department of information engineering1 ele1110c basic circuit theory dr. michael chang –mchang @...

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


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


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


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


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


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


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


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


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 )


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


Two-terminals device

• X can be a resistor, capacitor, or inductor

volt

Current in Current outX


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


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


• 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


• 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


Water analogy


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


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


Circuit analysis

• Kirchhoff’s voltage law (KVL)

– Sum of voltage drops around any closed loop is zero

10V

100

V = 0


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


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


Examples

• Resistors in series, what is R?

• Answer

– R = R1 + R2

=R1 R2 R ?


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


Resistors in parallel

• Answer

–

V

I =

R1

R2

R ?I1

I2

21

21

RRRR

R

I

V

(remember this formula!)


Proof

•

V

I =

R1

R2

R ?I1

I2

21

21

21

111RRR

RV

RV

RV

III

21

21

RRRR

R

I

V


Common tricks

• Two equal resistors in parallel

R

R = ?

2R

Rtotal


Common tricks

• Three equal resistors in parallel

R

= ?

3total

RR


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


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~


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


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


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


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


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


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


Principle of Superposition

• Output = sum of contributions from all energy sources

2V

2

10

5

2V 5V

2

10

5

5V

2

10

5+



• Contribution due to 2V source alone

– V1 = 1.25V

2V

2

10 V1

5=

2V

2

10/3 V1



• 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



• 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


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


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


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


Small signal model

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

– VOUT = k VIN

VIN

VOUT

VIN

VOUT Approximately linearSlope = k

2OUT INV aV


Large signal model

• Difficult to solve in general

– e.g weather forecast involves non-linear equations

• Can be solved by computer simulation (using supercomputers!)


Thevenin model

• Given an unknown two-port device

– How to model the device?

?


Thevenin model

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

=VThev

RThev?


A proof of Thevenin theorem

• VA = sum of contributions from all energy sources

VA

R

The unknown device


Apply superposition to the circuit

+ . . . +

R

R R

VA


• 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


• The unknown circuit still sees the same current I

VAR VA

I I


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 R=dV/dI = 0)

V

I


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


Divide the complex circuit into many simpler circuits

•

+ . . . +

I

VA = a1V1 + . . . + anVn+ an+1I

IV1

I

VA


To simplify

• If I=0, VA= a1V1 + . . . + anVn

– But VA is the same as the open circuit voltage VOC !!

• Since VA= a1V1 + . . . + anVn = VOC

• Therefore VA= VOC + an+1I

VA = a1V1 + . . . + anVn+ an+1I

I=0

VA=VOC


• What is an+1?

– All resistors can be combined into one

• So that VA (due to I) = an+1I = RThev * I

• VA = a1V1 + . . . + anVn+ an+1I

= VOC + RThev*I

I IRThevVAVA


• VA= VOC + RThev*I

• RThev = Output Impedance

I

VOC

RThevVA


Given a black box, how to find VThev and RThev ?

VThev

RThev

VThev = VOC

RThev = VOC / ISC

(VOC= open circuit voltage)(ISC = short circuit current)


A more practical way to find RThev

• Short circuit current may damage your circuit

• Use a resistor to measure RThev

•

I

OC

Thev

V VR

I

VOC

RThev

V


Thevenin model by calculation

• VOC = 20/7 V

• ISC = 2A

• Therefore RThev = 10/7

2V 5V

2ISC

5VOC


Use of Thevenin model

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

•

20/7 V

10VA10

VA

2V 5V

2 5

107

10 20* 2.5

10 7aV V V


Advantage of using Thevenin model

• VA can be found easily for different load

– VA =

RVA

20/7 V

2010 7

RR


Voltage divider

• Important concepts

– input impedance

– output impedance

– loading effect

• First, what is VOUT?

– VOUT =

= VIN / 2 = 15V

VOUT10

10 10 IN

kV

k k


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?


Loading effect

• If the load has infinite resistance, then VOUT = 15V

• If the divider is connected to a 10k load, what is VOUT?


• VOUT = VIN (5k/15k) = VIN / 3

= 10V (a big drop from 15V!)


