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Switch the *?!!# thing off! Clickers at the ready …. e. Introductory comments. Minor re-jig of content in 2011 Exams from past mostly relevant! Focus on practical Major practical exercise Practical dictates order of lecture content “My” section is slightly disjointed

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slide1

Switch the *?!!# thing off!

Clickers at the ready …

e

Alan Murray – University of Edinburgh

introductory comments
Introductory comments
  • Minor re-jig of content in 2011
    • Exams from past mostly relevant!
  • Focus on practical
    • Major practical exercise
    • Practical dictates order of lecture content
    • “My” section is slightly disjointed
  • Course Organiser: Prof Markus Mueller

Alan Murray – University of Edinburgh

resources
Resources
  • These powerpoints(Learn)
  • Notes under slides
  • Tutorials
  • EE1 “toybox”

Alan Murray – University of Edinburgh

syllabus alan murray
Syllabus : Alan Murray
  • Potential divider. Resistors and capacitors
  • RC circuit introduction.
  • RC circuits charge-discharge
  • Inductors and RL circuits, charge-discharge
  • Nodal analysis introduction
  • Nodal analysis examples
  • Op-Amps, introduction
  • Op-Amp circuits
  • Op-Amp worked examples
  • Real Op-Amps (limitations)
  • Diodes – “cartoon” version
  • Filters (introduction only)

Alan Murray – University of Edinburgh

agenda
Agenda
  • Potential dividers
  • Voltage and current sources
  • Resistors and capacitors

Alan Murray – University of Edinburgh

the potential divider analogy how high is the book

Height

=1.8m

0.4xHeight

2m

The potential divider: AnalogyHow high is the book?

Solution

Alan Murray – University of Edinburgh

the potential divider reality how high is the voltage
The potential divider: RealityHow high is the voltage?

1kΩ

Solution

9V

Voltage =?

2kΩ

1.5V

0V

Alan Murray – University of Edinburgh

potential dividers

Vtop

Rtop

Vmid

Rbottom

Vbottom

Potential dividers
  • Voltage at the mid-point depends upon a resistor RATIO
  • Do not forget the voltage at the bottom

DC simulation

AC simulation

Alan Murray – University of Edinburgh

adding resistors

A

I

I

I

In parallel (V1=V2):

In series (I1=I2):

A

R1

R1

R2

R2

V2

V1

B

B

Adding resistors

Alan Murray – University of Edinburgh

adding resistors1

V1

R1

R1

R2

R2

I

V2

Adding resistors

In series (I1=I2):

In parallel (V1=V2):

B

A

A

B

Alan Murray – University of Edinburgh

for example tutorial
For example (Tutorial)

Series

Parallel

Alan Murray – University of Edinburgh

aside voltage sources

R

VR=9V

9V

IR

VR

9V

Aside …Voltage sources
  • A perfect voltage source will make VR=9V ALWAYS
  • A real voltage source may not manage this
    • Battery?
    • Bench supply?
  • They are “imperfect”

Alan Murray – University of Edinburgh

aside voltage sources1

IR

VR

9V

Aside … Voltage sources
  • Real battery
    • Nonzero internal resistance
  • Some voltage “lost” across Rint
  • Lower load resistor?
    • More current
    • More loss over Rint

Rint

RL

VR<9V

9V

Alan Murray – University of Edinburgh

aside current sources

IR

R

1A

IR

1A

VR

Aside … Current sources
  • A perfect current source will make IR=1A ALWAYS
  • A real current source may not manage this
    • Bench supply?
    • MOSFET
    • Op-Amp circuit?
  • They are “imperfect”

Alan Murray – University of Edinburgh

capacitors
Capacitors

Alan Murray – University of Edinburgh

analogy capacitor

Small volume(“charge”)

Large volume(“charge”)

SameWater level(“Voltage”)

Analogy – capacitor

Current source

Current source

Large Capacitor

Small Capacitor

Alan Murray – University of Edinburgh

analogy capacitor resistor
Analogy – capacitor/resistor

Water current

Switch

Resistor

Voltage source

Pressure

Difference

Water level

Capacitor

Alan Murray – University of Edinburgh

analogy capacitor resistor1
Analogy – capacitor/resistor

Water current

Time

Water level

Time

Pressure

Difference

Time

Alan Murray – University of Edinburgh

analogy capacitor resistor2
Analogy – capacitor/resistor

Larger “capacitor” = more to fill

Water current

Animation

Time

Water level

Time

Pressure

Difference

Time

Alan Murray – University of Edinburgh

analogy capacitor resistor3
Analogy – capacitor/resistor

Larger “resistor” = less current = slower flow

Water current

Animation

Time

Water level

Time

Pressure

Difference

Time

Alan Murray – University of Edinburgh

resistor and capacitor comparison

I

V

+Q

V

Charge

-Q

I

Q

Large capacitance

Small resistance

Small capacitance

Large resistance

V

V

Resistor and capacitor“comparison”

Ohm’s Law

Definition of capacitance

Alan Murray – University of Edinburgh

capacitor q cv

+

+

+

+

+

+

+

+

+

+

+

-

-

-

-

-

-

-

-

-

-

-

Capacitor, Q=CV

C=Area x dielectric constantseparation

Opposite charges attract

Plates larger – more charge, bigger capacitance

Plates closer together – stronger force, more charge/area, bigger capacitance

Dielectric constant – charges in the dielectric join in to increase the force

Alan Murray – University of Edinburgh

capacitor resistor

VR

VC

Capacitor/Resistor

Q=3C

R

+Q

3V

C=1F

Time

-Q

VC

Q=3C

Time

VR

C initially DISCHARGED

Time

Alan Murray – University of Edinburgh

charging capacitors current source

I = const

V

V

time

Charging capacitors –current source
  • Q = CV
  • I = constant = rate of change of Q
  • I = dQ/dt = C dV/dt
  • dV/dt = I/C = constant
  • dV/dt is constant for constant current

High current

Low current

Alan Murray – University of Edinburgh

rc how does the maths work

R

I

C

VC

RC: how does the maths work?

