IE1206 Embedded Electronics Le1 Le2 PIC-block Documentation, - - PowerPoint PPT Presentation

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IE1206 Embedded Electronics Le1 Le2 PIC-block Documentation, - - PowerPoint PPT Presentation

Jul 10, 2023 48 likes •541 views

IE1206 Embedded Electronics Le1 Le2 PIC-block Documentation, Seriecom Pulse sensors I , U , R , P , serial and parallel Le3 Ex1 KC1 LAB1 Pulse sensors, Menu program Start of programing task Ex2 Le4 Kirchhoffs laws Node

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SLIDE 1

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
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SLIDE 2

William Sandqvist william@kth.se

Transformer

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SLIDE 3

William Sandqvist william@kth.se

Voltage ratio

2 1 2 1 2 2 1 1

d d d d N N U U t N U t N U = Φ = Φ =

N1 : N2

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SLIDE 4

William Sandqvist william@kth.se

Ideal transformer I0 = 0

N1⋅I0 = N1⋅ I1 – N2⋅ I2 Magnetisig current I0 ≈ 0 is small compared to the work currents I1 and I2. The transformer itself has a high inductance.

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SLIDE 5

William Sandqvist william@kth.se

Current ratio

2 1 2 1 1 2 2 2 1 1 2 1

) , ( N N U U I I I U I U I P P P = ≈

  • ⋅

= ⋅ = =

N1 : N2

slide-6
SLIDE 6

William Sandqvist william@kth.se

Eddy current losses

Eddy currents – currents inside the iron core is prevented with lacquered ( = isolation ) sheet metal.

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SLIDE 7

William Sandqvist william@kth.se

E I -core

  • EI-core is very economical to manufacture !
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SLIDE 8

William Sandqvist william@kth.se

E I -core

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SLIDE 9

William Sandqvist william@kth.se

Toroid

Toroid core has a low leakage field – so it will not disturb nearby electronics! How do one wind such a transformer?

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SLIDE 10

William Sandqvist william@kth.se

Automatic Winding of toroidal core

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SLIDE 11

William Sandqvist william@kth.se

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SLIDE 12

William Sandqvist william@kth.se

Transformer (15.4)

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SLIDE 13

William Sandqvist william@kth.se

Transformer (15.4)

2 1 1 2

2 1 2 1

=

  • =

I I U U

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SLIDE 14

William Sandqvist william@kth.se

Transformer (15.4)

2 1 1 2

2 1 2 1

=

  • =

I I U U 8 10 2 , 10 10

1 1 1 1

= ⋅ − =

  • =

− ⋅ − U U I R

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SLIDE 15

William Sandqvist william@kth.se

Transformer (15.4)

2 1 1 2

2 1 2 1

=

  • =

I I U U 8 10 2 , 10 10

1 1 1 1

= ⋅ − =

  • =

− ⋅ − U U I R 4 2 8 2 1

1 2

= = ⋅ =U U

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SLIDE 16

William Sandqvist william@kth.se

Transformatorn (15.4)

2 1 1 2

2 1 2 1

=

  • =

I I U U 8 10 2 , 10 10

1 1 1 1

= ⋅ − =

  • =

− ⋅ − U U I R 4 2 8 2 1

1 2

= = ⋅ =U U 4 , 1 2

1 2

= ⋅ = I I

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SLIDE 17

William Sandqvist william@kth.se

Transformer (15.4)

