ELE1110C Basic Circuit Theory

1
ELE1110C Basic Circuit Theory

• Dr. Michael Chang
• mchang _at_ ie.cuhk.edu.hk
• Room 811
• Marking scheme 30 mid-term, 70 final exam
• Newsgroup
• cuhk.ie.1110C
• IEG1810 Lab instructions
• record all your results in a A4-size log book
• Hand in your log book to the tutors immediately
  after each lab session

2
Textbooks for IEG1810 (lab) and ELE1110C/D

• Text
• Student Manual for the Art of Electronics by
  Hayes and Horowitz (1st ed., Cambridge University
  Press)
• Use by this course and the lab (IEG1810)
• Only use the first 12 chapters
• Reference
• The Art of Electronics by Horowitz and Hill (2nd
  ed., Cambridge University Press)
• more detailed explanation

3
Lab safety briefing and registration

• Lab period
• Starting after the 3rd week
• Every Mon/Tues/Wed/Thurs
• This Monday/Tuesday/Wednesday/Thursday
• 330-415pm in room 1009 (ERB)
• Briefing registration, first come first serve

4
About this course

• Devices
• resistor, capacitor, diode, transistor and their
  properties
• Transmission line
• Simple circuits
• Follower, amplifier, mirror, long-tail pair
• Complex circuits
• Operational amplifiers, logic gates, CMOS
• Principle in system building
• Negative feedback

5
Electron and Current

• Electron
• -ve charged particle
• 1 coulomb 6 x 108 electrons
• Current
• the rate of flow of electrons
• Unit Ampere
• 1 Ampere flow of 1 coulomb of charge per second
• Water analogy
• Electron is like water molecule
• Current is like the rate of flow of water

6
Potential difference

• Electron is a -ve charged particle, attracted by
  something that is positive
• The more ve side is said to have a ve potential
  or higher potential
• The difference in potential between two points is
  called potential difference or voltage

ve potential
Potential difference
e
-ve potential
7
Direction of Current

• By convention, current flows in opposite
  direction of electrons
• Electron flows from ve (lower) potential to ve
  (higher) potential
• current flows from higher potential to lower
  potential

ve potential
current
e
-ve potential
8
How to measure the potential difference (unit in
volt)?

• The larger the potential difference, the stronger
  the attraction, and the faster the electron can
  move (higher energy)

ve
energy
volt
e
9
How to measure the potential difference?

• The total energy gained is proportional to the
  potential difference and the number of charges
• Energy (Joule) potential difference (Volt)
  charge
• Definition of 1 volt
• If the energy produced by 1 Coulomb of charge is
  1 Joule, then the potential difference is 1 Volt
• Unit Volt ( Joule / Coulomb )

10
Energy and Power

• Energy measures the total amount of work done
• Power measures how fast the energy is dissipated
• power energy / time
• E.g. 1 J of energy is dissipated in 2
  seconds,
• power 0.5 J/s 0.5 Watt
• Power energy / time
• potential difference charge / time
• Power V I

11
Two-terminals device

• X can be a resistor, capacitor, or inductor

X
Current out
Current in
volt
12
Voltage and Current

• Apply a voltage V to a two-terminals device, 3
  possible outcomes
• Large current flow X is a conductor
• Small current flow X is a semiconductor
• No current flow X is an insulator
• The ratio of voltage and current is a measure of
  the conductivity of the device
• If X is a resistor, then the ratio is called
  resistance
• If X is a capacitor/inductor, then it is called
  reactance
• If X is unspecified, then it is called impedance

13
Voltage and Current

• Resistance R V/I (unit Ohm)
• Or V IR

I
R
V
This end denotes the reference point of the
voltage measurement
14

• Linear device
• Double the voltage, double the current
• The slope of V vs I is constant
• Non-linear device
• V vs I is not a straight line

V
V
R
I
I
Linear
Non-linear
15

• Linear devices
• Resistor (R)
• impedance is independent of frequency
• Inductor (L) and capacitor C
• Impedance is frequency-dependent
• Non-linear devices
• Anything other than RLC (resistor/inductor/capacit
  or)
• e.g. diode, transistor

16
Water analogy
17
VIR (Ohms law)

• R V / I
• 10V /0.1 A
• 100 W

? W
I 0.1A
10V
This end denotes the reference point of the
voltage measurement
18
100 watt light bulb

• Power 100 W (each second dissipates 100 J)
• Power VI, V240V, therefore I
  100/240 A
• Resistance of the light bulb V/I 576 W
• To calculate power
• Power VI, but since VIR, therefore
• Power

19
Circuit analysis

• Kirchhoffs voltage law (KVL)
• Sum of voltage drops around any closed loop is
  zero

100 W
S V 0
10V
20
What if the voltage drop around a loop is NOT
zero?

• This would mean that a single point can have a
  potential difference !!
• Which is impossible
• Therefore the voltage drop around a loop MUST be
  zero

21
Kirchhoffs current law (KCL)

• sum of the currents flowing into a point equals
  the sum of the currents flowing out
• Conservation of charge, what goes in, must come
  out

or
22
Examples

• Resistors in series, what is R?
• Answer
• R R1 R2

R1
R2
R ?