• 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?


Thevenin model

(30v)

(10k)

(10k)

(5K)

15V


Applying the Thevenin model

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


Output impedance RThev

• RThev is the resistance as seen by the outside world

– the output impedance of the circuit

– a very important parameter

=complexcircuit

External world seesa simple resistor


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


Output impedance

• Which circuit has a stiffer output voltage?

• Which circuit consumes more power?

=1k

=1k =100k

=100k


A general model for any linear circuit

• Input impedance and output impedance

– Input impedance = VIN / IIN

– Output impedance = RThev

Linear CircuitVIN

IIN

VOUT

IOUT


Example

• The model

– A black box approach

– Only interested in the input and output of a device

CD player Amplifier Speaker

AC AC

CD player Amplifier Speaker

R1

R2

R3

R4


CD to amplifier

• Output signal of CD player

– V1, measured in voltage

• Input signal to amplifier

– V2, measured in voltage

AC AC

R1

R2V1 V2

CD player Amplifier


•

• Maximum signal transfer

– Want V2 to be as large as possible

• Ideally

– R1 = 0

– R2 = infinite

22 1

1 2

RV V

R R


Amplifier to speaker

• Maximum power transfer

– Speaker needs energy to produce loud sound

– Power = V4*I

AC

R3

R4V3 V4

I

Amplifier Speaker


• If R4 = infinite

– Large V4, but I=0 !

– Power = 0

• If R4 = 0

– Large I, but V4=0 !

– Power =0

• So R4 cannot be too large nor too small

• For maximum power transfer, R3 = R4

– Try to prove this yourself


Five voltage dividers, which one is the best?


An imperfect voltmeter

• The voltmeter is not perfect because it has finite input impedance RIN

• From the following measurements, what is RIN?


Input impedance of analog voltmeter

• If R=100k, the measured voltage is only 8.05V

– 2V is dropped across 50k, 8V is dropped across RIN,

– therefore RIN = 50k*4 = 200k


• In general, if the load = RLOAD, then

• This is important !!

– Good voltage divider should have RThev much smaller than RLOAD

– But how small?

Thev

LOADOUT

Thev LOAD

RV V

R R


The 10X design rule

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


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

Circuit A

Input impedanceof circuit B RIN,B > 10 ROUT,A

ROUT,A


Colour code of resistor


• 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

Vin Vout


VOUT of stage B?

• What is the output impedance of circuit A?

• What is the input impedance of circuit B?


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

44

10

1 12 2


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


A complex circuit = sum of simple circuits


Lab equipments

• Function generator

– generate common waveforms for testing purposes

• sine wave

• square wave

• triangular (ramp) wave

• you can vary the signal’s amplitude and frequency

• Oscilloscope

– Enable us to see the periodic signal


Oscilloscope’s control

• Vertical control

– use to magnify the displayed signal

Magnify the displayed signal

One vertical division


Vertical control for channel 1e..g 20mV/DIVif signal amplitude=2.5 DIVamplitude = 50mV

Select which channel to display

Adjust the positionof the displayed signal

Input socket for channel 1


• 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


Coupling

• DC : display the voltage in absolute unit

• AC: only display the signal, dc voltage is removed (filtered)

0V

10V

AC only displays this part

DC displays the signal from 0V


Horizontal control

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


Example

• Vertical: 5 V/DIV, horizontal: 20ms/DIV

– signal amplitude ~ 12.4V (peak-to-peak)

– period ~ 60mS

– freq ~ 1/period

~ 16.6 Hz


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

Irregular triggering pointsScope start sweeping at wrong time

You see a mess

trigger pulse


Triggering

• Correct trigger gives a clean display

correct triggerstart horizontal sweepat the right time

Clean displayWhat you see is the overlapping of many sweep lines

Sync pulse


Triggering

• The control panel


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


Triggering

• + slope

• -ve slope

trigger

trigger


Triggering

• + (higher level)

• -ve (lower level)

Trigger on +ve leveland +ve slope

Trigger on -ve leveland -ve slope


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

department of information engineering1 ele1110c basic circuit theory dr. michael chang –mchang @...

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