1 Department of Information Engineering ELE1110C Basic Circuit Theory • Dr. Michael Chang – mchang @ 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
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Department of Information Engineering1 ELE1110C Basic Circuit Theory Dr. Michael Chang –mchang @ ie.cuhk.edu.hk –Room 811 Marking scheme:30% mid-term,
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1Department of Information Engineering
ELE1110C Basic Circuit Theory
• Dr. Michael Chang
– mchang @ 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
2Department of Information Engineering
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
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Lab safety briefing and registration
• Lab period :
– Starting after the 3rd week
– Every Mon/Tues/Wed/Thurs
• This Monday/Tuesday/Wednesday/Thursday
– 3:30-4:15pm in room 1009 (ERB)
– Briefing + registration, first come first serve
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About this course
• Devices– resistor, capacitor, diode, transistor and their
• 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
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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
-ve potential
Potential difference
e
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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
-ve potential
e
current
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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)
volt
+ve
e
energy
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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 )
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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
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Two-terminals device
• X can be a resistor, capacitor, or inductor
volt
Current in Current outX
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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
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Voltage and Current
• Resistance R = V/I (unit Ohm)
• Or V = IR
V
I
This end denotes the reference point of the voltage measurement
R
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• 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
I
V
LinearI
V
Non-linear
R
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• 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/capacitor)
– e.g. diode, transistor
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Water analogy
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V=IR (Ohm’s law)
• R = V / I
= 10V /0.1 A
= 100 ?
10V
I =0.1A
This end denotes the reference point of the voltage measurement
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100 watt light bulb
• Power = 100 W (each second dissipates 100 J)
• Power = VI, V=240V, therefore I = 100/240 A
• Resistance of the light bulb = V/I = 576
• To calculate power
– Power = VI, but since V=IR, therefore
– Power =2
2 VVI I R
R
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Circuit analysis
• Kirchhoff’s voltage law (KVL)
– Sum of voltage drops around any closed loop is zero
10V
100
V = 0
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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
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Kirchhoff’s 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
321 III
1I
2I
3I
or
0321 III
1I
2I
3I
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Examples
• Resistors in series, what is R?
• Answer
– R = R1 + R2
=R1 R2 R ?
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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
V
V1 V2
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Resistors in parallel
• Answer
–
V
I =
R1
R2
R ?I1
I2
21
21
RRRR
R
I
V
(remember this formula!)
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Proof
•
V
I =
R1
R2
R ?I1
I2
21
21
21
111RRR
RV
RV
RV
III
21
21
RRRR
R
I
V
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Common tricks
• Two equal resistors in parallel
R
R = ?
2R
Rtotal
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Common tricks
• Three equal resistors in parallel
R
= ?
3total
RR
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Common tricks
• Two very unequal resistors in parallel
– differ by a factor of 10 at least
R
10 RR
%101110
1010 2
error
RRR
RRtotal
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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~
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Linear circuit
• What is VOUT?
–
VIN
2
10 VOUT
5=
2V
2
10/3 VOUT
10 / 3 5
2 10 / 3 8OUT IN INV V V
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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
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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
2V 5V
2
10
a
VA
5
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By KCL
• Apply KCL to node ‘a’
2V 5V
2
10
a
VA
5
I1 I3
I2
1 2 3
2 5 0
2 5 102.5
A A A
A
I I I
V V V
V V
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You can define the direction of current in any way you like
2V 5V
2
10
a
VA
5
1 2 3 0
2 50
2 5 102.5
A A A
A
I I I
V V V
V V
I1 I3
I2
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By KVL
•
• I1 = -0.25A, I2=0.25A, VA=I2*10=2.5V
I1I2
2V 5V
2
10VA
5
1 1 2
2 1 2
2 2 5( ) 5 0
5 5( ) 10 0
I I I
I I I
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Principle of Superposition
• Output = sum of contributions from all energy sources
2V
2
10
5
2V 5V
2
10
5
5V
2
10
5+
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Principle of Superposition
• Contribution due to 2V source alone
– V1 = 1.25V
2V
2
10 V1
5=
2V
2
10/3 V1
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Principle of Superposition
• Contribution due to 5V source alone
– V2 = 1.25V
• VA = sum of contributions from 2 voltage sources
= V1 + V2
= 2.5V
5V
2
10V2
5
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Principle of Superposition
• Add an a.c. signal source VIN to the circuit, what is VA?
2V 5V
2
10VA
5
~
2V 5V
2
10
5 2
10
5
~
VIN
VIN
+=
VA = 2.5V + 0.625VIN
40Department of Information Engineering
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
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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
speakerspeaker
Total intensity = sums of individual contributions
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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
– Can’t simplify the it by the principle of superposition
• How to solve it?
2OUT INV aV
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Small signal model
• Assume the change of VIN (VIN)is small, so that the non-linear part can be approximated by a straight line