Experiment 2

Download Report

Transcript Experiment 2

1
Electronic Instrumentation
Experiment 9
•Part A:
Simulation of a Transformer
•Part B: Making an Inductor
•Part C: Measurement of Inductance
•Part D: Making a Transformer
Inductors & Transformers




How do transformers work?
How to make an inductor?
How to measure inductance?
How to make a transformer?
18 October 2003
Electronic Instrumentation
?
2
Some Interesting Inductors

Induction Heating
18 October 2003
Electronic Instrumentation
3
Some Interesting Inductors

Induction Heating in Aerospace
18 October 2003
Electronic Instrumentation
4
Some Interesting Inductors

Induction Forming
18 October 2003
Electronic Instrumentation
5
Some Interesting Inductors
Primary
Coil
Secondary
Coil

Coin Flipper
18 October 2003
Electronic Instrumentation
6
Some Interesting Inductors

GE Genura Light
18 October 2003
Electronic Instrumentation
7
Some Interesting Transformers

A huge range in sizes
18 October 2003
Electronic Instrumentation
8
Wall Warts
18 October 2003
Electronic Instrumentation
9
Some Interesting Transformers

High Temperature Superconducting Transformer
18 October 2003
Electronic Instrumentation
10
Household Power

7200V transformed to 240V for household use
18 October 2003
Electronic Instrumentation
11
Inductors-Review

General form of I-V relationship
dI
V L
dt

For steady-state sine wave excitation
Z L  j L
18 October 2003
V  jLI
Electronic Instrumentation
12
Inductors-Review
R1
R2
50
1k
V
V1
V
VOFF = 0
VAMPL = 1
FREQ = 1k
L1
1mH
0

Simple R-L Filter
• High Pass Filter
• Corner Frequency
18 October 2003
1 R
f 
 167kHz
2 L
Electronic Instrumentation
13
Inductors-Review
1.0V
0.8V
0.6V
0.4V
0.2V
0V
1.0Hz
10Hz
V(R1:2)
100Hz
1.0KHz
10KHz
100KHz
1.0MHz
10MHz
100MHz
V(L1:1)
Frequency
18 October 2003
Electronic Instrumentation
14
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
(  0 N  rc )
L
Henries
d
2
2
where this expression only holds when the length d is
very much greater than the diameter 2rc
18 October 2003
Electronic Instrumentation
15
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
18 October 2003
Electronic Instrumentation
16
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
18 October 2003
Electronic Instrumentation
17
Making an Inductor

If the coil length is much small than the
diameter (rw is the wire radius)
8rc
L   N rc {ln(
)  2}
rw
2
Such a coil is used in the
metal detector at the right
18 October 2003
Electronic Instrumentation
18
Making an Inductor

All wires have some finite resistance. Much of the
time, this resistance is negligible when compared with
other circuit components.
l
 Resistance of a wire is given by
R
s
A
l is the wire length
A is the wire cross sectional area (rw2)
s is the wire conductivity
18 October 2003
Electronic Instrumentation
19
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
18 October 2003
Electronic Instrumentation
20
Wire Resistance

Using the Megaconverter at
http://www.megaconverter.com/Mega2/
(see course website)
18 October 2003
Electronic Instrumentation
21
Transformers
Symbol for
transformer


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
18 October 2003
Electronic Instrumentation
22
Transformers
IS
IL
Note Current
Direction




Let the current through the primary be I S
Let the current through the secondary be I L
The voltage across the primary inductor is
jLI S  jMI L
The voltage across the secondary inductor is
jLI L  jMI S
18 October 2003
Electronic Instrumentation
23
Transformers

Sum of primary voltages must equal the source
VS  RS I S  jLS I S  jMI L

Sum of secondary voltages must equal zero
0  RL I L  jLL I L  jMI S
18 October 2003
Electronic Instrumentation
24
Transformers

Note the following simplifying information for
cylindrical or toroidal inductors
2
2
(  0 N  rc )
L
Henries
d
N
2
a LN
LL  a LS
S

For k  1
M  LS LL  a LS
18 October 2003
Electronic Instrumentation
2
2
L
 L
2
a2
25
Transformers

Cylinders (solenoids)

Toroids
18 October 2003
Electronic Instrumentation
26
18 October 2003
Electronic Instrumentation
27
Transformers

Transformers are designed so that the inductive
impedances Z L  jL are much larger than
any resistance in the circuit. Then, from the
second loop equation
0  RL I L  jLL I L  jMI S
jLL I L  jMI S
18 October 2003
N L IL  N S IS
Electronic Instrumentation
28
Transformers

The voltages across the primary and secondary
terminals of the transformer are related by
N S VL  N LVS
Note that the coil with more turns has the larger
voltage
18 October 2003
Electronic Instrumentation
29
Transformers

The input impedance of the primary winding
reflects the load impedance. It can be
determined from the loop equations
Z IN
V
 S

L
L
S
L

R

j

L

S
S
IS
 RL  jLL 
2
2
Z IN
N

 R
S


NL L

18 October 2003
Electronic Instrumentation
30
Transformer Rectifier
R1
V1
TX1
5
V
VOFF = 0
VAMPL = 120
FREQ = 60
D1
D1N4148
D4
D1N4148
D3
D1N4148
D2
33uF
R2
1k
D1N4148
0

V
C2
0
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.
18 October 2003
Electronic Instrumentation
31
Transformer Rectifier
120V
Filtered
80V
40V
-0V
Unfiltered
-40V
-80V
-120V
10.000s
10.005s
V(R1:2)
V(R3:2)
10.010s
V(D2:2)
10.015s
10.020s
10.025s
10.030s
10.035s
10.040s
10.045s 10.050s
V(R4:1)
Time
18 October 2003
Electronic Instrumentation
32
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.
18 October 2003
Electronic Instrumentation
33
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.
18 October 2003
Electronic Instrumentation
34
Determining Inductance
0  1

LC
f0  1
2 LC
Reminder—The parallel combination of L and
C goes to infinity at resonance.
jL 1 jC


jL
Z|| 

2
jL   1 jC 1   LC


18 October 2003
Electronic Instrumentation
35
L1
R1
100uH
50
V
V1
VOFF = 0
VAMPL = 1
FREQ = 1k
C1
.68uF
V
R2
50
0
1.0V
0.8V
0.6V
0.4V
0.2V
0V
1.0KHz
V(C1:1)
3.0KHz
10KHz
30KHz
100KHz
300KHz
1.0MHz
V(C1:2)
Frequency
18 October 2003
Electronic Instrumentation
36

Even 1 ohm of resistance in the coil can spoil
this response somewhat
1.0V
0.5V
SEL>>
0V
V(R3:2)
V(R4:1)
1.0V
0.5V
0V
1.0KHz
V(C1:1)
3.0KHz
10KHz
30KHz
100KHz
300KHz
1.0MHz
V(C1:2)
Frequency
18 October 2003
Electronic Instrumentation
37
Project 3: Beakman’s Motor

The coil in this motor can be characterized in
the same way
18 October 2003
Electronic Instrumentation
38
Optional Project: Paperclip
Launcher

A small disposable flash camera can be used to
build a magnetic paperclip launcher
18 October 2003
Electronic Instrumentation
39