How things work: an overview of astronomical instrumentation
Electronic Instrumentation - ECSE · 10/1/2014 Electronic Instrumentation 2 Inductors &...
Transcript of Electronic Instrumentation - ECSE · 10/1/2014 Electronic Instrumentation 2 Inductors &...
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Electronic Instrumentation
10/1/2014 1
Experiment 3 •Part A: Making an Inductor •Part B: Measurement of Inductance •Part C: Simulation of a Transformer •Part D: Making a Transformer
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10/1/2014 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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10/1/2014 Electronic Instrumentation 3
Part A
Inductors Review Calculating Inductance Calculating Resistance
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10/1/2014 Electronic Instrumentation 4
Inductors-Review
General form of I-V relationship
For steady-state sine wave excitation
V L dIdt
=
V j LI= ωZ j LL = ω
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10/1/2014 Electronic Instrumentation 5
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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10/1/2014 Electronic Instrumentation 6
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 πµ=
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10/1/2014 Electronic Instrumentation 7
Making an Inductor
Note that the constant µo = 4π x 10-7 H/m is required to have inductance in Henries (named after Joseph Henry of Albany)
For magnetic materials, we use µ instead, which can typically be 105 times larger for materials like iron
µ is called the permeability
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10/1/2014 Electronic Instrumentation 8
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
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10/1/2014 Electronic Instrumentation 9
Making an Inductor
If the coil length is much smaller 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 µ
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10/1/2014 Electronic Instrumentation 10
Calculating Resistance 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 (πrw
2) σ is the wire conductivity
AlR
σ=
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10/1/2014 Electronic Instrumentation 11
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 Siemen = 1/ohm
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10/1/2014 Electronic Instrumentation 12
Wire Resistance
Using the Megaconverter at http://www.megaconverter.com/Mega2/
(see course website)
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10/1/2014 Electronic Instrumentation 13
Part B: Measuring Inductance with a Circuit
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.
R1
47
C11u
L1
1
2
R2
0
C21u
V1
FREQ = 1kHzVAMPL = 0.2VOFF = 0
AC = .2
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10/1/2014 Electronic Instrumentation 14
Determining Inductance
Reminder—The parallel combination of L and C goes to infinity at resonance. (Assuming R2 is small.)
Zj L j C
j L j C
j LLC|| =
+
=−
ω ω
ω ω
ωω
1
1 1 2
LCf
LC πω
211
00 ==Vout Vin
R1
47
C11u
L1
1
2
R2
0
C21u
V1
FREQ = 1kHzVAMPL = 0.2VOFF = 0
AC = .2
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10/1/2014 Electronic Instrumentation 15
Determining Inductance
1,,
1
)1(1
1
00
2
||
||
==
===
+−=
+=
LjLjHresonanceat
smallR
LjHH
LjLCRLjH
ZRZ
H
LOHI
ωωω
ωωω
ω
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10/1/2014 Electronic Instrumentation 16
R1
47
C11u
L1
1
2
R2
0
C21u
V1
FREQ = 1kHzVAMPL = 0.2VOFF = 0
AC = .2
V
V
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10/1/2014 Electronic Instrumentation 17
Even 1 ohm of resistance in the coil can spoil this response somewhat
Coil resistance of a few Ohms
Coil resistance small
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10/1/2014 Electronic Instrumentation 18
Part C
Examples of Transformers Transformer Equations
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10/1/2014 Electronic Instrumentation 19
Transformers
Cylinders (solenoids)
Toroids
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10/1/2014 Electronic Instrumentation 20
Transformer Equations
2aRZ
II
LL
VV
NNa L
inL
S
S
L
S
L
S
L =====
Symbol for transformer
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10/1/2014 Electronic Instrumentation 21
Deriving Transformer Equations
Note that a transformer has 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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10/1/2014 Electronic Instrumentation 22
Transformers
Assumption 1: Both Inductor Coils must have similar properties: same coil radius, same core material, and same length.
