ENGG1015 1st Semester, 2012 - Home | Department of ... Theory Characterize a circuit by:...
Transcript of ENGG1015 1st Semester, 2012 - Home | Department of ... Theory Characterize a circuit by:...
Circuits
ENGG1015
1st Semester, 2012
Dr. Kenneth Wong
Department of Electrical and
Electronic Engineering
http://www.eee.hku.hk/~engg1015
How to connect to outside world?
1st semester, 2012 2
Input Output
Process
3 times?
Ball Rolls
Past Sensor Turns on
Laser
ENGG1015 - Dr. K. Wong
Lab#3
Lab#4
Input Stage: ADC
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Physical
World
Physical
World
Digital
Systems
ADC DAC
3, 5, 6, 7… 7.2, 6.1, 4.8, 3.14…
Process Output Input
ADC
Picking the ADC/resistor values
Assume:
High temp rt = rmin = Rref / 3
Low temp rt = rmax = Rref
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Rref
Vcc
0
rt
ADC vout
vout Vccrmin
Rref rminVcc
Rref3
Rref Rref
3
Vcc
4
vout Vccrmax
Rref rmaxVcc
Rref
Rref RrefVcc
2
Hi
Temp
Low
Temp
Set ADC threshold at
3Vcc
8
Hi
Temp
Low
Temp
“0”
“1”
Quick Check (revisit)
If we want the threshold at , which of
these statements is the best? 1. rmin = Rref / 3; rmax = Rref
2. rmin = Rref / 3; rmax = 2Rref
3. rmin = Rref / 3; rmax = 3Rref
4. rmin = Rref / 3; rmax = 4Rref
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2
ccV
vout
Rref
Vcc
0
rt
vout rt
Rref rtVcc
Quick Check (revisit)
If we want the threshold at , which of
these statements is the best? 1. rmin = Rref / 3; rmax = Rref
2. rmin = Rref / 3; rmax = 2Rref
3. rmin = Rref / 3; rmax = 3Rref
4. rmin = Rref / 3; rmax = 4Rref
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2
ccV
vout rt
Rref rtVcc
8
3;
2|max|
ccmidout
ccout
Vv
Vv
24
11;
3
2|max|
ccmidout
ccout
Vv
Vv
2;
4
3|max|
ccmidout
ccout
Vv
Vv
40
21;
5
4|max|
ccmidout
ccout
Vv
Vv
|min4
ccout
Vv
Circuit Theory
Characterize a circuit by:
Conservation laws
• govern currents and voltages in general
Constituent equations
• describe behavior of individual components
We will study only circuits with static behavior
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Rules Governing Flow
Rule 1: Currents flow in loops.
Example: flow of electrical current through a lamp
When the switch is closed, electrical current flows
through the loop.
The same amount of current flows into the lamp
(top path) and out of the lamp (bottom path).
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Rule 2: Like the waterflow, the flow of electrical
current (charged particles) is incompressible.
Example: water flow through an intersection
What comes in must go out.
Here
Kirchoff's Current Law (KCL): the sum of the
currents into a node is zero.
Rules Governing Flow
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1 2 3i i i
Rules Governing Flow
In electrical circuits, we represent current flow by
arrows on lines representing connections (wires).
The dot represents a “node” which represents a
connection of two or more segments.
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1 2 3i i i
Nodes Nodes are represented in circuit diagrams by
lines that connect circuit components.
The following circuit has three components, each
represented with a box.
There are two nodes, each represented by a dot.
The net current into or out of each of these nodes
is zero. Therefore
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1 2 3 0i i i
Rules Governing Flow
Voltages accumulate in loops.
Example: the series combination of two 1.5 V
batteries supplies 3 V.
Kirchoff's Voltage Law (KVL): the sum of the
voltages around a closed loop is zero.
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2nd Representation: Node Voltages Node voltages represent the voltage between each node in a
circuit and an arbitrarily selected ground node.
Node voltages and component voltages are different but
equivalent representations of voltage.
component voltages represent voltages across components.
node voltages represent voltages in a circuit.
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Resistor, Voltage and Current Sources Each component is represented by a relationship
between the voltage across the component and
the current through the component.
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Node-Voltage-and-Component-Current (NVCC) Method
Combining KCL, node voltages, and component equations leads to
the NVCC method for solving circuits:
Assign node voltage variables to every node except ground
(whose voltage is arbitrarily taken as zero).
Assign component current variables to every component in the
circuit.
Write one constitutive relation for each component in terms of the
component current variable and the component voltage, which is
the difference between the node voltages at its terminals.
Express KCL at each node except ground in terms of the
component currents.
