IE1206 Embedded Electronics PIC-block Documentation, Seriecom Pulse - - PowerPoint PPT Presentation

IE1206 Embedded Electronics

Transients PWM Phasor jω PWM CCP CAP/IND-sensor

Le1 Le3 Le6 Le8 Le2 Ex1 Le9 Ex4 Le7

Written exam

William Sandqvist william@kth.se

PIC-block Documentation, Seriecom Pulse sensors I, U, R, P, serial and parallel

Ex2 Ex5

Kirchhoffs laws Node analysis Two-terminals R2R AD Trafo, Ethernet contact

Le13

Pulse sensors, Menu program

Le4

KC1 LAB1 KC3 LAB3 KC4 LAB4

Ex3 Le5

KC2 LAB2

Two-terminals, AD, Comparator/Schmitt Step-up, RC-oscillator

Le10 Ex6

LC-osc, DC-motor, CCP PWM

LP-filter Trafo

Le12 Ex7

Display

Le11

• Start of programing task
• Display of programing task

William Sandqvist william@kth.se

electric fields

2 2 9 2 1 2 2 1

/C Nm 10 9 4 1 k 1 k k ⋅ = ⋅ = ⋅ ⋅ = ⋅ ⋅ = ε π r Q E r Q Q F

The force between charges can be calculated using Coulomb's Law. The force between like charges is repulsive, between different charges atractive. The electric field E at a point charge Q1 can be seen as the force on a "test charge", a "unit charge“ ( Q2 =+1 ). The electric lines of force are starting from a positive charge and end on a negative charge. The force lines may not cross each other. The constant k has a very big value, the electical forces are strong.

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Plate capacitor

pF/m 85 , 8 2 / 2

r 4 1 3 2 1

= ⋅ = = < = = = = > = ε ε ε ε ε ε ε ε ε d A C d A C d A C d A C d A C

A capacitor capacitance C is proportional to the area A and inversely proportional to flat distance d. If the insulation material between the plates is polarizable (ε) the capacitance is increased.

C1 ε0 C1 ε0 C4 ε C2 ε0 C3 ε0

d A C U Q C ε = =

William Sandqvist william@kth.se

Dielectric

pF/m 85 , 8

r

= ⋅ = ε ε ε ε

Most materials are polarizable, and will then increase the electric field, and the capacitance of the capacitor if placed between the plates. Titanite used in ceramic capacitors, the increases the capacitance 7500 times in comparison to vacuum or air. εr = 7500 εr is playing the same role for the electric field as µr does for the magnetic field.

William Sandqvist william@kth.se

Short d, Voltage rating

High capacitance value could be

• btained with a small flat distance d.

The drawback is that the risk increases for arcing between the plates. Each capacitor then has a maximum rated voltage which must not be exceeded. A capacitor for higher rated voltage are necessarily larger than a lower rated voltage if the capacitance is the same.

d U E U Q C = =

The electric field E of the capacitor is E=U/d. The air can withstand 2.5 kV/mm before arcing!

William Sandqvist william@kth.se

Big area A

High capacitance one can get with large area A. The capacitor can then be rolled, or type by multilayer type, so that "the component surface" is minimized despite the large inner surface.

Multilayer Capacitor with ceramic dielectrics ( = high εr ).

William Sandqvist william@kth.se

Very short distance d

The electrolytic capacitor is based on extremely small distance d between the

• electrodes. One electrode is an aluminum

foil, and the dielectric is a thin insulating

• xide layer on the foil. The other electrode

is the electrolyte itself which of course is in close contact with the surface of the foil. The capacitor must be polarized correctly, with the same polarity as when the oxide layer was formed. Otherwise the oxide layer is destructed and the capacitor is shorted! The capacitor is also destroyed if the rated voltage is exceeded.

William Sandqvist william@kth.se

Big area A and very short distance d

Tantal electrolytic capacitor have a "sponge formed" electrode. The total inner surface A becomes extremely large. The insulation consists of an oxide layer so even d is small. A 3.5 mm×2.5 mm× 5.5 mm, 4.7µF tantal electrolytic capacitor has the equivalent inner area of 40 cm2 !

