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程序代写案例-EE310
时间：2022-03-24
EE310 – Project 1
Dr Jackman Lin
jackman.lin@auckland.ac.nz
Electeng310
• This is an analogue design project
• You will evaluate, simulate, design, construct, and validate a potential solution to a client’s problem
• This course takes several different concepts (some learned, some not) and blends them into a practical design
• Analogue circuit design
• Amplifiers
• Transistor operation
• Oscillators
• Pulse width modulation
• Wireless communication
• Signal processing
• Filters
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 2
Learning Objectives
• By the end of the project, the junior engineers will be able to solve a fresh engineering problem systematically
• Confidently assess project requirements, then make and justify design decisions
• Develop confidence in using simulation tools to design analogue circuits
• Understand limitations posed by real life electronic components
• Learn to construct and verify designs using prototyping tools such as
• Can confidently build and validate a PCB design
• By the end of the project, junior engineers will gain experience in writing a professional report
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 3
Timeline
• Eight weeks (excluding semester break) to finish this project
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 4
Week Week beginning Monday Tuesday Wednesday Thursday Friday
1 28-Feb 10-12 INTRO 8-10 PROJECT 1
2 7-Mar 10-12Part 1 start Lab 1 Lab 2
8-10
Lab 3
3 17-Mar 10-12 Lab 4 Lab 5 8-10Lab 6
4 21-Mar 10-12 Part 2 startDesign/Simulation 1 Lab 7 Lab 8
8-10
Lab 9
5 28-Mar 10-12 Lab 10 Lab 11Test 1
8-10
Lab 12
6 4-Apr 10-12PCB Design
Lab 13
PCB Start
Lab 14
Design/Simulation 2
8-10
Lab 15
PCB DUE/test
7 11-Apr 10-12 Good Friday
Break
18-Apr Easter Uni Holiday
25-Apr ANZAC Day
8 2-May 10-12 REPORT PRESENTATION PRESENTATION
9 9-May Test 2
Design Meetings and Labs
• Two design meetings a week
• Class guidance
• Ask questions
• The more you ask, the easier your
design process will be
• Three labs a week
• Where you gain experience with
simulation tools and prototyping
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 5
Required Software
• LTSpice
• https://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html
• Altium
• Access through FlexIT
• https://www.auckland.ac.nz/en/students/my-tools/flex-it.html
• Student license
• https://www.altium.com/education/student-licenses
• Need UoA email address
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 6
Useful Resources
• What components are available?
• https://www.auckland.ac.nz/en/engineering/about-the-faculty/electrical-computer-and-software-
engineering/about/resources.html
• Click on the sharepoint site link
• ECSE Altium Library (for PCBs)
• Click on above link and look at the Altium files
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 7
Assessment Criteria
Marking – Project 1
• Design/Simulations – 20%
• Part 1 - 10% (March 22)
• Part 2 – 10% (April 7)
• Test (20%)
• Test 1 – 10% (April 1)
• Test 2 – 10% (May 10)
• Report – 15% (May 4)
• Presentation/Interview – 10% (May 5-6)
• Total: 65%
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 9
Revision
Previous related courses
• ELECTENG101
• Ohms law
• Resistors, capacitors, inductors
• ELECTENG291
• Superposition
• Kirchoffs voltage and current laws
• ELECTENG292
• Opamp theory
• Other courses (?)
• Transistors
• Diodes
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 11
Ohm’s Law
• The current through a resistor () is equal to the potential voltage across it () and the value of the resistance ()
=
= /
RVcc IR
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 12
Current through a capacitor
• The current through a capacitor () is equal to the value of the capacitance () and the rate of change of the voltage across
the capacitor (
)
• Rate of change of voltage over time is also known as a slew rate
=
• If
is high (like a perfect square wave rising edge), then will approach infinity.
• Undesirable as high currents will blow up the capacitor
• Do not connect a capacitor by itself in series with signals with high slew rates
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 13
iC CvC
Voltage across an inductor
• The voltage across an inductor () is equal to the value of the capacitance () and the rate of change of the current across
the inductor (
)
=
• If
is high, then will approach infinity.
• Undesirable as high voltages will cause corona effects
• Do not pump high currents at high slew rates into an inductor
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 14
LiL
Superposition Theorem
• In any linear circuit with multiple sources, the voltage and
currents can be solved by superposition
• Short out any voltage sources
• Open circuit any current sources
• Revise what happens if circuit components include capacitors
and inductors
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 15
R1 R3
R2V1
I1 I2 I3
V2
R1 R3
R2V1
I1 I2 I3
R1 R3
R2
I1 I2 I3
V2
Kirchoff’sLaws
• Kirchoff’s voltage law
• All voltages in a loop must add up to zero
• − − = 0
• − − = 0
• Kirchoff’s current law
• All the current flowing into a node must equal to the
current flowing out of the node
• = +
• Note that current flows have directions
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 16
R1 R3
R2Vcc
I1 I2 I3
Diodes and LEDs
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 17
• Diodes have a voltage drop across them when conducting
• Usually set to 0.7V if ideal
= 5 − ≈ 4.
= 4.
