CHAPTERS 1

1
CHAPTERS 1 2

• NETWORKS 1 ECE 09.201.01
• 3 SEPTEMBER 2008 Lecture 2 SECTION
  ONE
• ROWAN UNIVERSITY
• College of Engineering
• Dr Peter Mark Jansson, PP PE
• DEPARTMENT OF ELECTRICAL COMPUTER ENGINEERING
• Autumn Semester 2008 - Quarter One

2
Networks I

• Todays Learning Objectives
• Apply circuit parameters (v, i, r, p, etc.)
• Analyze DC circuits with passive elements
  including resistance
• Define analysis w.r.t. circuits
• Define active and passive circuit elements
• Apply Ohms law (vRi, Iv/r, pi2r, etc.)
• Analyze DC circuits with passive elements
  including resistance
• Analyze independent and dependent electrical
  sources

3
Review a few Admin Items

• Website visit
• Text Chapters Read
• Lab Homework Assignment
• Tool Kit required by lab 2
• Screwdrivers (Phillips and Flathead)
• Wire Cutters, Tweezers, Crimping Tool
• Needle nose pliers
• Digital Multi-meter
• Tool Box

4
chapter 1 key topics

• history of electricity - done
• electric circuits and current flow - done
• systems of units - done
• voltage - done
• power and energy in progress
• voltmeters and ammeters
• circuit analysis and design

5
passive sign convention (psc)

• positive current flows from positive voltage to
  negative voltage.

Is the current in this resistor positive or
negative?
Is the current in this element positive or
negative?
6
power and psc

• p v i
• Power is absorbed by an element adhering to the
  passive sign convention (sink)
• Power is supplied by an element not adhering to
  the passive sign convention (source)

7
power and psc example

• what is the power absorbed or supplied by the
  element below, when i 4A?
• power 12V x 4A 48 W
• does not adhere to passive sign convention,
• so power is supplied.

8
power and psc quiz

• what is the power absorbed or supplied by the
  element below, when i -2A?
• power -12V x -2A 24 W
• does adhere to passive sign convention,
• so power is absorbed.

9
power and energy

• p v i
• power voltage current (units watts)
• power is the time rate of expending energy
• energy power time (units Joules w-s)
• energy is the capacity to do work

10
power and energy

• energy force x distance
• power energy / time period (secs)

11
power and energy example

• a mass of 300 grams experiences a force of 200
  newtons. Find the energy (or work expended) if
  the mass moves 15 cm. Also find the power if the
  move is completed in 10 milliseconds.
• energy force x distance (N m)
• energy 200 x .15 30J
• power energy / second (J/secWatts)
• power 30J/10-2 sec 3000W 3kW

12
power and energy quiz

• a Motorola StarTAC cellular phone uses a small
  3.6V lithium ion battery with nominal stored
  energy of 200 joules. For how long will it power
  the phone if it draws a 3-mA current when in
  operation?

13
quiz solution

• 200 joules 200 watt-secs
• 3.6 V x 3 mA 1.08 x 10-2 watts
• 200 watt-secs / 1.08 x 10-2 watts
• 18,519 seconds
• 18,519 seconds / 3600 sec/hr
• 5.1 hours

14
Learning Check 1

• your iPod shuffle uses a small 3.7V polymer
  lithium battery with stored energy of 11,322
  joules. How many hours will it play tunes if it
  draws 70.81mA current when in operation?

15
voltmeters and ammeters

• dc current and voltage measurements are made
  with (analog or digital type) ammeters and
  voltmeters
• voltage measurements are made with red probe ()
  at point a, and black probe (-) at point b

16
voltmeters and ammeters

• current measurements require breaking into the
  circuit so the ammeter is in series with the
  current flow
• made with red probe () at point b, and black
  probe (-) at point c

17
ideal meters

• ammeters negligible voltage drop through it
• voltmeters negligible current flows into it

18
Learning Check 2

• Which can you measure without breaking the
  circuit open
• A) Voltage across an element
• B) Current through an element

19
circuit analysis and design

• analysis concerned with the methodological
  study of a circuit to determine direction and
  magnitude of one or more circuit variables (V, A)
  