William Sandqvist william@kth.se

Capacitors

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Supercap (9.2)

The backup capacitors of the type "Supercap" can be used as a power backup for memories - if one for example needs to move the phone from

• ne room to another without the phone forgetting its settings.

Make a rough estimate of how long the charge in the capacitor will last? Assume that C = 1 F and U is initially 5V. The equipment draws I = 10 mA and operates down to 2.5V.

t Q I U Q C ⋅ = =

William Sandqvist william@kth.se

Supercap (9.2)

min 4 s 250 10 10 5 . 2 As 5 , 2 ) 5 , 2 5 ( 1

3

= = ⋅ = ∆ = = − ⋅ = ∆ ⋅ = ∆

−

I Q t U C Q

t Q I U Q C ⋅ = =

The backup capacitors of the type "Supercap" can be used as a power backup for memories - if one for example needs to move the phone from

• ne room to another without the phone forgetting its settings.

Make a rough estimate of how long the charge in the capacitor will last? Assume that C = 1 F and U is initially 5V. The equipment draws I = 10 mA and operates down to 2.5V.

School’s ”biggest” supercap?

William Sandqvist william@kth.se

3000 F × 16 Research is going on for energy storage for routers in places where batteries woud have 'inappropriate' temperatures. For example, in the desert or in the arctic.

School TELECOMUNICATION SYSTEM LAB

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Capacitor transients

R C

1 ( ) ( )d d d d 1 d 1 d ( ) ( )d ( ) ( ) d d d d d

t t

E u u E i t R i z z C i(t) i(t) E i t R i z z R i t R C i t t t t C t C t = + ⇔ = ⋅ + = ⋅ + ⇒ = + ⇔ = ⋅ +

∫ ∫

C z z i C t q t u

t

∫

= =

C

d ) ( ) ( ) (

The voltage across the capacitor orginates from the collected charge.

C R e R E t i

t

⋅ = ⋅ =

−

τ

τ

) (

C R⋅ = τ

William Sandqvist william@kth.se

Capacitor transients

R C

1 ( ) ( )d d d d 1 d 1 d ( ) ( )d ( ) ( ) d d d d d

t t

E u u E i t R i z z C i(t) i(t) E i t R i z z R i t R C i t t t t C t C t = + ⇔ = ⋅ + = ⋅ + ⇒ = + ⇔ = ⋅ +

∫ ∫

C z z i C t q t u

t

∫

= =

C

d ) ( ) ( ) (

( )

t

E i t e R C R

τ

τ

−

= ⋅ = ⋅

The differential equation has the solution:

C R⋅ = τ

The voltage across the capacitor orginates from the collected charge.

William Sandqvist william@kth.se

Charging a capacitor

Time constant T = R⋅C

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Parallel connected capacitors

(Ex. 9.3) Two capacitors parallel-connected. What about the equivalent capacitance and its rated voltage? C1 = 4 µF 50V C2 = 2 µF 75V

William Sandqvist william@kth.se

Parallel connected capacitors

Capacitance is added, the parallel connection is the same as if plate surfaces were added. The capacitor with the worst withstanding voltage determines the equivalent capacitor rated voltage. It is in this capacitor the impact would occur. (Ex. 9.3) Two capacitors parallel-connected. What about the equivalent capacitance and its rated voltage? C1 = 4 µF 50V C2 = 2 µF 75V

William Sandqvist william@kth.se

Parallel connected capacitors

CERS = C1 + C2 = 4 + 2 = 6 µF 50V (Ex. 9.3) Two capacitors parallel-connected. What about the equivalent capacitance and its rated voltage? C1 = 4 µF 50V C2 = 2 µF 75V Capacitance is added, the parallel connection is the same as if plate surfaces were added. The capacitor with the worst withstanding voltage determines the equivalent capacitor rated voltage. It is in this capacitor the impact would occur.

William Sandqvist william@kth.se

Series connected capacitors

2 1 2 1 ERS

C C C C C + ⋅ =

Parallel coupling formula for resistors is comparable to series coupling capacitors formula! In a capacitive voltage divider the voltages are divided inversely with the capacitor capacitances. The smallest capacitor will have the highest voltage – will it withstand it?