• LEDs are driven from current
• Ranging from 1 – 100’s of mA
• Can be driven from almost any voltage, as long as the resistance R is set appropriately
R15V
Vf IdV1
Op-amps - Overview
• An op-amp is and integrated circuit (IC) that is typically used to amplify
small signals into larger ones for use.
• In theory, an ideal op-amp has:
• Infinite open loop voltage gain ()
• If + − − > 0, =
• If has not saturated (i.e. not at Vcc or 0 V) then = = ∞ =0
• Zero common-mode voltage gain
• If + = −, = 0
• Infinite input impedance
• − = + = 0
• Zero output impedance
• No limit on
• Infinite slew rate
• Can output infinite
• Infinite band-width
• Operates over an infinite frequency range.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 18
v+v-
Vcc
-Vcc vout
i-i+ -+ ioutvd
Op-amps – Virtual Earth Principle
• Only applies if a negative feedback impedance ( for this example) is connected in the op-amp circuit
• Op-amp operates in linear mode
• An ideal op-amp has infinite input impedance, so − = + = 0
• An ideal op-amp has infinite open loop gain,
• if the op-amp has not saturated, then − = + = 0 (for this example).
• If the VEP is valid, then the voltage at − = +
• VEP is valid when:
• − < <
• There is a feedback impedance on the negative terminal
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 19
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+
R2
vin
iR1 iR2vd
Op-amps – inverting amplifier
• Virtual earth principle applies
= 0
+ = 0 = −
• Currents through the resistors and
= − − =
= − − =
• Assuming an ideal op-amp:
− = 0
• Using Kirchoff’s current law, all the currents into the node at must add up to
0, so at the − node:
+ + − = 0
= −
= −
= −
−
=
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 20
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+
R2
vin
iR1 iR2vd
Op-amps – non-inverting amplifier
• VEP applies if − < < (output voltage is within operating rails)
− = + =
=
= (−)/
− = 0
= + −
−
=
− =
− 1 =
= 1 +
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 21
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+
R2
vin
iR1 iR2vd
System Overview
Project Outline
• As Junior Engineers, HELLA has tasked you with designing a speed detection system so that a following vehicle can gauge
the speed of the vehicle in front of it
• The data is encoded using the rear brake lights of the front vehicle (transmitter)
• The data is decoded using a sensor placed in the headlights of the rear vehicle (receiver)
• Your task is to design a proof of concept
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 23
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Systematic Design Approach
• What is the nature of the problem?
• You need to identify methods of solving the problem
• Take client requirements into account
• Range
• More!
• Cost (bulk pricing)
• Less!
• Reliability
• How do you define reliability?
• Will it work in adverse conditions?
• Does it meet standards required for vehicles?
• Response time
• Accuracy
• How do you define accuracy?
• Input = output (frequency)
• Low THD
• High SNR
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 24
Systematic Design Approach
• What is the nature of the problem?
• The data is encoded in a light signal
• How will we simplify the light signal (i.e. not use a car brake light)?
• How will we encode a message in the light signal?
• How will the range be affected by the light signal?
• How will the light signal be powered?
• What external factors can impact the range of the light, and how will your system deal with these factors.
• Can’t answer all of these questions right now but will need to be able to by the end of this course.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 25
System Block Diagram
• Need a method to encode the input voltage (Vin) (representing
speed) as a signal to transmit via brake lights
• Vin is a signal with whose frequency represents the
speed of the front vehicle
• Methods for transmission?
• The data is encoded using the rear brake lights of the
front vehicle (transmitter)
• Sending data through light
• The data is decoded using a sensor placed in the
headlights of the rear vehicle (receiver)
• Receiving data through a photodiode
• Once the data has been received
• Need to design a receiver to decode the data received
• What signal is being received?
• What should Vout be?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 26
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Approach
• Choose a starting point
• Transmitter or receiver?
• Identify methods of communicating the information for proof of
concept
• Use a single LED instead of a brake light to transmit data
• Identify known constraints:
• Input voltage signal from car to represent speed
• Battery voltage of cars to power the transmitter
• What needs to be done?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 27
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Transmitting data
• Directly connect the input signal onto the brake light?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 28
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Transmitting Data - Modulation
• Amplitude Modulation (AM)
• Data is encoded in the amplitude of the light
• As the input decreases, the intensity of the light also
decreases
• Less range at low speeds
• Can use lower modulation frequencies than FM techniques
to transfer information
• Potentially lower cost
• Frequency Modulation (FM)
• Data is encoded in the frequency of the light
• Does not depend on the intensity of the LED
• Low amplitudes are part of the information being sent
and received
• Needs higher modulation frequencies to transfer detailed
information
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 29
Pulse Width Modulation – Representing a Sinusoid
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 30
• Pulse Width Modulation (PWM) Data is encoded in the Duty Cycle of the light
• PWM can be used to send frequency information by manipulating the duty cycle of the brake light
• Representing an analogue signal in the digital domain
• A sinusoid can be represented by a PWM whose duty cycle represents its current amplitude
• = sin +
• can be any voltage between 1-3 V
• is 1 V
• sine is between 1 – 2.5 kHz
t(s)
V
Vin
Vtri
VPWM
Vtri,upper
Vtri,lower
Voffset A
Transmitting Data - Modulation
• All are suitable for this project
• Some are better than others
• Ease of implementation is based on the input signal
• In this year’s project, input is a 1 – 2.5 kHz frequency sinusoid
• 1 kHz represents slow speed (0km/h)
• 2.5 kHz represents fast speed (150 km/h)
• Input is frequency based so it makes sense to use
• FM
• PWM
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 31
Suggested approach
• Open ended project – you may choose what approach you want to take.
