS 16A Designing Information Devices and Systems I
Spring 2021 Midterm 2 Instructions

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We have a zero tolerance policy for violations of the Berkeley Honor Code.

EECS 16A, Spring 2021, Midterm 2 Instructions

EECS 16A Designing Information Devices and Systems I
Spring 2021 Midterm 2

1. HONOR CODE
If you have not already done so, please copy the following statements into the box provided for the honor
code on your answer sheet, and sign your name.

I will respect my classmates and the integrity of this exam by following this honor code. I affirm:

• I have read the instructions for this exam. I understand them and will follow them.

• All of the work submitted here is my original work.

• I did not reference any sources other than my two reference cheat sheets.

• I did not collaborate with any other human being on this exam.

2. (a) What other courses are you taking this semester? All answers will be awarded full credit; you can
be brief. (2 points)

(b) What has been your favorite part of 16A so far? All answers will be awarded full credit; you can
be brief. (2 points)

EECS 16A, Spring 2021, Midterm 2 2

3. Circuit Analysis (18 points)

For the circuit in the following diagram, answer parts (a) – (e).

You should not change the labels that are already given in the diagram. If you add any additional labels for
your analysis, you should show your labels in the answer sheet for the corresponding part(s).

−
+VS

−

A
I3

I4 I6

(a) (3 points) Redraw the circuit diagram in your answer sheet. Following the passive sign convention,
label (i) the current IS through the voltage source VS, (ii) the current I1 through the resistor R1, and (iii)
the voltage V3 across the resistor R3.

(b) (2 points) Write the KVL expression for the loop drawn in the circuit diagram in terms of voltages
VS, V1, and V2.

(d) (5 points) Given VS = 5 V, R1 = 1 kΩ, R2 = 4 kΩ, R3 = 2.5 kΩ, R4 = 1 kΩ, R5 = 4 kΩ, R6 = 5 kΩ,
solve for the values of the element voltages V1, V2, and the node voltage u. Show your work. You
can use any circuit analysis techniques you have learned in this course.

(e) (6 points) Given VS = 5 V, R1 = 1 kΩ, R2 = 4 kΩ, R3 = 2.5 kΩ, R4 = 1 kΩ, R5 = 4 kΩ, R6 = 5 kΩ.

i. If we combine R3, R4, R5, and R6 as an equivalent resistor Req connecting between the nodes
A and B, what is the value of Req?

ii. What are the values of the current I3 and the power dissipated by R3? Show your work.

EECS 16A, Spring 2021, Midterm 2 3

4. Capacitive TouchSki (12 points)
One of your friendly lab TAs is preparing to go skiing for the first time! As excited as she is, she’s very
worried about losing her balance. To ease her mind, she decides to apply what she knows about capacitors
to create a circuit that will indicate if there is excessive force applied to either ski.

In this question, we will examine a force-sensing circuit for a single ski.

(a) (3 points) To create a sufficiently large capacitance, your TA affixes conductive plates to both the
bottom of the boot and the top of the ski, with a thin insulating layer with permittivity ε in between.
The boot has area Aboot and overlaps completely with the ski. Measurements show that the thickness
t of the insulating layer varies with the force F as t = 1kF , where k is some constant. Write the
capacitance Cboot as a function of the force applied, the area of the boot, and constants.

(b) (4 points) In order to measure the capacitance Cboot, you are given the following circuit. Assume the
capacitors have no initial charge before connected to the voltage source.

−
+Vs

Cboot

Cfixed

−

Vboot

What is the voltage Vboot in terms of Vs, Cboot, and Cfixed?

(c) (5 points) Now, you’d like to control an LED based on the force applied to the ski. Redraw the
following circuit in your answer sheet, complete the circuit so it sets Vout = 5V when Vboot < 2.5V, and Vout = 0V when Vboot > 2.5V (you don’t need to consider the special case when Vboot = 2.5V).
You may use one comparator and up to two additional voltage sources.

−
+5 V

Cboot

Cfixed

−

Vboot

Vout

Rlim

LED

EECS 16A, Spring 2021, Midterm 2 4

5. Resistive Temperature Sensor (17 points)

Oh no! Predictably, your lab TA gets hurt on the first day of her ski trip and is instructed to ice her injury
regularly. However, she’s finding that the ice packs are often too cold or too warm and needs a way to track
their temperature.

Fortunately, she remembers from 16A that the resistance of many resistors is dependent on temperature!
Using this information, you decide to help her build a temperature-sensing device.
Note: in this problem, temperature T is measured in the unit of Celsius.