2 C 1 C ERS 2 C 1 C 2 C 2 C 1 C C1 ERS 2 C 1

1 1 1 C C C Q Q Q C Q C Q C Q E C Q U U U E

C

+ = ⇒ = = + = = ⇒ = + =

William Sandqvist william@kth.se

• Example. Series connected capacitors

(Ex. 9.4) Two capacitors are connected in series. Calculate the equivalent capacitance and specify how the voltage is divided between the capacitors. E = 10 V C1 = 6 µF C2 = 12 µF

2 1 2 1 ERS

C C C C C + ⋅ =

William Sandqvist william@kth.se

No current/charge can pass through a capacitor. Two series-connected capacitors must therefore always have the same charge! QC1 = QC2.

• Example. Series connected capacitors

(Ex. 9.4) Two capacitors are connected in series. Calculate the equivalent capacitance and specify how the voltage is divided between the capacitors. E = 10 V C1 = 6 µF C2 = 12 µF

2 1 2 1 ERS

C C C C C + ⋅ =

William Sandqvist william@kth.se

V 33 , 3 66 , 6 10 V 66 , 6 10 6 10 40 C 40 10 10 4 F 4 12 6 12 6

C1 C2 6 6 1 C1 6 ERS C2 2 C1 1 ERS 2 1

= − = − = = ⋅ ⋅ = = µ = ⋅ ⋅ = µ = + ⋅ = ⋅ = ⋅ = ⋅ = = =

− − −

U E U C Q U Q C U C U C E C Q Q Q

C C

No current/charge can pass through a capacitor. Two series-connected capacitors must therefore always have the same charge! QC1 = QC2.

• Example. Series connected capacitors

(Ex. 9.4) Two capacitors are connected in series. Calculate the equivalent capacitance and specify how the voltage is divided between the capacitors. E = 10 V C1 = 6 µF C2 = 12 µF

2 1 2 1 ERS

C C C C C + ⋅ =

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Energy in capacitor

2 E

2 1 U C W ⋅ =

2 C C C C C C C

2 1 d d d d d d d E C u u C t t u u C t p W u t u C u i p

E u u t t t t

⋅ ⋅ = ⋅ = ⋅ ⋅ = = ⇒ ⋅ = ⋅ =

∫ ∫ ∫

= = ∞ = = ∞ = =

t u C i t q t q C t u C Q U

C C

d d d d d d 1 d d = = ⇒ ⋅ = ⇒ =

Instantaneous power: Energy: Stored energy in the electrical field:

Remember the formula, but its allowed to skip the derivation …

William Sandqvist william@kth.se

Energy in capacitor

2 E

2 1 E C W ⋅ =

E

W ) ( ) ( ) ( t i t u t p

C

⋅ =

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Camera Flash

Electric energy in capacitor W ?

Ws , J 5 100 10 1000

2 6 2 1 2 2 1

= ⋅ ⋅ ⋅ = ⋅ ⋅ =

−

U C W

Capacitor charge Q ?

As C, 1 , 100 10 1000

6

= ⋅ ⋅ = ⋅ =

−

U C Q

The lightning current (mean value) I?

A 200 2000 / 1 1 , = = = t Q I

Power during flash discharge P ? How long to wait for next flash tLadda ?

kW 10 2000 / 1 5 = = = t W P s 10 10 10 100 10 1000

3 6 Ladda Ladda Ladda Ladda

= ⋅ ⋅ ⋅ = ⋅ = ⇒ ⋅ = =

− −

I U C t C t I C Q U Nowdays LED Flash? t W P t Q I U C Q U C W = = ⋅ = ⋅ ⋅ =

2 2 1

(Ex. 9.1)

Battery with Voltage converter Press

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Neon lamp

Blink-circuit with Neon-lamp at exercise …

(Ex. 10.9)

William Sandqvist william@kth.se

Simulate Neon lamp

Tryck på ESC, annars tar simuleringen aldrig slut …

William Sandqvist william@kth.se