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Experiment 3 Part A: Making an Inductor
11/13/2018 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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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 11/13/2018 Electronic Instrumentation
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Review RLC and Resonance
11/13/2018 Electronic Instrumentation
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Inductors & Transformers
How do transformers work? How to make an inductor? How to measure inductance? How to make a transformer? ? 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Part A Inductors Review Calculating Inductance Calculating Resistance 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Inductors-Review General form of I-V relationship For steady-state sine wave excitation 11/13/2018 Electronic Instrumentation
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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. 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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) 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Wire Resistance Using the Megaconverter at (see course website) 11/13/2018 Electronic Instrumentation
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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. 11/13/2018 Electronic Instrumentation
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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? 11/13/2018 Electronic Instrumentation
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Determining Inductance
Vin Vout Reminder—The parallel combination of L and C goes to infinity at resonance. (Assuming R2 is small.) 11/13/2018 Electronic Instrumentation
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Determining Inductance
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Electronic Instrumentation
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Electronic Instrumentation
Even 1 ohm of resistance in the coil can spoil this response somewhat Coil resistance small Coil resistance of a few Ohms 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Part C Examples of Transformers Transformer Equations 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Transformers Cylinders (solenoids) Toroids 11/13/2018 Electronic Instrumentation
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Transformer Equations
Symbol for transformer 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Transformers Assumption 1: Both Inductor Coils must have similar properties: same coil radius, same core material, and same length. 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Transformers Sum of primary voltages must equal the source Sum of secondary voltages must equal zero 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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, 11/13/2018 Electronic Instrumentation
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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] 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Transformers Find a common denominator and simplify By Assumption 2, RL is small compared to the impedance of the transformer, so 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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Transformer Equations
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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 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Part D Step-up and Step-down transformers Build a transformer 11/13/2018 Electronic Instrumentation
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Step-up and Step-down Transformers
Step-up Transformer Step-down Transformer Note that power (P=VI) is conserved in both cases. 11/13/2018 Electronic Instrumentation
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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? 11/13/2018 Electronic Instrumentation
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Some Interesting Inductors
Induction Heating 11/13/2018 Electronic Instrumentation
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Some Interesting Inductors
Induction Heating in Aerospace 11/13/2018 Electronic Instrumentation
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Some Interesting Inductors
Induction Forming 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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Some Interesting Inductors
GE Genura Light 11/13/2018 Electronic Instrumentation
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Some Interesting Transformers
A huge range in sizes 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Household Power 7200V transformed to 240V for household use 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
Wall Warts Transformer 11/13/2018 Electronic Instrumentation
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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? 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
In Class Problem #1 Vout Vin 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
In Class Problem #1 Vout Vin 11/13/2018 Electronic Instrumentation
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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) 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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 ∞) 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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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 11/13/2018 Electronic Instrumentation
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Electronic Instrumentation
In Class Problem #1 What is H at the resonant frequency, ω0? 11/13/2018 Electronic Instrumentation
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In Class Problem #2 11/13/2018 Electronic Instrumentation
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In Class Problem #2 11/13/2018 Electronic Instrumentation
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