Download 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?
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Some Interesting Inductors

Induction Heating
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Some Interesting Inductors

Induction Heating in Aerospace
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Some Interesting Inductors

Induction Forming
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Some Interesting Inductors
Primary
Coil
Secondary
Coil

Coin Flipper
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Some Interesting Inductors

GE Genura Light
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Some Interesting Transformers

A huge range in sizes
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Wall Warts
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Some Interesting Transformers

High Temperature Superconducting Transformer
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Household Power

7200V transformed to 240V for household use
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Inductors-Review

General form of I-V relationship
dI
V L
dt

For steady-state sine wave excitation
Z L  jL
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V  jLI
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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
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1 R
f 
 167kHz
2 L
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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
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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
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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
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Some Typical Permeabilities
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
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
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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
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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
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Some Typical Conductivities
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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
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Wire Resistance

Using the Megaconverter at
http://www.megaconverter.com/Mega2/
(see course website)
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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
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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
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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
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Transformers

Note the following simplifying information for
cylindrical or toroidal inductors
2
2
(  0 N  rc )
L
Henries
d
NL
2
a
LL  a LS
N
S

For k  1
M  LS LL  a LS
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2
L
 L
2
a2
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Transformers

Cylinders (solenoids)

Toroids
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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
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N L IL  N S IS
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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
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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
 RS  jLS 
IS
 RL  jLL 
2
2
Z IN
N

  S N  RL

L
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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.
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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
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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.
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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.
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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


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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
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
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
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Project 3: Beakman’s Motor

The coil in this motor can be characterized in
the same way
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Optional Project: Paperclip
Launcher

A small disposable flash camera can be used to
build a magnetic paperclip launcher
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