23
Proof

• By KCL, current through the resistors are the
  same
• V V1 V2 IR1 IR2 I ( R1 R2 )
• therefore R R1 R2

R1
R2
R ?
I

V1
V2
V
24
Resistors in parallel

• Answer

R1
I1
R ?
I

I
R2
I2
V
V
(remember this formula!)
25
Proof

R1
I1
R ?
I

I
R2
I2
V
V
26
Common tricks

• Two equal resistors in parallel

R
?
R
27
Common tricks

• Three equal resistors in parallel

R
?
28
Common tricks

• Two very unequal resistors in parallel
• differ by a factor of 10 at least

10 R
R

R
29
Common tricks

• Two very unequal resistors in series
• ignore the smaller resistor
• error is again less than 10
• OK
• the tolerance of resistors is 5 - 10 anyway

R
10 R
10 R

30
Linear circuit

• What is VOUT?

5W
2W
2W

VOUT
VOUT
10W
10/3 W
VIN
2V
31
Linear circuit

• VOUT varies linearly with VIN
• Plot VOUT vs VIN, you get a straight line
• Resistive (and also capacitive and inductive)
  circuits are known as linear circuit because the
  output varies linearly with the input (energy
  source)
• If we have more than one energy source, linear
  circuits have the very useful property that the
  output is equal to the sum of all contributions
  from the energy sources
• Known as the Principle of Superposition

32
What is VA?

• If you can solve this problem, you can solve any
  linear circuit problems
• Many different approaches, choose one you like
• By KCL
• By KVL
• By the principle of superposition

a
5W
2W
VA
10W
2V
5V
33
By KCL
I1

• Apply KCL to node a

I3
a
I2
5W
2W
VA
10W
2V
5V
34
You can define the direction of current in any
way you like
I1

I3
a
I2
5W
2W
VA
10W
2V
5V
35
By KVL

• I1 -0.25A, I20.25A, VAI2102.5V

5W
2W
VA
10W
2V
5V
I2
I1
36
Principle of Superposition

• Output sum of contributions from all energy
  sources

5W
2W
10W
2V
5V
5W
5W
2W
2W

10W
10W
2V
5V
37
Principle of Superposition

• Contribution due to 2V source alone
• V1 1.25V

5W
2W
2W

V1
V1
10W
10/3 W
2V
2V
38
Principle of Superposition

• Contribution due to 5V source alone
• V2 1.25V
• VA sum of contributions from 2 voltage sources
• V1 V2
• 2.5V

5W
2W
V2
10W
5V
39
Principle of Superposition

• Add an a.c. signal source VIN to the circuit,
  what is VA?

5W
2W
VA
10W
2V
5V

VIN
5W
2W
5W
2W


10W
10W
2V
5V

VIN
VA 2.5V 0.625VIN
40
Linear system

• Linear circuit is an example of linear system
• Linear system is the most important model used in
  engineering
• What is a model?
• A model is a simplification of the real world
• We make this simplification (or approximation)
  because the real world is too complicated
• e.g. we model a complicated circuit by a number
  of simpler circuits
• Divide and conquer

41
Linear system

• You make this linear assumption everyday
• The sound you hear,
• and the light you see,
• are the sum of contributions from individual
  energy sources

speaker
speaker
Total intensity sums of individual contributions
42
Non-linear system

• Example
• The plot of VOUT vs VIN is non-linear
• For a non-linear system
• The output is NOT equal to the sum of
  contributions from individual energy sources
• Cant simplify the it by the principle of
  superposition
• How to solve it?

43
Small signal model

• Assume the change of VIN (dVIN)is small, so that
  the non-linear part can be approximated by a
  straight line
• dVOUT k dVIN

VOUT
dVOUT
Approximately linear Slope k
VIN
dVIN
44
Large signal model

• Difficult to solve in general
• e.g weather forecast involves non-linear
  equations
• Can be solved by computer simulation (using
  supercomputers!)

45
Thevenin model

• Given an unknown two-port device
• How to model the device?