• problem statement
• situation and assumptions
• goal and requirements
• plan ? act ? verify ? if correct, solved
• if not, plan ? act ? verify ? iterate as needed

20
chapter 2 key topics

• engineering and linear models
• active and passive circuit elements
• resistors Ohms Law
• independent sources
• dependent sources
• transducers
• switches

21
models

• A model is an object or pattern of objects or an
  equation that represents an element or circuit.
• Some examples of models
• model airplane
• person wearing designer clothes
• V I R

22
circuit models

• in our work in Networks I we will construct
  models of elements that will be interconnected to
  form models of DC circuits. (while these will
  illuminate our understanding of the real thing,
  they are not the real thing)

23
circuit analysis

• the purpose of making circuit models is so we
  can perform mathematical and theoretical analyses
  prior to making the real thing. the goal of
  circuit analysis is to predict the quantitative
  electrical behavior (voltage current) of
  physical systems so we can explain the overall
  operation of the circuit.

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LINEARITY implies

• SUPERPOSITION
• In a single element
• if the application of
• i1 yields v1 and i2 yields v2 then
• i1 i2 will yield v1 v2
• HOMOGENEITY
• In a single element
• if i1 is multiplied by k (a constant) then
• the application of ki1 will yield kv1

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example

• Determine why the following elements demonstrate
  a linear response, or why they do not
• Element 1
• v 3i
• Element 2
• v 5i 2
• 2 volunteers to go to the white board

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linearity is key to networks I

• we will only consider linear models of circuits
  in this course
• any device or element that does not satisfy both
  the principles of superposition and homogeneity
  is considered non-linear

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Learning Check 3

• Determine if the following element demonstrates a
  linear response, or why it does not
• Element A
• i 60v

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active passive elements

• A passive element absorbs energy.
• What does it do with the energy?
• Would the power through this element be or - ?
• Learning Check 4
• Give an example of a passive element.
• An active element is capable of supplying energy.
• Where does it get the energy?
• Is the power or - ?
• Learning Check 5
• Give an example of an active element.

29
resistance

• Property of an element or device that impedes the
  flow of current.
• And we have Ohms Law
• Which came first?

30
resistors

• A few things we need to know
• R 1/G (G is called conductance)
• If a resistor heats up, its resistance changes.
• The power absorbed by a resistor can be
  represented (modeled) two ways
• p vi v(v/R) v2/R or v2G
• p vi iRi i2R or i2/G
• The energy delivered to a resistor is

31
open short circuits

• Open - a break in the circuit where no current
  flows.
• Short - a connector between two elements with no
  voltage drop.

open
v(t) 0 i(t) ? 0 (if there is a source in the
circuit)
i(t) 0 v(t) ? 0 (if there is a source in the
circuit)
short
32
sources

• A thing that can supply energy.
• The energy can come in the form of
• current
• voltage
• power?
• There are two types of sources
• Independent - constant no matter what you hook it
  to.
• Dependent - the value is tied to some other point
  in the circuit.

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ideal independent sources

• Ideal independent sources maintain their assigned
  value indefinitely.

An ideal voltage source will maintain its voltage
value and sustain ANY value of current.
An ideal current source will maintain its current
value and sustain ANY value of voltage.
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sources / series connections

• series elements connected in series have the
  same current running through them

i
35
sources / parallel connections

• parallel elements connected in parallel have
  the same voltage

Ended here
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Sample problems

• 2-4.2
• 2-4.7 Learning Check 6
• 2-5.1
• 2-5.2

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ideal dependent sources

• Voltage and current sources can be controlled by
  either a voltage or a current somewhere else in
  the circuit.

voltage sources
current sources
vd r ic or vd b vc
id g vc or id d ic


r, b, g and d are the gains of these sources
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the key dependent sources

• CCVS current-controlled voltage source
• VCVS voltage-controlled voltage source
• VCCS voltage-controlled current source
• CCCS current-controlled current source

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example

• CCCS exercise 2.7-1, p. 37

40
a very important example
c
c
b
ic
ic
vbe
ic gmvbe
b
rp
vbe
e
e
41
transducers

• devices that convert physical quantities into
  electrical quantities
• pressure
• temperature (iTk)
• position potentiometer
• Example 2-8.2, p. 39

