IE1206 Embedded Electronics - KTH...Ex6 Le10 LC-osc, DC-motor, CCP PWM LP-filter Trafo Le12 Ex7...

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 sensorsI, U, R, P, serial and parallel

Ex2

Ex5

Kirchhoffs laws Node analysis Two-terminals R2R AD

Trafo, Ethernet contactLe13

Pulse sensors, Menu program

Le4

KC1 LAB1

KC3 LAB3

KC4 LAB4

Ex3Le5 KC2 LAB2 Two-terminals, AD, Comparator/Schmitt

Step-up, RC-oscillator

Le10Ex6 LC-osc, DC-motor, CCP PWM

LP-filter TrafoLe12 Ex7 Display

Le11

•••• Start of programing task

•••• Display of programing task


Transformer


Voltage ratio

2

1

2

1

2211 d

d

d

d

N

N

U

U

tNU

tNU

=

Φ=Φ=

N1 : N2


Ideal transformer I0 = 0

N1⋅I0 = N1⋅ I1 – N2⋅ I2

Magnetisig current I0 ≈ 0 is smallcompared to the work currents I1 and I2. The transformer itself has a high inductance.


Current ratio

2

1

2

1

1

2

2211

0021 )0,(

N

N

U

U

I

I

IUIU

IPPP

=≈

⇒⋅=⋅==

N1 : N2


Eddy current losses

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


E I -core

• EI-core is very economical to manufacture!


E I -core


Toroid

Toroid core has a low leakage field – so it will not disturb nearby electronics!

How do one wind such a transformer?


Automatic Winding of toroidal core


Transformer (15.4)


Transformer (15.4)

2

1

1

2

2

1

2

1

=

⇒=

I

I

U

U


Transformer (15.4)

2

1

1

2

2

1

2

1

=

⇒=

I

I

U

U

8102,010010 1111 =⋅−=⇒=−⋅− UUIR


Transformer (15.4)

2

1

1

2

2

1

2

1

=

⇒=

I

I

U

U

8102,010010 1111 =⋅−=⇒=−⋅− UUIR

42

8

2

112 ==⋅= UU


Transformatorn (15.4)

2

1

1

2

2

1

2

1

=

⇒=

I

I

U

U

8102,010010 1111 =⋅−=⇒=−⋅− UUIR

42

8

2

112 ==⋅= UU 4,01

212 =⋅= II


Transformer (15.4)

2

1

1

2

2

1

2

1

=

⇒=

I

I

U

U

8102,010010 1111 =⋅−=⇒=−⋅− UUIR

42

8

2

112 ==⋅= UU 4,01

212 =⋅= II

Ω=== 104,0

4

2

22 I

UR


2

2

2

121

2

2

2

2

1

21

2

22

1

1

1

2

22

1

11

RN

NR

I

U

N

N

IN

N

UN

N

I

U

I

UR

I

UR

⋅

=

⋅

====

←

RN

N ⋅

2

2

1

Transforming impedances


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 ?



)4/(

12

1

1

221

2

CCZ

CZ

ωω

ω

=⋅=

⇒=

←





)4/(

12

1

1

221

2

CCZ

CZ

ωω

ω

=⋅=

⇒=

←

16 Fµ4 Fµ




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.

H36

4444

4

64444

4

ERS =+

+⋅+

⋅

+⋅+

=L


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

??

Inductive coupling


d

du r i

t

ϕ= ⋅ +

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

11 1 1 1 1 1 2

d

du r i i L i M

t

ϕ ϕ= ⋅ + = ⋅ + ⋅In same way: 2

2 2 2 2 2 2 1

d

du r i i L i M

t

ϕ ϕ= ⋅ + = ⋅ + ⋅

Induction

Inductive coupling


1 21 1 1 1

2 12 2 2 2

d d

d dd d

d d

i iu r i L M

t ti i

u r i L Mt 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 ωω ω

= ⋅ + += ⋅ + +

jω-method:

± M is called mutual inductance

21LL

Mk =

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%)

Series with mutual inductance


Series connection has the same current

212111 LLL IMjILjU ωω ±= 121222 LLL IMjILjU ωω ±=

1 2 1 2 12 21

1 2( )L L L LI I I U U U M M M

U I j L M L Mω= = = + = = ⇒

= ⋅ ± + ±

1 2( 2 )U

j L L MI

ω= + ±

11121 LL IUML 22212 LL IUML

Derive:

Series with mutual inductance


MLLLTOT 221 ++= MLLLTOT 221 −+=

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 adot convention in schematics.

M-dot M-dot M-dot M-dot

”Dot” convention


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

In parallel with mutual inductance


MLL

MLLLTOT 221

221

−+−⋅=

MLL

MLLLTOT 221

221

++−⋅=

TOTL TOTL

Parallel connected coils Antiparal conected coils

Ex. 15.7 Series connection


51 =L 102 =L 153 =L

212 =M 323 =M

113 =M

[H]

Ex. 15.7 Series connection


51 =L 102 =L 153 =L

212 =M 323 =M

113 =M

[H]

LTOT =

L1 + M12 – M13 +

L2 + M12 – M23 +

L3 – M23 – M13 =

= 5 +2 –1 + 10 + 2 – 3 + 15 –3 –1 = 26 [H]

Measuring the mutual inductance?


+TOTL −TOTL

MLLLTOT 221 ++=+ MLLLTOT 221 −+=−

Measuring the mutual inductance?


+TOTL −TOTL

MLLLTOT 221 ++=+ MLLLTOT 221 −+=−

4−+ −= TOTTOT LLM

Variometer (to an antique radio)


)(

221αfM

MLLLTOT=

±+=

A bad actuator can become a good sensor


1906

The industry's "rugged" position sensor


Differential transformer


LVDT Linear Variable Differential Transformer

The secondary coils are connected in series but with opposite polarity – when the core is in the middle U = 0.

core

primary coil

secondary coilsecondary coil

LVDT design



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

LVDT principle

LVDT probe

Output signal changes phase180°°°° exactly when the core pass the middle point.


A XOR-gate kan indicate this change.

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 …



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?

IE1206 Embedded Electronics - KTH...Ex6 Le10 LC-osc, DC-motor, CCP PWM LP-filter Trafo Le12 Ex7...

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