Solve the resulting equations.
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Analyzing Simple Circuits Analyzing simple circuits is straightforward.
The voltage source determines the voltage across the resistor,
v = 1V, so the current through the resistor is i = v/R = 1/1 = 1A.
The current source determines the current through the resistor,
i =1A, so the voltage across the resistor is v = iR = 1 × 1 = 1V.
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What is the current through the resistor
below?
1. 1A
2. 2A
3. 0A
4. None of the above
Quick Check
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What is the current through the resistor
below?
The voltage source forces the voltage across the
resistor to be 1V. Therefore, the current through
the resistor is 1V/1 = 1A.
Does the current source do anything?
Quick Check
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Does the current source do anything?
Since the voltage across the resistor equals that
across the voltage source, the current flows through
the resistor is 1A, which equals the current source.
So, the voltage source provides zero current!
Quick Check
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Common Patterns
Few common patterns that facilitate design and
analysis are:
Resistors in series
Resistors in parallel
Voltage dividers
Current dividers
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Resistors in Series The series combination of two resistors is equivalent to a
single resistor whose resistance is the sum of the two
original resistances.
The resistance of a series combination is always larger than
either of the original resistances.
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1 2sR R R 1 2v R i R i sv R i
Resistors in Parallel The parallel combination of two resistors is equivalent to a
single resistor whose conductance (1/resistance) is the sum
of the two original conductances.
The resistance of a parallel combination is always smaller
than either of the original resistances. 1st semester, 2012 ENGG1015 - Dr. K. Wong 22
1 2
1 2 1 21 21 1
1 2 1 2 1 2
1 1 1 1||p
p R R
R R R RR R R
R R R R R R R
Quick Check
What is the equivalent resistance of the
following circuit?
1. 1
2. 2
3. 0.5
4. 3
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Voltage Divider
Resistors in series act as voltage dividers.
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1 2
11 1
1 2
22 2
1 2
VI
R R
RV R I V
R R
RV R I V
R R
Current Divider
Resistors in parallel act as current dividers.
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1 2
1 2 1 2 21
1 1 1 1 2 1 2
1 2 1 2 12
2 2 2 1 2 1 2
||
|| 1
|| 1
V R R I
R R R R RVI I I I
R R R R R R R
R R R R RVI I I I
R R R R R R R
High Level Design - Output
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Process Output Input Temp. Light
Digitally controlled thermo warning light
ADC DAC
0, 1, 2, 3 … 3, 2, 1, 0…
Connecting to the Output Specifications (given):
• “1” 9V Light on
• “0” 0V Light off
Do not confuse between logical “1” with “1 volt”, and logical “0” with “0 volt”.
Logical values “0” and “1” should not be used to drive output directly
These internal discrete values (e.g. 18.9, 23, etc) must be translated into suitable analog output values • Suitable V, I, R
A digital-analog convertor (DAC) converts discrete input values into analog output voltage values
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Final System Block Diagram
Strictly speaking a digital processing system
Can be made far more complex by more elaborated
ADC, DAC and digital processing
Can be made far simpler by reducing the boundary
between sub-systems. 1st semester, 2012 ENGG1015 - Dr. K. Wong 29
Rref
Vcc
0
rt
ADC invert DAC vout
Simple version – boundary breaking
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Rref
Vcc
0
rt
ADC invert DAC vADC
Temp. rt vADC procin procout vout
High low ~0 “0” “1” ~Vcc (9 V)
Lo high ~Vcc “1” “0” 0
Can we bypass all intermediate stages?
Simple Version – Single Stage
Caveat: • resistance is not really 0 or infinite
• Make sure enough current is available through lamp when rt is large
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Vcc
rt
vout
rlamp
Hi
Temp
Low
Temp
vout Vccrlamp
rt rlamp
rt 0vout Vcc
rt vout 0
Loading Inserting (or changing the value of) a component
alters all of the voltages and currents in a circuit.
Consider identical lamps connected in series
across a battery.
Because the same current passes through both
lamps, they are equally bright.
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Quick Check
What happens if we add the third lamp?
Closing the switch will make:
1. lamp 1 brighter
2. lamp 2 dimmer
3. 1. and 2.
4. lamps 1, 2, & 3 equally bright
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Loading
Q: What's different about a circuit?
A: A new component generally alters the currents
at the nodes to which it connects.
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Buffering
Effects of loading can be diminished or eliminated
with a buffer.
An “ideal” buffer is an amplifier that
senses the voltage at its input without drawing
any current, and
sets its output voltage equal to the measured
input voltage.
We will discuss how to use op-amps to make
buffers in next lecture (after Reading Week).
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