2 1 1 2

2 1 2 1

=

  • =

I I U U 8 10 2 , 10 10

1 1 1 1

= ⋅ − =

  • =

− ⋅ − U U I R 4 2 8 2 1

1 2

= = ⋅ =U U 4 , 1 2

1 2

= ⋅ = I I Ω = = = 10 4 , 4

2 2 2

I U R

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SLIDE 18

William Sandqvist william@kth.se

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SLIDE 19

William Sandqvist william@kth.se

2 2 2 1 2 1 2 2 2 2 1 2 1 2 2 2 1 1 1 2 2 2 1 1 1

R N N R I U N N I N N U N N I U I U R I U R ⋅

  • =

⋅

  • =

= = =

←

R N N ⋅

  • 2

2 1

Transforming impedances

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SLIDE 20

William Sandqvist william@kth.se

2 2 2 1 2 1 2 2 2 2 1 2 1 2 2 2 1 1 1 2 2 2 1 1 1

R N N R I U N N I N N U N N I U I U R I U R ⋅

  • =

⋅

  • =

= = =

←

R N N ⋅

  • 2

2 1

Transforming impedances

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SLIDE 21

William Sandqvist william@kth.se

  • Ex. Transforming impedances

A transformer has the voltage ratio 240V/120V. We have two capacitors 1µF and 16 µF. How should one connect to get 5 µF ?

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SLIDE 22

William Sandqvist william@kth.se

  • Ex. Transforming impedances

) 4 / ( 1 2 1 1

2 2 1 2

C C Z C Z ω ω ω = ⋅ =

  • =

←

A transformer has the voltage ratio 240V/120V. We have two capacitors 1µF and 16 µF. How should one connect to get 5 µF ?

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SLIDE 23

William Sandqvist william@kth.se

  • Ex. Transforming impedances

) 4 / ( 1 2 1 1

2 2 1 2

C C Z C Z ω ω ω = ⋅ =

  • =

←

16 F µ 4 F µ

A transformer has the voltage ratio 240V/120V. We have two capacitors 1µF and 16 µF. How should one connect to get 5 µF ?

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SLIDE 24

William Sandqvist william@kth.se

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SLIDE 25

William Sandqvist william@kth.se

Series and parallel connection of inductors

(Ex. 15.6) Assuming that none of the coils parts magnetic lines of force with each other but are completely independent components, they can be treated series and parallel inductors just as if they were resistors.

H 3 6 4 4 4 4 4 6 4 4 4 4 4

ERS

= + + ⋅ + ⋅

  • +

⋅ + = L

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SLIDE 26

William Sandqvist william@kth.se

Series and parallel connection of inductors?

We have previously studied serial and parallel coils as if they were completely independent components that do not share magnetic lines with each other. We are now treating coils with interconnected flow

? ?

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SLIDE 27

Inductive coupling

William Sandqvist william@kth.se

d d u r i t ϕ = ⋅ +

A portion of the flow in the coil 1 is interconnected with flow from the coil 2.

1 1 1 1 1 1 1 2

d d u r i i L i M t ϕ ϕ = ⋅ + = ⋅ + ⋅ In same way:

2 2 2 2 2 2 2 1

d d u r i i L i M t ϕ ϕ = ⋅ + = ⋅ + ⋅ Induction

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SLIDE 28

Inductive coupling

William Sandqvist william@kth.se 1 2 1 1 1 1 2 1 2 2 2 2

d d d d d d d d i i u r i L M t t i i u r i L M t t = ⋅ + + = ⋅ + +

1 1 1 1 1 2 2 2 2 2 2 1

j j j j U r I L I MI U r I L I MI ω ω ω ω = ⋅ + + = ⋅ + + jω-method: ± M is called mutual inductance

2 1L

L M k = Coupling factor:

The coupling factor indicates how much of the flow a coil has in common with another coil

An ideal transformer has coupling factor k = 1 (100%)

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SLIDE 29

Series with mutual inductance

William Sandqvist william@kth.se

Series connection has the same current

2 12 1 1 1 L L L

I M j I L j U ω ω ± =

1 21 2 2 2 L L L

I M j I L j U ω ω ± =

1 2 1 2 12 21 1 2

( )