VS

VS=VR+VC

IC=IS=IR

VR=RIR

QC=CVC

IC=dQC

dt

IC= CdVC

dt

Alan Murray – University of Edinburgh

rc charge and discharge demonstration of the formula

Vfinish – Vstart= = “journey”

1

RC charge (and discharge) – demonstration of the formula.

Start with (1-et/RC)

Add Vstart

“Stretch” … ie x(Vfinish - Vstart)

Vfinish

Vstart + (Vfinish - Vstart)x(1-et/RC) … 

Vstart + (1-et/RC) – right shape and start

Vstart

(1-et/RC) – right shape

Time

Alan Murray – University of Edinburgh

resistor charging capacitor

VC

Vfinish

Vstart

I

Istart

R

I

C

VC

time

time

Resistor charging capacitor

VR

Challenge? Find Vstart, Vfinish, Istart , Ifinish

Some examples follow …

Alan Murray – University of Edinburgh

this is worth remembering
This is worth remembering …

Alan Murray – University of Edinburgh

resistor charging capacitor1

Exercise …

check this givesthe same answer

finish

start

start

time

time

Resistor charging capacitor

R=1Ω

VCstart=0V

VC

=3V

Vfinish

3V

VC

C=2F

VR=3V-VC

Vstart

=0V

I

Istart

=3A

Alan Murray – University of Edinburgh

check differentiate v c
Check – differentiate VC

Same answer J

Alan Murray – University of Edinburgh

resistor dis charging capacitor

RC larger – longer time constant

Exercise for you …

check this givesthe same answer

Resistor discharging capacitor

R=5Ω

Vstart=6V

VC

Vstart

1V

6V

VC

C=4F

Vfinish

time

VR

time

Istart

Simulation

Simulation (tol)

Alan Murray – University of Edinburgh

clicker question

VC

(a)

VC

VC

(b)

VC

(c)

(d)

Clicker Question

i

R=10Ω

ii

2V

VC

C=1F

I= -0.5A

Capacitor initially discharged

Switch from (i) to (ii) and then backto (i) again

Solution

Alan Murray – University of Edinburgh

clicker question1
Clicker Question

R=10Ω

VCstart

VCfinish

Istart

Ifinish

Work through it here!

2V

2V

0A

0A

a

10V

2V

VC

C=1F

I

10V

10V

0.2A

1A

b

8V

8V

1.2A

1.2A

c

12V

12V

0.8A

0.8A

d

Alan Murray – University of Edinburgh

worked example
Worked example

Vcomp=8V

3 seconds

R

Vin

C

Capacitor is initially discharged.

Choose R and C to make the comparator signal after 3 seconds

10V

Alan Murray – University of Edinburgh

worked example1
Worked example

How logs work

RC=1.86 (ideal)

Choose R=1.2kΩ, C=1.5mF

RC=1.8

VC(3)=8.1V, or 8V at 2.9sec (not 3)

This may or may not be good enough …

Depends upon the application.

And then, of course, R = R±5%, C=C ±5% …

Alan Murray – University of Edinburgh

adding capacitors

A

A

C2

C1

C1

C2

B

B

Adding Capacitors

In parallel:

In series:

Alan Murray – University of Edinburgh

example from tutorial again
Example from Tutorial again

Series

Parallel

Alan Murray – University of Edinburgh

forward look capacitors and ac signals

This is the capacitor’s “resistance” (actually “reactance”)

High for low frequency

Low for high frequency

Forward look – capacitors and AC signals

Simulation (DC)

Simulation (DC)

Compare with V=RI

Simulation (AC)

Simulation (AC)

Alan Murray – University of Edinburgh

post script decoupling

3V supply

Digital Chip

Post Script – “decoupling”

Digital signals = sharp edges

Sharp edges = large currents for short periods

Large current = loss of voltage over the internal impedance of Vsupply

This causes Vsupply to “bounce” in sympathy with digital signals

Solution?

Place a “current storage” device (ie a reservoir of charge) close to the chip

Capacitor to the rescue …

Vsupply

Alan Murray – University of Edinburgh

post script decoupling1

3V supply

Post Script – “decoupling”

Add a capacitor to decouple the power supply to ground

Large current required to create a sharp edge?

Comes from Cdecouple, not from 3V supply

3V supply must simply keep Cdecouple “topped up”.

Analogy – food!

Q(lots of)

Cdecouple

Currentrequired

Digital Chip

Alan Murray – University of Edinburgh

summary
Summary
  • Potential dividers – how to analyse
    • Try to remember the equation
    • Don’t forget the potential at the bottom!
  • Capacitors =- charge/discharge
    • Simple way to concoct the equation and graph

Alan Murray – University of Edinburgh