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

1st semester, 2012 ENGG1015 - Dr. K. Wong 3

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


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




2

ccV

vout

Rref

Vcc

0

rt

vout rt

Rref rtVcc

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


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).


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.



1 2 3i i i


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.


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


1 2 3 0i i i


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.


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.


Resistor, Voltage and Current Sources Each component is represented by a relationship

between the voltage across the component and

the current through the component.


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.


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.


What is the current through the resistor

below?

1. 1A

2. 2A

3. 0A

4. None of the above

Quick Check


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


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


Common Patterns

Few common patterns that facilitate design and

analysis are:

Resistors in series

Resistors in parallel

Voltage dividers

Current dividers


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.


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


Voltage Divider

Resistors in series act as voltage dividers.


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.


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

Quick Check

Find Vo

1. 2V

2. 4V

3. 6V

4. 8V


High Level Design - Output


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


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


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


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.


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


Loading

Q: What's different about a circuit?

A: A new component generally alters the currents

at the nodes to which it connects.


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).


In conclusion… Primitives:

• Resistor

• Voltage source

• Current source

Means of Combination: • Wiring

Means of Abstraction: • Equivalent resistances

Common Patterns: • Resistors in series

• Resistors in parallel

• Voltage dividers

• Current dividers


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