S
L
S
L
LLa
NNalet =∴=2
2
220
220
)(
)(
S
L
cS
cL
S
L
NN
drN
drN
LL
==πµ
πµ
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10/1/2014 Electronic Instrumentation 23
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
IS
IL
j LI j MIS Lω ω−
j LI j MIL Sω ω−
IS IL Note Current Direction
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10/1/2014 Electronic Instrumentation 24
Transformers
Sum of primary voltages must equal the source
Sum of secondary voltages must equal zero
V R I j L I j MIS S S S S L= + −ω ω
0 = + −R I j L I j MIL L L L Sω ω
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10/1/2014 Electronic Instrumentation 25
Transformers
Assumption 2: The transformer is designed such that the impedances are much larger than any resistance in the circuit. Then, from the second loop equation
LjZ ω=
0 = + −R I j L I j MIL L L L Sω ω
j L I j MIL L Sω ω≈ 2222SLL IMIL ≈
LS
L
LM
II
≈∴
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10/1/2014 Electronic Instrumentation 26
Transformers k is the coupling coefficient
• If k=1, there is perfect coupling. • k is usually a little less than 1 in a good transformer.
Assumption 3: Assume perfect coupling (k=1)
We know M2=k2 LS LL= LS LL and
Therefore,
S
L
LLa =
aLLs
LLL
LM
II
LL
LS
LS
L 1===≈∴
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10/1/2014 Electronic Instrumentation 27
Transformers
The input impedance of the primary winding reflects the load impedance.
It can be determined from the loop equations • 1] • 2]
Divide by 1] IS. Substitute 2] and M into 1]
StotalinL RZZZS
−==
( )Z VI R j L L L
R j LINS
SS S
S L
L L= − = + +ω ω
ω2
V R I j L I j MIS S S S S L= + −ω ω0 = + −R I j L I j MIL L L L Sω ω
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10/1/2014 Electronic Instrumentation 28
Transformers
Find a common denominator and simplify
By Assumption 2, RL is small compared to the impedance of the transformer, so
LL
LSIN RLj
RLjZ+
=ωω
2aR
LRLZ L
L
LSIN ==
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10/1/2014 Electronic Instrumentation 29
Transformers
It can also be shown that 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.
Detailed derivation of transformer equations http://hibp.ecse.rpi.edu/~connor/education/transformer_notes.pdf
N V N VS L L S=
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10/1/2014 Electronic Instrumentation 30
Transformer Equations
2aRZ
II
LL
VV
NNa L
inL
S
S
L
S
L
S
L =====
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10/1/2014 Electronic Instrumentation 31
Part D
Step-up and Step-down transformers Build a transformer
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10/1/2014 Electronic Instrumentation 32
Step-up and Step-down Transformers Step-up Transformer
12
12
12
12
LL
IIVVNN
>
<>>
Step-down Transformer
12
12
12
12
LL
IIVVNN
<
><<
Note that power (P=VI) is conserved in both cases.
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10/1/2014 Electronic Instrumentation 33
Build a Transformer Wind secondary coil directly over primary coil “Try” for half the number of turns At what frequencies does it work as expected with
respect to voltage? When is ωL >> R?
S
L
S
L
VV
NNa ==
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10/1/2014 Electronic Instrumentation 34
Some Interesting Inductors
Induction Heating
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10/1/2014 Electronic Instrumentation 35
Some Interesting Inductors
Induction Heating in Aerospace
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10/1/2014 Electronic Instrumentation 36
Some Interesting Inductors
Induction Forming
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10/1/2014 Electronic Instrumentation 37
Some Interesting Inductors
Coin Flipper
Primary
Coil
Secondary
Coil
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10/1/2014 Electronic Instrumentation 38
Some Interesting Inductors
GE Genura Light
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10/1/2014 Electronic Instrumentation 39
Some Interesting Transformers
A huge range in sizes
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10/1/2014 Electronic Instrumentation 40
Some Interesting Transformers
High Temperature Superconducting Transformer
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10/1/2014 Electronic Instrumentation 41
Household Power
7200V transformed to 240V for household use
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10/1/2014 Electronic Instrumentation 42
Wall Warts
Transformer