(a) (6 points) You have different types of resistive bars available in your lab. For each of the following
two resistive bars, express the total resistance in terms of the given quantities and dimensions.

resistivity of copper = ρCo(1+αT ) Ω · cm
resistivity of nickel = ρNo(1+βT ) Ω · cm

Copper
Nickel

5 cm
5 cm

2 cm

2
cm

ii.

Coppe
r

Nicke
l

10 cm

1 cm

EECS 16A, Spring 2021, Midterm 2 5

(b) (5 points) You have the following circuit that has a temperature dependent resistive bar RT and a resis-
tor with fixed resistance R f . For this part only, assume Vs = 5 V, R f = 4 kΩ, and RT has resistivity
ρT = 100(1+0.01T ) Ω · cm and cross-sectional area A = 1 cm2.

−
+Vs

R f

−

Vmeas

Figure 5.1: Circuit diagram for parts (b) and (c).

You want to be able to measure temperature T within the range −10°C ≤ T ≤ 30°C. You also want to
limit the current flow through the resistive bar to be no more than 1 mA. Find the minimum length of
the resistive bar RT such that the current limit is met for all temperatures in the specified range.

i. Draw how you would attach an ideal voltmeter to the circuit in Figure 5.1, in order to mea-
sure the voltage across RT .

ii. Instead of an ideal voltmeter, you only have a practical voltmeter that can be modeled as an ideal
voltmeter coming with a parallel internal resistance Rint , shown below. You connect the practical
voltmeter to the same two nodes where you would attach the ideal voltmeter. Assuming RT =
1000 Ω for this part, determine the minimum value of Rint such that the equivalent resistance
across the voltmeter is no less than 99% of RT .

Rint V

EECS 16A, Spring 2021, Midterm 2 6

6. Data Conversion Circuits (22 points)

(a) (4 points) Photonic circuits use light to communicate. We still need to convert the light into electricity
by a photodiode to process it. We can model the photodiode as a current source Is. Sometimes it is
necessary at the receiver side to adjust the transmitted voltage level Vout , and one way to do this is
using a voltage source Vbias. Consider this simple photonic receiver circuit:

−
+ Vbias

Vout

Using superposition, solve for the voltage Vout in terms of Is, Vbias, Rs, and Rb. Show your work.

(b) (4 points) The previous receiver circuit may have problems with loading. Instead, we may use an
op-amp, such as in this circuit:

−

−
+ Vbias

Vout

Calculate the voltage at the output Vout in terms of Is, Vbias, and R. Show your work. You will not
receive full credit for directly copying a formula from your cheat sheet.

EECS 16A, Spring 2021, Midterm 2 7

(c) (4 points) We need some circuits to convert between our analog voltage values and some digital repre-
sentation stored in 1s and 0s. We mentioned digital-to-analog converter circuits, or DACs, in lecture.
Let’s inspect one here:

−
+ VDD

N−3

N−2

N−1

−

Vout

Note that there are N resistors and N switches in the circuit. Depending on some input digital code,
one of the switches is closed, connecting the output to some node in the resistor ladder.
If only the ith switch is closed (0≤ i≤ N−1), what is the output voltage Vout in terms of VDD, i, N,
and R?

EECS 16A, Spring 2021, Midterm 2 8

(d) (4 points) The dual to DAC circuits are analog-to-digital converters, or ADC circuits. Here is an
example of one, using resistors and comparators:

−
+ VDD

−

+
b0

−

+
b1

−

+
b2

−
+Vin

Note: The red wires in the diagram are regular wires, but have been colored to show that they do not
touch the crossing black wires.
The resistor ladder gives us a set of reference voltages to compare against. We use a set of comparators
to compare the input voltage Vin against these reference levels, and we get out a corresponding digital
code b0, b1, and b2.
Assume that VDD = 1V, and that the comparators are connected to rails VDD = 1V and VSS = 0V. If
Vin is 0.3V, what are the outputs b0, b1, and b2?

EECS 16A, Spring 2021, Midterm 2 9

(e) (6 points) These DAC and ADC circuits help us represent numbers using voltage values. We would
like to build some blocks that let us compute, e.g. add and multiply, with these numbers. We call this
“analog computing,” and we saw an example of this previously in the “artificial neuron” circuit. These
analog compute circuits have potentially massive speed benefits over comparable digital compute cir-
cuits. (Take EECS151 and EE140 for more details).

DAC

Compute ADC

Consider one such compute circuit below, the differential amplifier. This is a common circuit in audio
amplifiers but is also a useful tool for mathematical computing. Find the output Vout in terms of V1,
V2, R1, and R2.

