Complement Arithmetic
1. Ones complement (flip all bits)
11010
00101
2. Twos complement
Take ones complement, add 1, neglect carry
11010 00101
+1
Copy from right until first 1 encountered, then
invert (not reverse) the rest.
110
N 10
N
invert copy
2's com

Example
Find a range of Thevenin equivalent circuits for the network shown in Figure 1 when resistors with a 10%
tolerance are used.
First we should determine the maximum and minimum resistance of every resistor.
For 100 10% is 90 and 110 .
For 330 10% is

ELEC 21 1
Spring Semester 2014
Final Exam
You must show all work to receive credit
Circle your nal answers 1. (14 pts) Given that i = 2 A, va = 3 V and vc = -5 V (a) Using KVL, solve for V], and (b)
What is the power for element A and is it absorbed or su

Solving Mesh Currents (planar networks)
Assign mesh currents (clockwise), one current for each open area (pane) of the circuit
Write mesh equations (KVL)
Simplify equations to standard form
Solve using determinants, substitution or calculator
The process

Example: Analysis a Wye-Wye System
Given:
- Balanced positive sequence Y-connected 60 Hz source
- VY = 1000 V (Peak line-to-neutral voltage)
- Balanced Y-connected load each consisting of L=0.1 H and R=50 connected in series.
Find:
- Line currents
- Line-

CHAPTER 2: RESISTIVE CIRCUITS
1.
2.
3.
4.
5.
Series/Parallel
Voltage/Current division
Solve circuits: node voltages, mesh currents
Norton and Thevenin equivalent circuits
Superposition
Series Resistances
The elements are connected end to end and the same

Non-Ideal Op-Amps
What if open-loop gain is not infinite?
Assume infinite input resistance for op-amp:
v
vo = AOL vx
so vx = o
AOL
vi vx
R1
v v
i2 = x o
i1 = i2
R2
v
v
vi o o vo
AOL
AOL
=
R1
R2
i1 =
R2
vo
R1
=
R2
vi
1+
R1
1+
AOL
R2
for
R1
Av
-0.3

Filters: Summary
First order low-pass filter: Characterized by DC gain and fB
First order high-pass filter: Characterized by gain at = and fB
Series resonant circuit: Characterized by f0 and Qs
Band-pass filter: Vout defined across the resistor
B=
f0
Qs
I

Example: Given is the current of a C = 0.1 F capacitor as a function of time. At t0 the voltage of the
capacitor is equal to zero. Find charge, voltage, power, and stored energy.
0 ms t 2 ms
i (t ) = 1 mA
i (t ) = 1 mA 2 ms t 4 ms
4 ms t 6 ms
i (t ) = 1 m

Name K81 .2
ELEC 21 1
Fall Semester 2013
Final Exam
You must show all work to receive credit
Circle vmlr nal answers l. (8 pts) Using KCL solve for Ix.
2. (10 pts) What is the power for each element and is it absorbed or supplied by the
element? State h

Decibels, Cascading, and Logarithmic Frequency Scales
When comparing different filters, it is often easier when using decibels.
Decibels
H ( f ) dB = 20 log H ( f ) H ( f ) = 10
H( f )
dB
20
For voltage and current, multiply the
logarithm of the transfer

Example:
First order high pass filter with transfer function of -30 dB at f = 60 Hz.
What is the breaking frequency fB?
A slope of +20 dB/decade means that 60 Hz to fB is
30 dB
= 1.5 decades .
20 dB/decade
f
# of decades = log 2 where f2 > f1
f1
1.5 =

Bode plots
A Bode plot is a graph of the decibel magnitude of a transfer function versus logarithmic frequency.
Magnitude plot:
H ( f ) dB vs. log ( f ) (possible to plot a large dynamic range of magnitude and frequency).
Consider a first-order low pass f

Phasors
Sinusoidal steady-state currents and voltages can be represented by vectors called phasors.
Phasors provide a convenient way to combine sinusoids that are not necessarily in phase with each other.
Consider the AC voltage:
v1 (t ) = V1 cos(t + 1 )

Inductance
Inductors are made by coiling wire around some type of form (made from magnetic material).
Current flowing through the inductor creates a magnetic field.
When the current changes, the resulting magnetic flux changes, and this induces voltage ac