• Meet client requirements
• Range, cost, reliability, etc
• You will be taught how to design the PWM technique
• Concepts taught in this approach are universal
• You are expected to know how to design a PWM transmitter/receiver even an alternative approach is chosen
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 32
Transmitter Design
Transmitter Block Diagram
• Where to start?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 34
Input Signal
Conditioner PWM Generator Amplifier
Vsupply
Vinput
Vcon PWM
Pulse Width Modulation
Pulse Width Modulation – Duty cycle
• A method of representing a signal using a square wave
• The duty cycle of the square wave represents the amplitude to the input signal
• Duty cycle
• The amount of time that a signal is on compared to the total period of the
signal
• A 50% duty cycle ( = 0.5) square wave will be on for ½ of the period, and
then off for the second half.
• Average value of this signal:
= 1�−// = 1
�
−
4
4
+�
−
−
0 +�
4
0
= 1
−
4
4
= 1 4 − −4 = 1 ∗ 2 = 12
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 36
A
D = 0.5
ton
toff/2
-T/2 T/2V
-T/4 T/4
toff/2
T
Pulse Width Modulation – Duty cycle
• A 75% duty cycle ( = 0.75) square wave will be on for ¾ (from -3T/8 to 3T/8) of
the period, and then off for the last ¼ (-T/2 to -3T/8, and 3T/8 to T/2) period.
• If A = 5V, then a 75% duty cycle square wave represents a DC signal at 3.75 V
• Average value of this signal:
= 1�−// = 1
�
−
3
8
3
8
+�
−
−
3
8 0 +�
3
8
0
= 1
−
3
8
3
8
= 1 8 − −8 = 1 ∗ 8 = 34
• PWM is very useful to control the brightness of an LED
• 50% duty cycle results in approximately half brightness
• 75% duty cycle is approximately 75% brightness
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 37
A
D = 0.75
ton
toff/2
-T/2 T/2V
-3T/8 3T/8
toff/2 T
Pulse Width Modulation – Duty cycle example
• Use generic Duty cycle (D)
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 38
Pulse Width Modulation - Power
• Pulse Width Modulation decreases amplitude of the signal with respect to the input signal
• Low duty cycle = low brightness = low range
• Determines the power of the signal
• Assume that there is a voltage across a resistor
= 1
�
−/
/ ()
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 39
t(s)
A
D = 0.5
D = 0.75
T
ton
toff
ton
toff-T/4 T/4
-3T/8 3T/8
A
-T/2 T/2V
Pulse Width Modulation - Power
= 1
�
−/
/ ()
• Let be some PWM signal with a duty cycle
• For −
< <
, =
• Otherwise = 0
= 1
�
−/
/
= 1
−
=
2 − −2
=
• Power output of the transmitted signal is directly proportional to the duty
cycle of the PWM!
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 40
t(s)
A
D = 0.5
D = 0.75
T
ton
toff
ton
toff-T/4 T/4
-3T/8 3T/8
A
-T/2 T/2V
Pulse Width Modulation - Generation
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 41
• PWM signals can be generated by using a comparator circuit
• Reference signal is a triangle wave
• Control signal can be any waveform
• When the two signal are equal, the output of the comparator will switch states
t(s)
A
D = 0.5
ton
toff
-T/4 T/4A
-T/2 T/2
V
Vcon = A/2
Vtriv+v-
Vcc
-Vcc vout
i-i+ -+ ioutvd
Pulse Width Modulation – Representing a Sinusoid
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 42
• A sinusoid can be represented by a PWM whose duty cycle represents its current amplitude
• = sin +
• can be any voltage between 1-3 V
• is 1 V
• is between 1 – 2.5 kHz
• If the triangle wave is required to modulate the PWM signal how does:
• The frequency of the triangle wave impact the PWM signal?
• The amplitude of the triangle wave impact the PWM signal?
t(s)
V
Vin
Vtri
VPWM
Vtri,upper
Vtri,lower
Voffset A
Pulse Width Modulation - Summary
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 43
• The brightness of the LED can be controlled by changing the duty cycle of the control signal
• PWM can be used to send a sinusoidal signal by modulating (encoding) it on a higher frequency carrier
• The power of the LED is directly proportional to the duty cycle of the control signal
• PWMs can be generated by using a comparator
• Triangle wave carrier
• Reference signal (AC or DC)
Triangle Wave Generator
Theory
Triangle Wave Generator
• So now we know that in order to generate a PWM signal, a triangle wave is needed.
