electronic instrumentation 1 experiment 9 part a: simulation of a transformer part b: making an...

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Electronic InstrumentationExperiment 9

•Part A: Simulation of a Transformer•Part B: Making an Inductor•Part C: Measurement of Inductance•Part D: Making a Transformer

18 October 2003 Electronic Instrumentation 2

Inductors & Transformers

How do transformers work? How to make an inductor? How to measure inductance? How to make a transformer?

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Some Interesting Inductors

Induction Heating



Induction Heating in Aerospace

http://www.ameritherm.com/videoindex.html



Induction Forming



Coin Flipper

Primary

Coil

Secondary

Coil



GE Genura Light


Some Interesting Transformers

A huge range in sizes


Wall Warts


Some Interesting Transformers

High Temperature Superconducting Transformer


Household Power

7200V transformed to 240V for household use


Inductors-Review

General form of I-V relationship

For steady-state sine wave excitation

V Ld I

d t

V j L I Z j LL


Inductors-Review

Simple R-L Filter• High Pass Filter• Corner Frequency

R2

1k

0

V VL1

1mH

R1

50

V1

FREQ = 1kVAMPL = 1VOFF = 0

fR

LkH z

1

21 6 7


Inductors-Review

Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz 100MHzV(R1:2) V(L1:1)

0V

0.2V

0.4V

0.6V

0.8V

1.0V


Making an Inductor

For a simple cylindrical inductor (called a solenoid), we wind N turns of wire around a cylindrical form. The inductance is ideally given by

where this expression only holds when the length d is very much greater than the diameter 2rc

Henriesd

rNL c )( 22

0


Making an Inductor

Note that the constant o = 4 x 10-7 H/m is

required to have inductance in Henries (named after Joseph Henry of Albany)

For magnetic materials, we use instead, which can typically be 105 times larger for materials like iron

is called the permeability


Some Typical Permeabilities

Air 1.257x10-6 H/m Ferrite U M33 9.42x10-4 H/m Nickel 7.54x10-4 H/m Iron 6.28x10-3 H/m Ferrite T38 1.26x10-2 H/m Silicon GO steel 5.03x10-2 H/m supermalloy 1.26 H/m


Making an Inductor

If the coil length is much small than the diameter (rw is the wire radius)

Such a coil is used in the metal detector at the right

}2)8

{ln(2 w

cc r

rrNL


Making an Inductor

All wires have some finite resistance. Much of the time, this resistance is negligible when compared with other circuit components.

Resistance of a wire is given by

l is the wire length

A is the wire cross sectional area (rw2)

is the wire conductivity

A

lR


Some Typical Conductivities

Silver 6.17x107 Siemens/m Copper 5.8x107 S/m Aluminum 3.72x107 S/m Iron 1x107 S/m Sea Water 5 S/m Fresh Water 25x10-6 S/m Teflon 1x10-20 S/m


Wire Resistance

Using the Megaconverter at http://www.megaconverter.com/Mega2/

(see course website)

http://www.megaconverter.com/Mega2/


Transformers

Note that for a transformer, the symbol shows two inductors. One is the primary (source end) and one is the secondary (load end): LS & LL

The inductors work as expected, but they also couple to one another through their mutual inductance: M2=k2 LS LL

Symbol for transformer


Transformers

Let the current through the primary be Let the current through the secondary be The voltage across the primary inductor is

The voltage across the secondary inductor is

I S

I L

j L I j M IS L

j L I j M IL S

IS IL

Note Current Direction


Transformers

Sum of primary voltages must equal the source

Sum of secondary voltages must equal zero

V R I j L I j M IS S S S S L

0 R I j L I j M IL L L L S


Transformers

Note the following simplifying information for cylindrical or toroidal inductors

For k 1

L a LL S 2 a NN

L

S

Henriesd

rNL c )( 22

0

M L L a L LaS L S

L 2 22

2


Transformers

Cylinders (solenoids)

Toroids


Transformers

Transformers are designed so that the inductive impedances are much larger than any resistance in the circuit. Then, from the second loop equation

Z j LL

0 R I j L I j M IL L L L S

j L I j M IL L S N I N IL L S S


Transformers

The voltages across the primary and secondary terminals of the transformer are related by

Note that the coil with more turns has the larger voltage

N V N VS L L S


Transformers

The input impedance of the primary winding reflects the load impedance. It can be determined from the loop equations

Z VI R j L L L

R j LINS

SS S

S L

L L

2

Z NN RIN

S

LL

2


Transformer Rectifier

Adding a full wave rectifier to the transformer makes a low voltage DC power supply, like the wall warts used on most of the electronics we buy these days.

D2

D1N4148

V

0

V1

FREQ = 60VAMPL = 120VOFF = 0

R1

5

TX1

D4

D1N4148

0

R2

1k

D3

D1N4148

D1

D1N4148C2

33uF

V


Transformer Rectifier

Time

10.000s 10.005s 10.010s 10.015s 10.020s 10.025s 10.030s 10.035s 10.040s 10.045s 10.050sV(R1:2) V(R3:2) V(D2:2) V(R4:1)

-120V

-80V

-40V

-0V

40V

80V

120V

Filtered

Unfiltered


Determining Inductance Calculate it from dimensions and material

properties Measure using commercial bridge (expensive

device) Infer inductance from response of a circuit.

This latter approach is the cheapest and usually the simplest to apply. Most of the time, we can determine circuit parameters from circuit performance.


Determining Inductance

For this circuit, a resonance should occur for the parallel combination of the unknown inductor and the known capacitor. If we find this frequency, we can find the inductance.


Determining Inductance

Reminder—The parallel combination of L and C goes to infinity at resonance.

Zj L j C

j L j C

j L

L C||

1

1 1 2

LCf

LC

211

00


R1

50 C1

.68uF

V1

FREQ = 1kVAMPL = 1VOFF = 0

V

0

L1

100uH

R2

50

V

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHz 300KHz 1.0MHzV(C1:1) V(C1:2)

0V

0.2V

0.4V

0.6V

0.8V

1.0V


Even 1 ohm of resistance in the coil can spoil this response somewhat

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHz 300KHz 1.0MHzV(C1:1) V(C1:2)

0V

0.5V

1.0V

V(R3:2) V(R4:1)0V

0.5V

1.0V

SEL>>


Project 3: Beakman’s Motor

The coil in this motor can be characterized in the same way


Optional Project: Paperclip Launcher

A small disposable flash camera can be used to build a magnetic paperclip launcher

electronic instrumentation 1 experiment 9 part a: simulation of a transformer part b: making an...

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