?
46
Thevenin model

• Any linear circuit can be simplified to a voltage
  source VThev and an impedance RThev

?
RThev

VThev
47
A proof of Thevenin theorem

• VA sum of contributions from all energy sources

The unknown device
R
48
Apply superposition to the circuit
R
R
. . .
R
49

• But if R is changed, we have to repeat the
  tedious calculation
• A simpler model for calculation
• Model the output by adding a current source

50

• The unknown circuit still sees the same current I

I
I
51
What is an ideal voltage source ?

• A source that has constant voltage, but zero
  impedance
• V vs I plot
• The slope (V/I) is zero
• Increase in current, no change in voltage
• zero impedance
• (or RdV/dI 0)

V
I
52
What is an ideal current source?

• A source that gives out constant current
• V vs I plot
• The slope (V/I) is infinite
• dV/dI infinite
• Or a tiny increase in current causes infinite
  change in voltage
• Behaves as if it has infinite impedance

V
I
53
Divide the complex circuit into many simpler
circuits

VA a1V1 . . . anVn an1I
I
VA
I
. . .
V1
I
54
To simplify
VA a1V1 . . . anVn an1I

• If I0, VA a1V1 . . . anVn
• But VA is the same as the open circuit voltage
  VOC !!
• Since VA a1V1 . . . anVn VOC
• Therefore VA VOC an1I

I0
VAVOC
55

• What is an1?
• All resistors can be combined into one
• So that VA (due to I) an1I RThev I
• VA a1V1 . . . anVn an1I
• VOC RThevI

RThev
VA
I
I
VA
56

• VA VOC RThevI
• RThev Output Impedance

I
RThev
VA
VOC
57
Given a black box, how to find VThev and RThev ?
VThev VOC RThev VOC / ISC (VOC open
circuit voltage) (ISC short circuit current)
RThev
VThev
58
A more practical way to find RThev

• Short circuit current may damage your circuit
• Use a resistor to measure RThev

I
RThev
V
VOC
59
Thevenin model by calculation

• VOC 20/7 V
• ISC 2A
• Therefore RThev 10/7 W

5W
2W
ISC
VOC
5V
2V
60
Use of Thevenin model

• Output is connected to a 10W resistor, what is
  VA?

5W
10/7 W
2W
VA
VA
10W
10W
5V
2V
20/7 V
61
Advantage of using Thevenin model

• VA can be found easily for different load
• VA

10/7 W
VA
R
20/7 V
62
Voltage divider

• Important concepts
• input impedance
• output impedance
• loading effect
• First, what is VOUT?
• VOUT
• VIN / 2 15V

VOUT
63
Voltage divider

• Is this a good voltage divider?
• A good voltage divider should
• behave like an ideal voltage source
• Provides constant voltage
• Is this the case?

64
Loading effect

• If the load has infinite resistance, then VOUT
  15V
• If the divider is connected to a 10k load, what
  is VOUT?

65

• VOUT VIN (5k/15k) VIN / 3
• 10V (a big drop from 15V!)

66

• The divider is droopy
• output voltage is load-dependent, it is not a
  good voltage divider
• Ideal divider should be stiff
• output voltage is constant over a wide range of
  load
• How to build a better divider?

67
Thevenin model
(30v)
(10k)
(5K)
15V
(10k)
68
Applying the Thevenin model

• If RLoad 10k, then VOUT VThev (10k/15k)
  10V

69
Output impedance RThev

• RThev is the resistance as seen by the outside
  world
• the output impedance of the circuit
• a very important parameter

complex circuit

External world sees a simple resistor
70
Fast way to calculate RTh

• remove all energy sources
• Replace voltage source by short circuit
• Replace current source by open circuit
• RTh is the resistance viewed from the output

71
Output impedance

• Which circuit has a stiffer output voltage?
• Which circuit consumes more power?

100k
1k
100k
1k
72
A general model for any linear circuit

• Input impedance and output impedance
• Input impedance VIN / IIN
• Output impedance RThev

IOUT
IIN
Linear Circuit
VIN
VOUT
73
Example

• The model
• A black box approach
• Only interested in the input and output of a
  device

CD player
Amplifier
Speaker
R3
R1
R2
R4
CD player Amplifier
Speaker
74
CD to amplifier

• Output signal of CD player
• V1, measured in voltage
• Input signal to amplifier
• V2, measured in voltage

R1
R2
V2
V1
CD player Amplifier
75

• Maximum signal transfer
• Want V2 to be as large as possible
• Ideally
• R1 0
• R2 infinite

76
Amplifier to speaker
R3

• Maximum power transfer
• Speaker needs energy to produce loud sound
• Power V4I

I
R4
V3
V4
Amplifier Speaker
77

• If R4 infinite
• Large V4, but I0 !
• Power 0
• If R4 0
• Large I, but V40 !
• Power 0
• So R4 cannot be too large nor too small
• For maximum power transfer, R3 R4
• Try to prove this yourself

78
Five voltage dividers, which one is the best?
79
An imperfect voltmeter

• The voltmeter is not perfect because it has
  finite input impedance RIN
• From the following measurements, what is RIN?