• Need to set the frequency of the triangle wave
• Need to set the amplitude of the triangle wave
• Vin covers a certain range
• Triangle wave needs to cover this range
• How do we generate a triangle wave?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 45
Op-amps - Integrator
• If = 1
• ∫ = ∫
• = +
• If = −1
• ∫ = ∫−
• = − +
• If the input is a square wave, then the output will be a triangle wave
• How can we achieve a square wave input?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 46
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+vin
iR1 iC1vd
C1
vC1
Op-amps - Comparators
• If +> − then the output =
• If +< − then the output = −
• As an example, set − = 0
• Let + be a triangle wave
• What will the output look like?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 47
v+v-
Vcc
-Vcc vout
i-i+ -+ ioutvd
Triangle Wave Generator – Circuit
• Basic structure of a triangle wave generator
• Three resistors (R1, R2, R3), one capacitor (C1), two op-amps (U1, U2)
• To make the circuit easy to derive:
• Set the opamp to run off ± (+ = −−)
• Set the positive terminal of U1 to 0V
• Set the reference signal of the non-inverting comparator to 0V
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 48
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
Triangle Wave Generator – Integrator Derivation
• How can we begin to analyze this circuit?
• Revise the basic operation of op-amps
• Virtual earth principle
• When presented with a new circuit, break the circuit into understandable
blocks
• Integrator
• Comparator
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 49
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
Triangle Wave Generator – Integrator Derivation
• Virtual earth principle
• Input impedance
• Gain
• =
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 50
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
Triangle Wave Generator – Integrator Derivation
• State 1: Vsq is high
• Let = +
• = −−
• −= ,− = −−
•
= −−−
• State 2: Vsq is low
• Let = −
• = −−−
• −= ,− = −−−
•
= −−
• This shows us that the slope of the triangle wave can be determined, but
there is still no way to set the time (), and thus the frequency of the
triangle wave.
• This also means we don’t have a definite way of setting the amplitude of the
triangle wave yet.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 51
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Triangle Wave Generator – Expected waveforms
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 52
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
Triangle Wave Generator – Inverting comparator with hysteresis
• Add a positive feedback resistor (R3)
• This provides a hysteresis band for the comparator
• Set the triangle wave amplitude
• Noise rejection
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 53
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Triangle Wave Generator – Inverting comparator with hysteresis
• Focus on must the comparator
• Use the superposition theorem
• 1: Set = 0
= +
• 2: Set = 0
= +
• Solve
= + + +
= + − + +
= + −
• We also know that = + when is just above 0V
• Call this 0+
• = − when is just below 0V
• Call this 0−
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 54
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
-
+R2
R3
VsqV+U2V-V2Vtri
Triangle Wave Generator – Inverting comparator with hysteresis
= + −
Scenario 1:
• We want the square wave to transition from + to −
• Therefore = 0−
• = ,
• = +
= 0 − (+)
, = −+
• Scenario 2:
• We want the square wave to transition from − to +
• Therefore = 0+
• = ,
• = −+
= 0 − (−+)
, = +
• The hysteresis band for a 0V reference, dual rail comparator can be defined as:
, − , = (+ + −)
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 55
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
-
+R2
R3
VsqV+U2V-V2Vtri
Triangle Wave Generator – Inverting comparator with hysteresis
• This means that the amplitude of the Triangle wave is known:
= (,−,)
=
= , − ,
= , − ,
= 2+
+
=
= 1
=
4
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 56
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
dt
dVtri
V(R2/R3)
-V(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with 4 Vp-p , centered at 0V (no offset). Using ideal op-amps
running off ±12 V rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 57
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 58
• Step 1: Draw out the waveforms
• Step 2: Calculate parameters
• , = −4 = −
• , = 4 =
• 2 = 12
3
• =
•
= 4
50−6
=
= 000
• 750 − =
• = 750−6
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 59
• Step 3: Make some decisions
= 750 −
• Set = Ω, = 750
• Set = Ω, = Ω
• Step 4: Sanity check
=
4
= 4 ∗ ∗ ∗ 750 − = 000
• Step 5: Double Sanity check
• LTSPICE Simulation
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 60
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 61
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Summary
• Basic configuration and derivation of an ideal triangle wave generator is given
• Op-amps are assumed to be ideal
• Double sided rails for simplicity
• Design example given for a 2 kHz, 4 V symmetric triangle wave
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 62
Triangle wave generator – where to in labs?