CHAPTER 11: BASIC AMPLIFIERS
Amplifiers are used to increase the amplitudes of electrical signals.
For example, sensors typically produce weak signals that need amplification before they can be used.
Ideally, amplifiers preserve the input waveform with in

CHAPTER 1 VOLTAGE AND CURRENT, POWER AND ENERGY, KCL, KVL, OHMS LAW
Why Study Electrical Engineering?
To pass the Fundamentals of Engineering (FE) Examination
So you can lead projects in your own field
To be able to operate and maintain electrical systems

Circuits with multiple ideal voltage sources
We have solved an example when the branch has an ideal voltage source. We pick the reference node of
one end of the source and we have one less unknown node that we need to solve.
Now we should see how to solve

Thevenin and Norton Equivalent Circuits
Inside box can be independent sources or dependent sources if controlling variable is inside box.
Thevenin Equivalent Circuits
Consider the Thevenin equivalent with open circuit terminals:
The Thevenin source voltag

Power supplies and efficiency
External power must be delivered to amplifiers via power supplies.
Power supplies provide different DC voltages.
Average power supplied is the product of the average current and voltage.
Total power = sum of power supplie

Summary of Phasors
v(t ) = Vm cos(t + 1 ) Vm 1
i (t ) = I m cos(t + 2 ) I m 2
Im
Vm
1
Im
2
Re
Recall: cos ( t + ) = Re exp ( j ( t + ) ) = Re [ cos( t + ) + j sin( t + )]
Phasors rotate CCW at a rate of rad/sec
Phasors can be thought of as a snapshot in t

Power in AC Circuits
I=
V Vm0
=
= I m
Z Z
where I m =
Vm
Z
Z = R + jX
Z is only resistive:
Vm 0
= I m 0
R
p(t ) = Vm I m cos 2 (t )
1 T
Vm I m cos 2 t dt
T 0
T
1
= Vm I m ( 12 + 12 cos 2t )dt
0
T
V I
= m m = VRMS I RMS
2
p av =
ELEC211Fall2012Day18
Page

Chapter 7: Logic Circuits
So far, weve focused on analog circuits continuous signals, e.g. sinusoids
Digital circuits binary (discrete) signals
Positive logic:
Logic 1= high, true, on
Logic 0= low, false, off
Example: TTL logic family
Other logic families

4" Name key I H
ELEC 21 1
Spring Semester 2013
Final Exam
Yea must shew all work to receive credit
Circle year nal answers 1. (8 pts) Using KCL solve for Ix.
7 ' I)! +gA+3,4C.,4)_1m_ M :0
Ix: cfw_2379/171'5
2. (10 pts) What is the power for each eleme

Name KEV )
ELEC 21 1
Spring Semester 2014
Hour Exam 3
You must show all work to receive credit'
Circle your nal answers I. (6 pts) Sketch 2' versus v to scale for the following circuit. Assume a 0.6 V drop in the
forward bias direction.
2. (10 pts) As

Chapter 5: Steady State Sinusoidal Analysis
So far, weve studied primarily DC circuits, and a little AC with capacitors and inductors.
Sinusoidal voltages and currents
v ( t ) = Vm cos ( t + )
Vm peak voltage
angular frequency (rad/sec)
phase angle (rad

Example 1:
Find vo
The circuit is assumed to be linear and the
superposition principle can be used.
Shorting one voltage source and leaving its
resistor (both terminals at ground), leaving only
previous inverting configuration:
Rf
Rf
voA
voB
=
=
vA
RA
vB

ELEC 21 1
Spring Semester 2013
Hour Exam 2
You must Show all work to receive credit
Circle your nal answers
Name
LEXM 1 Given
(12 pts)*E the following circuit:
a. (4 pts) What IS the time constant?
b. (4 pts) What is vc(t) as a mction of time (do not sket

Name EEY
ELEC 21 1
Spring Semester 2014
Hour Exam 1
You must show all work to receive credit
Firoln vnnr nal anenrnre . ) b
l. (llspts) Solve for Ix and Vg Zl ' :1. 0
ll
2. (wpts) What is the power for each source? Is the power being supplied or absorb

Thevenin/Norton Equivalent circuits
Voc = Vt = I sc Z t = I n Z t
Simply use phasors and complex
impedances
Short circuit current: two loop equations
Open circuit voltage: one loop equation
Thevenin impedance: equivalent impedance
Z eq = Z t = [50 + ( j 2