80
Input impedance of analog voltmeter

• If R100k, the measured voltage is only 8.05V
• 2V is dropped across 50k, 8V is dropped across
  RIN,
• therefore RIN 50k4 200k

81

• In general, if the load RLOAD, then
• This is important !!
• Good voltage divider should have RThev much
  smaller than RLOAD
• But how small?

82
The 10X design rule

• Input impedance of B should be at least 10 times
  larger than the output impedance of A

83
10X design rule

• If ROUT,A is 10 times smaller than RIN,B
• then B receives at least 90 of the signal, the
  loss is less than 10, acceptable
• More importantly, the input impedance of B is
  large enough to be treated as if it is an open
  circuit
• Simpler calculation, no need to need the circuit
  of B

ROUT,A
Circuit A
Input impedance of circuit B RIN,B gt 10
ROUT,A
84
Colour code of resistor
85

• Why it is important to make sure circuit B can be
  treated as if it is an open circuit?
• Because this is the assumption we always make in
  circuit analysis !
• that the output is an open circuit

Vout
Vin
86
VOUT of stage B?

• What is the output impedance of circuit A?
• What is the input impedance of circuit B?

87
VOUT of stage B?

• Input impedance of B is 10 times the output
  impedance of A
• Loading effect is negligible (10X rule)
• VOUT VIN
• Accurate result
• VOUT VIN
• The error is less than 10 , OK

88
The use of 10X rule

• 10X rule follows the most important design
  principle in engineering
• Divider and conquer
• Divide a complex circuit into many simple
  circuits

89
A complex circuit sum of simple circuits
90
Lab equipments

• Function generator
• generate common waveforms for testing purposes
• sine wave
• square wave
• triangular (ramp) wave
• you can vary the signals amplitude and frequency
• Oscilloscope
• Enable us to see the periodic signal

91
Oscilloscopes control

• Vertical control
• use to magnify the displayed signal

Magnify the displayed signal
One vertical division
92
Input socket for channel 1
Vertical control for channel 1 e..g 20mV/DIV if
signal amplitude2.5 DIV amplitude 50mV
Select which channel to display
Adjust the position of the displayed signal
93

• Coupling
• dc
• GND
• ac
• GND (this means Ground level)
• display the ground (0V) signal (appear as a
  straight line on the scope)
• for beginner always set vertical to GND first
  so as to find the position of 0V

94
Coupling

• DC display the voltage in absolute unit
• AC only display the signal, dc voltage is
  removed (filtered)

10V
AC only displays this part
DC displays the signal from 0V
0V
95
Horizontal control

• Changing the time/DIV allows you to expand or to
  compress the signal waveform horizontally

96
Example

• Vertical 5 V/DIV, horizontal 20ms/DIV
• signal amplitude 12.4V (peak-to-peak)
• period 60mS
• freq 1/period
• 16.6 Hz

97
Trigger

• trigger is a sequence of short sync pulses that
  tell the scope to start displaying the signal
• if the timing signal is not correct, you see a
  mess

trigger pulse
You see a mess
Irregular triggering points Scope start sweeping
at wrong time
98
Triggering

• Correct trigger gives a clean display

Sync pulse
Clean display What you see is the overlapping of
many sweep lines
correct trigger start horizontal sweep at the
right time
99
Triggering

• The control panel

100
Where to get the triggering signal?

• External trigger
• e.g. if the sine wave is generated by a function
  generator, then you can use the SYNC output of
  the function generator as the triggering signal
• The best way to get the triggering signal
• Internal trigger
• Extracted from the input signal based on
• slope
• level
• Less clean, but often used because reliable
  external trigger cannot be found

101
Triggering

• slope
• -ve slope

trigger
trigger
102
Triggering

• (higher level)
• -ve (lower level)

Trigger on ve level and ve slope
Trigger on -ve level and -ve slope
103
Triggering

• Trigger coupling
• dc trigger based on the dc signal
• ac trigger based on the ac signal ( i.e. only
  use the varying part) the usual choice
• LF REJ derived the trigger signal from the input
  signal after the low frequency (LF) part is
  removed
• HF REJ derived the trigger signal from the input
  signal after the high frequency (HF) part is
  removed