1. Follow the assignment sheet
2. Set up an Ltspice simulation using ideal components to confirm the theory
1. Make decisions on frequency
2. Voltage swing
3. Modify the simulation by using a single sided voltage rail
1. Decide on your voltages
2. Do you need to derive any equations?
4. Modify the simulation by replacing components with real life counterparts
1. Op-amps
2. Comparators
3. E12 value resistors and capacitors
5. Fill in the assignment sheet
6. Ask questions in labs
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 63
Dr Jackman Lin
jackman.lin@auckland.ac.nz
Electeng310
• This is an analogue design project
• You will evaluate, simulate, design, construct, and validate a potential solution to a client’s problem
• This course takes several different concepts (some learned, some not) and blends them into a practical design
• Analogue circuit design
• Amplifiers
• Transistor operation
• Oscillators
• Pulse width modulation
• Wireless communication
• Signal processing
• Filters
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 2
Learning Objectives
• By the end of the project, the junior engineers will be able to solve a fresh engineering problem systematically
• Confidently assess project requirements, then make and justify design decisions
• Develop confidence in using simulation tools to design analogue circuits
• Understand limitations posed by real life electronic components
• Learn to construct and verify designs using prototyping tools such as
• Can confidently build and validate a PCB design
• By the end of the project, junior engineers will gain experience in writing a professional report
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 3
Timeline
• Eight weeks (excluding semester break) to finish this project
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 4
Week Week beginning Monday Tuesday Wednesday Thursday Friday
1 28-Feb 10-12 INTRO 8-10 PROJECT 1
2 7-Mar 10-12Part 1 start Lab 1 Lab 2
8-10
Lab 3
3 17-Mar 10-12 Lab 4 Lab 5 8-10Lab 6
4 21-Mar 10-12 Part 2 startDesign/Simulation 1 Lab 7 Lab 8
8-10
Lab 9
5 28-Mar 10-12 Lab 10 Lab 11Test 1
8-10
Lab 12
6 4-Apr 10-12PCB Design
Lab 13
PCB Start
Lab 14
Design/Simulation 2
8-10
Lab 15
PCB DUE/test
7 11-Apr 10-12 Good Friday
Break
18-Apr Easter Uni Holiday
25-Apr ANZAC Day
8 2-May 10-12 REPORT PRESENTATION PRESENTATION
9 9-May Test 2
Design Meetings and Labs
• Two design meetings a week
• Class guidance
• Ask questions
• The more you ask, the easier your
design process will be
• Three labs a week
• Where you gain experience with
simulation tools and prototyping
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 5
Required Software
• LTSpice
• https://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html
• Altium
• Access through FlexIT
• https://www.auckland.ac.nz/en/students/my-tools/flex-it.html
• Student license
• https://www.altium.com/education/student-licenses
• Need UoA email address
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 6
Useful Resources
• What components are available?
• https://www.auckland.ac.nz/en/engineering/about-the-faculty/electrical-computer-and-software-
engineering/about/resources.html
• Click on the sharepoint site link
• ECSE Altium Library (for PCBs)
• Click on above link and look at the Altium files
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 7
Assessment Criteria
Marking – Project 1
• Design/Simulations – 20%
• Part 1 - 10% (March 22)
• Part 2 – 10% (April 7)
• Test (20%)
• Test 1 – 10% (April 1)
• Test 2 – 10% (May 10)
• Report – 15% (May 4)
• Presentation/Interview – 10% (May 5-6)
• Total: 65%
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 9
Revision
Previous related courses
• ELECTENG101
• Ohms law
• Resistors, capacitors, inductors
• ELECTENG291
• Superposition
• Kirchoffs voltage and current laws
• ELECTENG292
• Opamp theory
• Other courses (?)
• Transistors
• Diodes
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 11
Ohm’s Law
• The current through a resistor () is equal to the potential voltage across it () and the value of the resistance ()
=
= /
RVcc IR
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 12
Current through a capacitor
• The current through a capacitor () is equal to the value of the capacitance () and the rate of change of the voltage across
the capacitor (
)
• Rate of change of voltage over time is also known as a slew rate
=
• If
is high (like a perfect square wave rising edge), then will approach infinity.
• Undesirable as high currents will blow up the capacitor
• Do not connect a capacitor by itself in series with signals with high slew rates
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 13
iC CvC
Voltage across an inductor
• The voltage across an inductor () is equal to the value of the capacitance () and the rate of change of the current across
the inductor (
)
=
• If
is high, then will approach infinity.
• Undesirable as high voltages will cause corona effects
• Do not pump high currents at high slew rates into an inductor
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 14
LiL
Superposition Theorem
• In any linear circuit with multiple sources, the voltage and
currents can be solved by superposition
• Short out any voltage sources
• Open circuit any current sources
• Revise what happens if circuit components include capacitors
and inductors
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 15
R1 R3
R2V1
I1 I2 I3
V2
R1 R3
R2V1
I1 I2 I3
R1 R3
R2
I1 I2 I3
V2
Kirchoff’sLaws
• Kirchoff’s voltage law
• All voltages in a loop must add up to zero
• − − = 0
• − − = 0
• Kirchoff’s current law
• All the current flowing into a node must equal to the
current flowing out of the node
• = +
• Note that current flows have directions
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 16
R1 R3
R2Vcc
I1 I2 I3
Diodes and LEDs
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 17
• Diodes have a voltage drop across them when conducting
• Usually set to 0.7V if ideal
= 5 − ≈ 4.
= 4.
• LEDs are driven from current
• Ranging from 1 – 100’s of mA
• Can be driven from almost any voltage, as long as the resistance R is set appropriately
R15V
Vf IdV1
Op-amps - Overview
• An op-amp is and integrated circuit (IC) that is typically used to amplify
small signals into larger ones for use.