L L L L

I I I U U U M M M U I j L M L M ω = = = + = =

  • =

⋅ ± + ±

1 2

( 2 ) U j L L M I ω = + ±

1 1 12 1 L L

I U M L

2 2 21 2 L L

I U M L

Derive:

slide-30
SLIDE 30

Series with mutual inductance

William Sandqvist william@kth.se

M L L LTOT 2

2 1

+ + = M L L LTOT 2

2 1

− + =

Series connection has the same current I1 = I2 =I M can can contribute or counter act to the flow, this gives ±

  • sign. Therefore, coil winding polarity is usually indicated by a

dot convention in schematics. M-dot M-dot M-dot M-dot

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SLIDE 31

”Dot” convention

William Sandqvist william@kth.se

An increasing current in to a dot results in induced voltages with directions that would give increasing currents out of other dots.

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SLIDE 32

”Dot” convention

William Sandqvist william@kth.se

An increasing current in to a dot results in induced voltages with directions that would give increasing currents out of other dots.

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SLIDE 33

In parallel with mutual inductance

William Sandqvist william@kth.se

M L L M L L LTOT 2

2 1 2 2 1

− + − ⋅ = M L L M L L LTOT 2

2 1 2 2 1

+ + − ⋅ =

TOT

L

TOT

L

Parallel connected coils Antiparal conected coils

slide-34
SLIDE 34
  • Ex. 15.7 Series connection

William Sandqvist william@kth.se

5

1 =

L 10

2 =

L 15

3 =

L 2

12 =

M 3

23 =

M 1

13 =

M

[H]

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SLIDE 35
  • Ex. 15.7 Series connection

William Sandqvist william@kth.se

5

1 =

L 10

2 =

L 15

3 =

L 2

12 =

M 3

23 =

M 1

13 =

M

[H] LTOT = L1 + M12 – M13 + L2 + M12 – M23 + L3 – M23 – M13 = = 5 +2 –1 + 10 + 2 – 3 + 15 –3 –1 = 26 [H]

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SLIDE 36

William Sandqvist william@kth.se

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SLIDE 37

Measuring the mutual inductance?

William Sandqvist william@kth.se

+ TOT

L

− TOT

L M L L LTOT 2

2 1

+ + =

+

M L L LTOT 2

2 1

− + =

−

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SLIDE 38

Measuring the mutual inductance?

William Sandqvist william@kth.se

+ TOT

L

− TOT

L M L L LTOT 2

2 1

+ + =

+

M L L LTOT 2

2 1

− + =

−

4

− + −

=

TOT TOT

L L M

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SLIDE 39

Variometer (to an antique radio)

William Sandqvist william@kth.se

) ( 2

2 1

α f M M L L LTOT = ± + =

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SLIDE 40

William Sandqvist william@kth.se

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SLIDE 41

A bad actuator can become a good sensor

William Sandqvist william@kth.se

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SLIDE 42

The industry's "rugged" position sensor

William Sandqvist william@kth.se

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SLIDE 43

Differential transformer

William Sandqvist william@kth.se

LVDT Linear Variable Differential Transformer The secondary coils are connected in series but with

  • pposite polarity – when the core is in the middle U = 0.

core

primary coil secondary coil secondary coil

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SLIDE 44

LVDT design

William Sandqvist william@kth.se

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SLIDE 45

William Sandqvist william@kth.se

The output voltage is relatively high – it makes this a popular sensor …

LVDT principle

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SLIDE 46

LVDT probe

Output signal changes phase 180° ° ° ° exactly when the core pass the middle point.

William Sandqvist william@kth.se

A XOR-gate kan indicate this change.

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SLIDE 47

A LVDT probe can keep track on that the thicknes is correct. Guess application? It is important to ensure that the ATM does not distribute "double" bills …

William Sandqvist william@kth.se

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SLIDE 48

William Sandqvist william@kth.se

Periodic differential transformer

Renywell Spherical encoder LVDT-principel witin a core, and then keep track on how many cores that have passed. A similar sensor?

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SLIDE 49

William Sandqvist william@kth.se