1. Experiment 3 Part A: Making an Inductor
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Experiment 3
Part A: Making an Inductor
Part B: Measurement of Inductance
Part C: Simulation of a Transformer
Part D: Making a Transformer

2. Review RLC and Resonance
How can the transfer function be greater than 1?
At resonance, impedance value is a minimum
At resonance, impedance of inductor and capacitor cancel each other out (equal in magnitude, phase is opposite)
So circuit is “purely” resistive at resonance
H depends on the position of Vout
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3. Review RLC and Resonance
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4. Inductors & Transformers
How do transformers work?
How to make an inductor?
How to measure inductance?
How to make a transformer? ?
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5. Electronic Instrumentation
Part A
Inductors Review
Calculating Inductance
Calculating Resistance
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6. Electronic Instrumentation
Inductors-Review
General form of I-V relationship
For steady-state sine wave excitation
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7. 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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8. Electronic Instrumentation
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
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9. Electronic Instrumentation
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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10. Some Typical Permeabilities
Air x10-6 H/m
Ferrite U M x10-4 H/m
Nickel x10-4 H/m
Iron x10-3 H/m
Ferrite T x10-2 H/m
Silicon GO steel x10-2 H/m
supermalloy 1.26 H/m
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Electronic Instrumentation

11. Electronic Instrumentation
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
Form
Diameter
=2rc
Coil
Length (d)
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12. 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 (prw2)
s is the wire conductivity
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13. 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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14. Electronic Instrumentation
Wire Resistance
Using the Megaconverter at
(see course website)
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15. 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.
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16. Electronic Instrumentation
In Class Problem #1
Vout
Vin
What is ZLC (assuming R2 is very small)?
What does R2 represent?
What is its transfer function (equation)?
What is H at low and high frequencies?
What is H at the resonant frequency, ω0?
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17. Determining Inductance
Vin
Vout
Reminder—The parallel combination of L and C goes to infinity at resonance. (Assuming R2 is small.)
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18. Determining Inductance
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19. Electronic Instrumentation
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20. Electronic Instrumentation
Even 1 ohm of resistance in the coil can spoil this response somewhat
Coil resistance small
Coil resistance of a few Ohms
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21. Electronic Instrumentation
Part C
Examples of Transformers
Transformer Equations
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22. Electronic Instrumentation
Transformers
Cylinders (solenoids)
Toroids
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23. Transformer Equations
Symbol for transformer
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24. 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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25. Electronic Instrumentation
Transformers
Assumption 1: Both Inductor Coils must have similar properties: same coil radius, same core material, and same length.
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26. Electronic Instrumentation
Transformers IS IL
Note Current Direction
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
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27. Electronic Instrumentation
Transformers
Sum of primary voltages must equal the source
Sum of secondary voltages must equal zero
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28. Electronic Instrumentation
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
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29. Electronic Instrumentation
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,
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30. Electronic Instrumentation
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]
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31. Electronic Instrumentation
Transformers
Find a common denominator and simplify
By Assumption 2, RL is small compared to the impedance of the transformer, so
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32. Electronic Instrumentation
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
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33. Transformer Equations
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34. Electronic Instrumentation
In Class Problem #2
Ns:NL
VGEN=120V
RL=20 Ω
NL=1
NS=12 Vs VL
VGEN
1. Find VL if RS~0
Find VL if Rs= 1 k Ω
Hint: Is VGEN = VS? Under what conditions is this not true? How would you find VS? Need Zin Is
Zin Vs VL
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35. Electronic Instrumentation
Part D
Step-up and Step-down transformers
Build a transformer
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36. Step-up and Step-down Transformers
Step-up Transformer
Step-down Transformer
Note that power (P=VI) is conserved in both cases.
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37. Electronic Instrumentation
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?
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38. Some Interesting Inductors
Induction Heating
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39. Some Interesting Inductors
Induction Heating in Aerospace
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40. Some Interesting Inductors
Induction Forming
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41. Some Interesting Inductors
Coin Flipper
Flash camera circuits charge 6 capacitors
Large current in primary coil
Large current induced in coin (larger by ratio of turns)
Current in coin creates electromagnet of opposite polarity (Repel!)
Primary
Coil
Secondary
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42. Some Interesting Inductors
GE Genura Light
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43. Some Interesting Transformers
A huge range in sizes
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44. Electronic Instrumentation
Household Power
7200V transformed to 240V for household use
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45. Electronic Instrumentation
Wall Warts
Transformer
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46. Electronic Instrumentation
In Class Problem #1
Vout
Vin
What is ZLC (assuming R2 is very small)?
What does R2 represent?
What is its transfer function (equation)?
What is H at low and high frequencies?
What is H at the resonant frequency, ω0?
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Electronic Instrumentation

47. Electronic Instrumentation
In Class Problem #1
Vout
Vin
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48. Electronic Instrumentation
In Class Problem #1
Vout
Vin
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49. Electronic Instrumentation
In Class Problem #1
What is H at low frequencies?
This can be determined from the magnitude so
Remember these steps!
Take the lowest power in the numerator and denominator of the equation
Write down x1, y1, x2, and y2 (can do this in your head)
Use the magnitude equation (square and square root numerator and denominator)
Simplify (this is the answer if approaching 0)
Take limit as it approaches 0 (this is the answer at 0)
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Electronic Instrumentation

50. Electronic Instrumentation
In Class Problem #1
What is H at low frequencies?
Step 1: Take lowest power in numerator and denominator
Step 2: Find x1, y1, x2, y2
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Electronic Instrumentation

51. Electronic Instrumentation
In Class Problem #1
What is H at low frequencies?
Step 3: Use the magnitude equation
Step 4: Simplify
Step 5: Take limit as ω approaches 0
Answer is that it becomes very small or 0
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Electronic Instrumentation

52. Electronic Instrumentation
In Class Problem #1
What is H at high frequencies?
This can be determined from the magnitude so
Remember these steps!
Take the highest power in the numerator and denominator of the equation
Write down x1, y1, x2, and y2 (can do this in your head)
Use the magnitude equation (square and square root numerator and denominator)
Simplify (this is the answer if approaching ∞)
Take limit as it approaches 0 (this is the answer at ∞)
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Electronic Instrumentation

53. Electronic Instrumentation
In Class Problem #1
What is H at high frequencies?
Step 1: Take highest power in numerator and denominator
Step 2: Find x1, y1, x2, y2
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Electronic Instrumentation

54. Electronic Instrumentation
In Class Problem #1
What is H at high frequencies?
Step 3: Use the magnitude equation
Step 4: Simplify
Step 5: Take limit as ω approaches ∞
Answer is that it becomes very small or 0
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55. Electronic Instrumentation
In Class Problem #1
What is H at the resonant frequency, ω0?
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56. Electronic Instrumentation
In Class Problem #2
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57. Electronic Instrumentation
In Class Problem #2
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