• In theory, an ideal op-amp has:
• Infinite open loop voltage gain ()
• If + − − > 0, =
• If has not saturated (i.e. not at Vcc or 0 V) then = = ∞ =0
• Zero common-mode voltage gain
• If + = −, = 0
• Infinite input impedance
• − = + = 0
• Zero output impedance
• No limit on
• Infinite slew rate
• Can output infinite
• Infinite band-width
• Operates over an infinite frequency range.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 18
v+v-
Vcc
-Vcc vout
i-i+ -+ ioutvd
Op-amps – Virtual Earth Principle
• Only applies if a negative feedback impedance ( for this example) is connected in the op-amp circuit
• Op-amp operates in linear mode
• An ideal op-amp has infinite input impedance, so − = + = 0
• An ideal op-amp has infinite open loop gain,
• if the op-amp has not saturated, then − = + = 0 (for this example).
• If the VEP is valid, then the voltage at − = +
• VEP is valid when:
• − < <
• There is a feedback impedance on the negative terminal
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 19
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+
R2
vin
iR1 iR2vd
Op-amps – inverting amplifier
• Virtual earth principle applies
= 0
+ = 0 = −
• Currents through the resistors and
= − − =
= − − =
• Assuming an ideal op-amp:
− = 0
• Using Kirchoff’s current law, all the currents into the node at must add up to
0, so at the − node:
+ + − = 0
= −
= −
= −
−
=
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 20
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+
R2
vin
iR1 iR2vd
Op-amps – non-inverting amplifier
• VEP applies if − < < (output voltage is within operating rails)
− = + =
=
= (−)/
− = 0
= + −
−
=
− =
− 1 =
= 1 +
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 21
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+
R2
vin
iR1 iR2vd
System Overview
Project Outline
• As Junior Engineers, HELLA has tasked you with designing a speed detection system so that a following vehicle can gauge
the speed of the vehicle in front of it
• The data is encoded using the rear brake lights of the front vehicle (transmitter)
• The data is decoded using a sensor placed in the headlights of the rear vehicle (receiver)
• Your task is to design a proof of concept
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 23
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Systematic Design Approach
• What is the nature of the problem?
• You need to identify methods of solving the problem
• Take client requirements into account
• Range
• More!
• Cost (bulk pricing)
• Less!
• Reliability
• How do you define reliability?
• Will it work in adverse conditions?
• Does it meet standards required for vehicles?
• Response time
• Accuracy
• How do you define accuracy?
• Input = output (frequency)
• Low THD
• High SNR
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 24
Systematic Design Approach
• What is the nature of the problem?
• The data is encoded in a light signal
• How will we simplify the light signal (i.e. not use a car brake light)?
• How will we encode a message in the light signal?
• How will the range be affected by the light signal?
• How will the light signal be powered?
• What external factors can impact the range of the light, and how will your system deal with these factors.
• Can’t answer all of these questions right now but will need to be able to by the end of this course.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 25
System Block Diagram
• Need a method to encode the input voltage (Vin) (representing
speed) as a signal to transmit via brake lights
• Vin is a signal with whose frequency represents the
speed of the front vehicle
• Methods for transmission?
• The data is encoded using the rear brake lights of the
front vehicle (transmitter)
• Sending data through light
• The data is decoded using a sensor placed in the
headlights of the rear vehicle (receiver)
• Receiving data through a photodiode
• Once the data has been received
• Need to design a receiver to decode the data received
• What signal is being received?
• What should Vout be?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 26
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Approach
• Choose a starting point
• Transmitter or receiver?
• Identify methods of communicating the information for proof of
concept
• Use a single LED instead of a brake light to transmit data
• Identify known constraints:
• Input voltage signal from car to represent speed
• Battery voltage of cars to power the transmitter
• What needs to be done?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 27
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Transmitting data
• Directly connect the input signal onto the brake light?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 28
Transmitter Receiver
Vsupply
Vin Vout
Vsupply
Transmitting Data - Modulation
• Amplitude Modulation (AM)
• Data is encoded in the amplitude of the light
• As the input decreases, the intensity of the light also
decreases
• Less range at low speeds
• Can use lower modulation frequencies than FM techniques
to transfer information
• Potentially lower cost
• Frequency Modulation (FM)
• Data is encoded in the frequency of the light
• Does not depend on the intensity of the LED
• Low amplitudes are part of the information being sent
and received
• Needs higher modulation frequencies to transfer detailed
information
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 29
Pulse Width Modulation – Representing a Sinusoid
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 30
• Pulse Width Modulation (PWM) Data is encoded in the Duty Cycle of the light
• PWM can be used to send frequency information by manipulating the duty cycle of the brake light
• Representing an analogue signal in the digital domain
• A sinusoid can be represented by a PWM whose duty cycle represents its current amplitude
• = sin +
• can be any voltage between 1-3 V
• is 1 V
• sine is between 1 – 2.5 kHz
t(s)
V
Vin
Vtri
VPWM
Vtri,upper
Vtri,lower
Voffset A
Transmitting Data - Modulation
• All are suitable for this project
• Some are better than others
• Ease of implementation is based on the input signal
• In this year’s project, input is a 1 – 2.5 kHz frequency sinusoid
• 1 kHz represents slow speed (0km/h)
• 2.5 kHz represents fast speed (150 km/h)
• Input is frequency based so it makes sense to use
• FM
• PWM
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 31
Suggested approach
• Open ended project – you may choose what approach you want to take.