42
switches
Make before break SPDT
SPST
SPDT
43
examples

• Exercises 2-9.1 and 2-9.2
• p. 40

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ch. 1 2 important concepts

• Circuits current voltage power
• Passive sign convention
• Active and Passive elements
• Linearity - superposition homogeneity
• Resistors and Ohms Law
• Sources - Ideal, independent and dependent
• Opens and Shorts
• Switches

45
chapter 3 - overview

• electric circuit applications
• define node, closed path, loop
• Kirchoffs Current Law
• Kirchoffs Voltage Law
• a voltage divider circuit
• parallel resistors and current division
• series V-sources / parallel I-sources
• resistive circuit analysis

46
resistive circuits

• we are ready to make working circuits with
  resistive elements and both independent and
  dependent sources.
• words we know short, open, resistor
• new words
• node
• closed path
• loop

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more definitions

• node a junction where two or more are connected
• closed path a traversal through a series of
  nodes ending at the starting node
• loop

48
an illustration
R1
NODE

V
R2

ARE THESE TWO NODES OR ONE NODE?
49
Gustav Robert Kirchhoff

• 1824-1887
• two profound scientific laws published in 1847
• how old was he?

50
Kirchhoffs laws

• Kirchhoffs Current Law (KCL)
• The algebraic sum of the currents into a node at
  any instant is zero.
• Kirchhoffs Voltage Law (KVL)
• The algebraic sum of the voltages around any
  closed path in a circuit is zero for all time.

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KCL
Assume passive sign convention
52

Node 1
Node 2
Node 3
Node 1 I - i1 0 Node 2 i1 - i2 - i3
0 Node 3 i2 i3 - I 0 i2 v2/R2 i3
v3/R3
Use KCL and Ohms Law
53

Node 1
Node 2
v2
v3
Node 3
Node 1 I - i1 0 Node 2 i1 - i2 - i3
0 Node 3 i2 i3 - I 0 i2 v2/R2 i3
v3/R3
Use KCL and Ohms Law CURRENT DIVIDER
54
Learning check 7

• what is relationship between v2 and v3 in
  previous example?
• lt, gt,

55
KVL
i V/(R1 R2) vR1 iR1 VR1 /(R1 R2) vR2
iR2 VR2/(R1 R2)
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SERIES RESISTORS
NOTE
i V/(R1 R2) vR1 iR1 VR1 /(R1 R2) vR2
iR2 VR2/(R1 R2) VOLTAGE DIVIDER
57
SERIES RESISTORS

• resistors attached in a string can be added
  together to get an equivalent resistance.

58
Learning check 8

• what is value of Req in previous example when
  the three resistors are replaced with the
  following 4 new resistor values?
• 1 k?, 100?, 10?, and 1?

59
PARALLEL RESISTORS

• resistors attached in parallel can be simplified
  by adding their conductances (G) together to get
  an equivalent resistance (R1/G).

Geq Gr1 Gr2 etc.. When you only have
two Req (R1R2)/(R1R2)
60
Learning checks 9 10

• 8. what is value of Req in previous example?
• 9. what is the new value of Req when the two
  parallel resistors are replaced 2 new resistor
  values shown below?
• 10? and 40?

61
series voltage sources

• when connected in series, a group of voltage
  sources can be treated as one voltage source
  whose equivalent voltage ? all source voltages
• unequal voltage sources are not to be connected
  in parallel

62
parallel current sources

• when connected in parallel, a group of current
  sources can be treated as one current source
  whose equivalent current
• ? all source currents
• unequal current sources are not to be connected
  in series

63
PROBLEM SOLVING METHOD
va
vb
_
_
node3
node1
node2


Rb
Ra
ib
ia

ivs

vc

ic
vis
vs
Rc
is
_
_
_
node4
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Homework for next Tuesday

• See website for Assignment 1
• show all work for any credit
• Dorf Svoboda, pp. 16-18, pp. 44-45
• Complete HW 1 for next Tuesday
• Complete Lab HW Assignment 1 for Next Tuesday
  Individually!