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Experiment 3

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  1. 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 http://ecow.engr.wisc.edu/cgi-bin/getbig/ece/271/allie/labmanuals/1271l1sp03.doc Electronic Instrumentation

  3. Review RLC and Resonance http://ecow.engr.wisc.edu/cgi-bin/getbig/ece/271/allie/labmanuals/1271l1sp03.doc Electronic Instrumentation

  4. Inductors & Transformers • How do transformers work? • How to make an inductor? • How to measure inductance? • How to make a transformer? ? Electronic Instrumentation

  5. Part A • Inductors Review • Calculating Inductance • Calculating Resistance Electronic Instrumentation

  6. Inductors-Review • General form of I-V relationship • For steady-state sine wave excitation Electronic Instrumentation

  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. Electronic Instrumentation

  8. 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 Electronic Instrumentation

  9. 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 Electronic Instrumentation

  10. 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 Electronic Instrumentation

  11. Making an Inductor • If the coil length is much smaller than the diameter (rwis the wire radius) Such a coil is used in the metal detector at the right Form Diameter =2rc Coil Length (d) Electronic Instrumentation

  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 Electronic Instrumentation

  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 Electronic Instrumentation

  14. Wire Resistance • Using the Megaconverter at http://www.megaconverter.com/Mega2/ (see course website) Electronic Instrumentation

  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. Electronic Instrumentation

  16. 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? Electronic Instrumentation

  17. Determining Inductance Vin Vout • Reminder—The parallel combination of L and C goes to infinity at resonance. (Assuming R2 is small.) Electronic Instrumentation

  18. Determining Inductance Electronic Instrumentation

  19. Electronic Instrumentation

  20. Even 1 ohm of resistance in the coil can spoil this response somewhat Coil resistance small Coil resistance of a few Ohms Electronic Instrumentation

  21. Part C • Examples of Transformers • Transformer Equations Electronic Instrumentation

  22. Transformers • Cylinders (solenoids) • Toroids Electronic Instrumentation

  23. Transformer Equations Symbol for transformer Electronic Instrumentation

  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 Electronic Instrumentation

  25. Transformers • Assumption 1: Both Inductor Coils must have similar properties: same coil radius, same core material, and same length. Electronic Instrumentation

  26. 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 Electronic Instrumentation

  27. Transformers • Sum of primary voltages must equal the source • Sum of secondary voltages must equal zero Electronic Instrumentation

  28. 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 Electronic Instrumentation

  29. 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, Electronic Instrumentation

  30. 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] Electronic Instrumentation

  31. Transformers • Find a common denominator and simplify • By Assumption 2, RL is small compared to the impedance of the transformer, so Electronic Instrumentation

  32. 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 Electronic Instrumentation

  33. Transformer Equations Electronic Instrumentation

  34. 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 Electronic Instrumentation

  35. Part D • Step-up and Step-down transformers • Build a transformer Electronic Instrumentation

  36. Step-up and Step-down Transformers Step-down Transformer Step-up Transformer Note that power (P=VI) is conserved in both cases. Electronic Instrumentation

  37. 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? Electronic Instrumentation

  38. Some Interesting Inductors • Induction Heating Electronic Instrumentation

  39. Some Interesting Inductors • Induction Heating in Aerospace Electronic Instrumentation

  40. Some Interesting Inductors • Induction Forming Electronic Instrumentation

  41. Primary Coil Secondary Coil 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!) Electronic Instrumentation

  42. Some Interesting Inductors • GE Genura Light Electronic Instrumentation

  43. Some Interesting Transformers • A huge range in sizes Electronic Instrumentation

  44. Household Power • 7200V transformed to 240V for household use Electronic Instrumentation

  45. Wall Warts Transformer Electronic Instrumentation

  46. 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? Electronic Instrumentation

  47. In Class Problem #1 Vout Vin Electronic Instrumentation

  48. In Class Problem #1 Vout Vin Electronic Instrumentation

  49. 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) Electronic Instrumentation

  50. 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 Electronic Instrumentation