−

+
R1

Vout
V1

EECS 16A, Spring 2021, Midterm 2 10

7. Aid to the Resistance (13 points)

The main ship of the Resistance Fleet is in trouble! They have recruited you to help fix the issue. The
on-board technicians have determined that the resistor grid in the main console is faulty (one of the resistors
must be fried). It is your job to replace the grid with something of equivalent resistance. However, because
of severe budget cuts in the Resistance’s EE department, you can only use a single resistor connected
between nodes A and B to replace the resistor grid. The technicians hand you the diagram below of what
the resistor grid looked like. All resistors in the diagram have resistance value R.

repeating forever ->

(a) (5 points) Find the equivalent resistance of the following piece of the resistor grid between nodes A
and B in terms of R.
Hint: If a resistor has no current flowing through it, what is it equivalent to?

EECS 16A, Spring 2021, Midterm 2 11

(b) (5 points) Find the equivalent resistance of the following piece of the resistor grid between nodes A
and B in terms of R.
Hint: (i) Because the pattern is infinite, the equivalent resistance of the circuit in the red box and the
equivalent resistance of the circuit in the blue box are equal.
(ii) The solutions to the quadratic equation ax2 +bx+ c = 0 are −b±

√
b2−4ac

2a .

repeating forever ->

(c) (3 points) Suppose the equivalent resistance for the piece of resistor grid in part (a) is αR, and the
equivalent resistance for the piece of resistor grid in part (b) is βR, where α and β are known real
numbers for this part. What should be the value of the resistor you use to replace the entire grid
with, in terms of R, α , and β?

EECS 16A, Spring 2021, Midterm 2 12

8. Explosive Tesla Coil!! (19 points)

Renowned as the father of alternating current technology, the brilliant
Nikola Tesla created countless inventions which were truly beyond his
time. One of such inventions was the Tesla Coil, a device that could
continuously generate safe lightning! While we do not yet have all the
background knowledge needed for the full circuitry, we can still make an
effective model of this device with a capacitor network.

Loosely stated, the Tesla coil circuit charges up a specially-designed,
massive capacitor (labeled CT here) until it reaches a certain threshold of
charge. The effective capacitor model is shown in Figure 8.1, where VS is
the charging voltage source, each C are identical charge-loading capacitors,
and CT is the capacitor that models our Tesla Coil.

The capacitor CT charges over a repeated series of cycles.
Each cycle involves two stages:

• Stage A – The φB switches in Figure 8.1 open and then the φA switches close.
In this stage the loading capacitors C are charged by Vs.

• Stage B – The φA switches in Figure 8.1 open and then the φB switches close.
In this stage the loading capacitor C charges are shared with the Tesla coil capacitor CT .

−
+Vs

φA

φB

−

Figure 8.1: Tesla coil effective circuit model.

EECS 16A, Spring 2021, Midterm 2 13

(a) (4 points) Draw the equivalent circuit diagram for each stage (A and B). To receive full credit,
make sure each diagram you draw has only the relevant circuit elements, i.e. the diagram should not
include any elements that are not connected in a closed circuit.

(b) (3 points) If we would like to model the three identical loading capacitors as a single equivalent ca-
pacitor labeled CL, what value should we choose for CL to ensure that the circuit has the same
behavior? Your answer should be in terms of C.

(c) (6 points) Suppose that all capacitors in the device start off without any charge. Compute the charge
QT and the voltage VT across the Tesla coil capacitor CT after the circuit completes a cycle (going
from stage A to stage B).
All final solutions should be in terms of the known circuit constants (Vs, C, and CT ).
Hint: You may use the simplified equivalent loading capacitor model CL through your work, then plug
C back in at the end.

(d) (6 points) Now suppose that the Tesla coil capacitor CT starts with an initial charge Q0, which was
collected as a result of previous cycles.

i. Compute the charge QT and the voltage VT across the Tesla coil capacitor CT after the circuit
completes a cycle (going from stage A to stage B). For simplicity, you can assume the loading
capacitors still start off without any charge.

ii. Compute the ratio σ of energy stored on CT before and after this cycle (so σ = Eafter/Ebefore).
You can get partial credit for writing the expressions for Ebefore and Eafter.
At which value of initial charge Q0 do we no longer add energy to the coil after a cycle?

All final solutions should be in terms of the known circuit constants (Vs, C, CT , and Q0).
Hint: It may be helpful to simplify the final answer of σ in the form:

σ =

(
3
(CT

)
+___

3
(CT

)
+___

)2
where the ___ spaces are yet to be discovered by you!

EECS 16A, Spring 2021, Midterm 2 14

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