• Meet client requirements
• Range, cost, reliability, etc
• You will be taught how to design the PWM technique
• Concepts taught in this approach are universal
• You are expected to know how to design a PWM transmitter/receiver even an alternative approach is chosen
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 32
Transmitter Design
Transmitter Block Diagram
• Where to start?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 34
Input Signal
Conditioner PWM Generator Amplifier
Vsupply
Vinput
Vcon PWM
Pulse Width Modulation
Pulse Width Modulation – Duty cycle
• A method of representing a signal using a square wave
• The duty cycle of the square wave represents the amplitude to the input signal
• Duty cycle
• The amount of time that a signal is on compared to the total period of the
signal
• A 50% duty cycle ( = 0.5) square wave will be on for ½ of the period, and
then off for the second half.
• Average value of this signal:
= 1�−// = 1
�
−
4
4
+�
−
−
0 +�
4
0
= 1
−
4
4
= 1 4 − −4 = 1 ∗ 2 = 12
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 36
A
D = 0.5
ton
toff/2
-T/2 T/2V
-T/4 T/4
toff/2
T
Pulse Width Modulation – Duty cycle
• A 75% duty cycle ( = 0.75) square wave will be on for ¾ (from -3T/8 to 3T/8) of
the period, and then off for the last ¼ (-T/2 to -3T/8, and 3T/8 to T/2) period.
• If A = 5V, then a 75% duty cycle square wave represents a DC signal at 3.75 V
• Average value of this signal:
= 1�−// = 1
�
−
3
8
3
8
+�
−
−
3
8 0 +�
3
8
0
= 1
−
3
8
3
8
= 1 8 − −8 = 1 ∗ 8 = 34
• PWM is very useful to control the brightness of an LED
• 50% duty cycle results in approximately half brightness
• 75% duty cycle is approximately 75% brightness
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 37
A
D = 0.75
ton
toff/2
-T/2 T/2V
-3T/8 3T/8
toff/2 T
Pulse Width Modulation – Duty cycle example
• Use generic Duty cycle (D)
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 38
Pulse Width Modulation - Power
• Pulse Width Modulation decreases amplitude of the signal with respect to the input signal
• Low duty cycle = low brightness = low range
• Determines the power of the signal
• Assume that there is a voltage across a resistor
= 1
�
−/
/ ()
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 39
t(s)
A
D = 0.5
D = 0.75
T
ton
toff
ton
toff-T/4 T/4
-3T/8 3T/8
A
-T/2 T/2V
Pulse Width Modulation - Power
= 1
�
−/
/ ()
• Let be some PWM signal with a duty cycle
• For −
< <
, =
• Otherwise = 0
= 1
�
−/
/
= 1
−
=
2 − −2
=
• Power output of the transmitted signal is directly proportional to the duty
cycle of the PWM!
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 40
t(s)
A
D = 0.5
D = 0.75
T
ton
toff
ton
toff-T/4 T/4
-3T/8 3T/8
A
-T/2 T/2V
Pulse Width Modulation - Generation
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 41
• PWM signals can be generated by using a comparator circuit
• Reference signal is a triangle wave
• Control signal can be any waveform
• When the two signal are equal, the output of the comparator will switch states
t(s)
A
D = 0.5
ton
toff
-T/4 T/4A
-T/2 T/2
V
Vcon = A/2
Vtriv+v-
Vcc
-Vcc vout
i-i+ -+ ioutvd
Pulse Width Modulation – Representing a Sinusoid
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 42
• A sinusoid can be represented by a PWM whose duty cycle represents its current amplitude
• = sin +
• can be any voltage between 1-3 V
• is 1 V
• is between 1 – 2.5 kHz
• If the triangle wave is required to modulate the PWM signal how does:
• The frequency of the triangle wave impact the PWM signal?
• The amplitude of the triangle wave impact the PWM signal?
t(s)
V
Vin
Vtri
VPWM
Vtri,upper
Vtri,lower
Voffset A
Pulse Width Modulation - Summary
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 43
• The brightness of the LED can be controlled by changing the duty cycle of the control signal
• PWM can be used to send a sinusoidal signal by modulating (encoding) it on a higher frequency carrier
• The power of the LED is directly proportional to the duty cycle of the control signal
• PWMs can be generated by using a comparator
• Triangle wave carrier
• Reference signal (AC or DC)
Triangle Wave Generator
Theory
Triangle Wave Generator
• So now we know that in order to generate a PWM signal, a triangle wave is needed.
• Need to set the frequency of the triangle wave
• Need to set the amplitude of the triangle wave
• Vin covers a certain range
• Triangle wave needs to cover this range
• How do we generate a triangle wave?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 45
Op-amps - Integrator
• If = 1
• ∫ = ∫
• = +
• If = −1
• ∫ = ∫−
• = − +
• If the input is a square wave, then the output will be a triangle wave
• How can we achieve a square wave input?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 46
Vcc
-Vcc vout
i-i+ -+ ioutR1 v- v+vin
iR1 iC1vd
C1
vC1
Op-amps - Comparators
• If +> − then the output =
• If +< − then the output = −
• As an example, set − = 0
• Let + be a triangle wave
• What will the output look like?
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 47
v+v-
Vcc
-Vcc vout
i-i+ -+ ioutvd
Triangle Wave Generator – Circuit
• Basic structure of a triangle wave generator
• Three resistors (R1, R2, R3), one capacitor (C1), two op-amps (U1, U2)
• To make the circuit easy to derive:
• Set the opamp to run off ± (+ = −−)
• Set the positive terminal of U1 to 0V
• Set the reference signal of the non-inverting comparator to 0V
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 48
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
Triangle Wave Generator – Integrator Derivation
• How can we begin to analyze this circuit?
• Revise the basic operation of op-amps
• Virtual earth principle
• When presented with a new circuit, break the circuit into understandable
blocks
• Integrator
• Comparator
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 49
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
Triangle Wave Generator – Integrator Derivation
• Virtual earth principle
• Input impedance
• Gain
• =
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 50
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
Triangle Wave Generator – Integrator Derivation
• State 1: Vsq is high
• Let = +
• = −−
• −= ,− = −−
•
= −−−
• State 2: Vsq is low
• Let = −
• = −−−
• −= ,− = −−−
•
= −−
• This shows us that the slope of the triangle wave can be determined, but
there is still no way to set the time (), and thus the frequency of the
triangle wave.
• This also means we don’t have a definite way of setting the amplitude of the
triangle wave yet.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 51
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Triangle Wave Generator – Expected waveforms
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 52
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
Triangle Wave Generator – Inverting comparator with hysteresis
• Add a positive feedback resistor (R3)
• This provides a hysteresis band for the comparator
• Set the triangle wave amplitude
• Noise rejection
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 53
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Triangle Wave Generator – Inverting comparator with hysteresis
• Focus on must the comparator
• Use the superposition theorem
• 1: Set = 0
= +
• 2: Set = 0
= +
• Solve
= + + +
= + − + +
= + −
• We also know that = + when is just above 0V
• Call this 0+
• = − when is just below 0V
• Call this 0−
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 54
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
-
+R2
R3
VsqV+U2V-V2Vtri
Triangle Wave Generator – Inverting comparator with hysteresis
= + −
Scenario 1:
• We want the square wave to transition from + to −
• Therefore = 0−
• = ,
• = +
= 0 − (+)
, = −+
• Scenario 2:
• We want the square wave to transition from − to +
• Therefore = 0+
• = ,
• = −+
= 0 − (−+)
, = +
• The hysteresis band for a 0V reference, dual rail comparator can be defined as:
, − , = (+ + −)
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 55
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
-
+R2
R3
VsqV+U2V-V2Vtri
Triangle Wave Generator – Inverting comparator with hysteresis
• This means that the amplitude of the Triangle wave is known:
= (,−,)
=
= , − ,
= , − ,
= 2+
+
=
= 1
=
4
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 56
Vsq
t(s)
+V
V
Vtri
-V
Vth,low
Vth,high
-V
+V
-Vsq/(R1C1)
Vsq/(R1C1)
dt
dVtri
V(R2/R3)
-V(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with 4 Vp-p , centered at 0V (no offset). Using ideal op-amps
running off ±12 V rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 57
R1
C1
-
+
-
+R2
R3
Vtri
VsqV+V+ U1 U2V- V-
IR1
IC1
V2
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 58
• Step 1: Draw out the waveforms
• Step 2: Calculate parameters
• , = −4 = −
• , = 4 =
• 2 = 12
3
• =
•
= 4
50−6
=
= 000
• 750 − =
• = 750−6
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 59
• Step 3: Make some decisions
= 750 −
• Set = Ω, = 750
• Set = Ω, = Ω
• Step 4: Sanity check
=
4
= 4 ∗ ∗ ∗ 750 − = 000
• Step 5: Double Sanity check
• LTSPICE Simulation
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 60
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Design Example
• You are tasked to design a 2 kHz symmetric triangle wave with a 4 Vp-p amplitude. Using ideal op-amps running off ±12 V
rails, choose the appropriate values for R1, R2, R3, and C1.
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 61
t(s)
+12
V
Vtri
-12
Vth,low
Vth,high
-12
+12
-12/(R1C1)
12/(R1C1)
dt = 1/(2*2 kHz) = 250 us
dVtri = 4V 12(R2/R3)
-12(R2/R3)
Triangle Wave Generator – Summary
• Basic configuration and derivation of an ideal triangle wave generator is given
• Op-amps are assumed to be ideal
• Double sided rails for simplicity
• Design example given for a 2 kHz, 4 V symmetric triangle wave
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 62
Triangle wave generator – where to in labs?
1. Follow the assignment sheet
2. Set up an Ltspice simulation using ideal components to confirm the theory
1. Make decisions on frequency
2. Voltage swing
3. Modify the simulation by using a single sided voltage rail
1. Decide on your voltages
2. Do you need to derive any equations?
4. Modify the simulation by replacing components with real life counterparts
1. Op-amps
2. Comparators
3. E12 value resistors and capacitors
5. Fill in the assignment sheet
6. Ask questions in labs
Jackman Lin, Department of Electrical, Computer, Software Engineering (2022) 63
