Electronic Instrumentation

Size: px

Start display at page:

Download "Electronic Instrumentation"

Thomas Stafford
5 years ago
Views:

1 10/1/014 1 Electronic Instrumentation Experiment 3 Part A: Making an Inductor Part B: Measurement of Inductance Part C: imulation of a Transformer Part D: Making a Transformer

2 Inductors & Transformers How do transformers work? How to make an inductor? How to measure inductance? How to make a transformer?? 10/1/014 Electronic Instrumentation

3 Part A Inductors Review Calculating Inductance Calculating Resistance 10/1/014 Electronic Instrumentation 3

4 Inductors-Review General form of I-V relationship V di dt For steady-state sine wave excitation Z j ω V jωi 10/1/014 Electronic Instrumentation 4

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. 10/1/014 Electronic Instrumentation 5

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 ( µ 0 N π r d c ) Henries where this expression only holds when the length d is very much greater than the diameter r c 10/1/014 Electronic Instrumentation 6

7 Making an Inductor Note that the constant µ o 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 10 5 times larger for materials like iron µ is called the permeability 10/1/014 Electronic Instrumentation 7

8 ome Typical Permeabilities Air 1.57x10-6 H/m Ferrite U M33 9.4x10-4 H/m Nickel 7.54x10-4 H/m Iron 6.8x10-3 H/m Ferrite T38 1.6x10 - H/m ilicon GO steel 5.03x10 - H/m supermalloy 1.6 H/m 10/1/014 Electronic Instrumentation 8

9 Making an Inductor If the coil length is much smaller than the diameter (r w is the wire radius) µ N r c 8r {ln( r } uch a coil is used in the metal detector at the right w c ) 10/1/014 Electronic Instrumentation 9

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 (πr w ) σ is the wire conductivity R σ l A 10/1/014 Electronic Instrumentation 10

11 ome Typical Conductivities ilver 6.17x10 7 iemens/m Copper 5.8x10 7 /m Aluminum 3.7x10 7 /m Iron 1x10 7 /m ea Water 5 /m Fresh Water 5x10-6 /m Teflon 1x10-0 /m iemen 1/ohm 10/1/014 Electronic Instrumentation 11

Wire Resistance Using the Megaconverter at http://www.megaconverter.

12 Wire Resistance Using the Megaconverter at (see course website) 10/1/014 Electronic Instrumentation 1

13 Part B: Measuring Inductance with a Circuit R1 47 R FREQ 1kHz VAMP 0. VOFF 0 AC. V1 C 1u C1 1u 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. 10/1/014 Electronic Instrumentation 13

14 Determining Inductance Vin FREQ 1kHz VAMP 0. VOFF 0 AC. V1 R1 47 C 1u C1 1u 1 Vout R 1 ω C f 1 π C Reminder The parallel combination of and C goes to infinity at resonance. (Assuming R is small.) Z 0 jω 1 jωc jω j + C ω 1 1 ω jωc 10/1/014 Electronic Instrumentation 14

15 10/1/014 Electronic Instrumentation 15 Determining Inductance 1,, 1 ) 1( j j H resonance at small R j H H j C R j H Z R Z H O HI ω ω ω ω ω ω ω

16 V R1 47 V R VOFF 0 VAMP 0. FREQ 1kHz AC. V1 C 1u C1 1u /1/014 Electronic Instrumentation 16

17 Even 1 ohm of resistance in the coil can spoil this response somewhat Coil resistance small Coil resistance of a few Ohms 10/1/014 Electronic Instrumentation 17

18 Part C Examples of Transformers Transformer Equations 10/1/014 Electronic Instrumentation 18

19 Transformers Cylinders (solenoids) Toroids 10/1/014 Electronic Instrumentation 19

20 Transformer Equations ymbol for transformer a N V I Z in N V I R a 10/1/014 Electronic Instrumentation 0

21 Deriving Transformer Equations Note that a transformer has two inductors. One is the primary (source end) and one is the secondary (load end): & The inductors work as expected, but they also couple to one another through their mutual inductance: M k 10/1/014 Electronic Instrumentation 1

22 10/1/014 Electronic Instrumentation Transformers Assumption 1: Both Inductor Coils must have similar properties: same coil radius, same core material, and same length. a N N a let 0 0 ) ( ) ( c c N N d r N d r N π µ π µ

23 Transformers Note Current Direction et the current through the primary be I et the current through the secondary be I The voltage across the primary inductor is jωi jωmi The voltage across the secondary inductor is jωi jωmi I I 10/1/014 Electronic Instrumentation 3

24 Transformers um of primary voltages must equal the source V R I + jω I jωmi um of secondary voltages must equal zero 0 R I + jω I jωmi 10/1/014 Electronic Instrumentation 4

25 Transformers Assumption : The transformer is designed such that the impedances Z jω are much larger than any resistance in the circuit. Then, from the second loop equation jω I 0 R I + jω I jωmi jωmi I I M I M I 10/1/014 Electronic Instrumentation 5

26 Transformers k is the coupling coefficient If k1, there is perfect coupling. k is usually a little less than 1 in a good transformer. Assumption 3: Assume perfect coupling (k1) We know M k and a Therefore, I I M s 1 a 10/1/014 Electronic Instrumentation 6

27 Transformers The input impedance of the primary winding reflects the load impedance. Z Z R It can be determined from the loop equations V R I + jω I jωmi 1] ] Z Divide by 1] I. ubstitute ] and M into 1] Z IN 0 R I + jω I jωmi V ω I R jω + in total ( R + jω ) 10/1/014 Electronic Instrumentation 7

28 Transformers Find a common denominator and simplify Z IN jω R j ω + R By Assumption, R is small compared to the impedance of the transformer, so Z R 10/1/014 Electronic Instrumentation 8 IN R a

29 Transformers It can also be shown that the voltages across the primary and secondary terminals of the transformer are related by N V Note that the coil with more turns has the larger voltage. Detailed derivation of transformer equations N V 10/1/014 Electronic Instrumentation 9

30 Transformer Equations a N V I Z in N V I R a 10/1/014 Electronic Instrumentation 30

31 Part D tep-up and tep-down transformers Build a transformer 10/1/014 Electronic Instrumentation 31

32 10/1/014 Electronic Instrumentation 3 tep-up and tep-down Transformers tep-up Transformer I I V V N N > < > > tep-down Transformer I I V V N N < > < < Note that power (PVI) is conserved in both cases.

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 ω >> R? N V a N V 10/1/014 Electronic Instrumentation 33

34 ome Interesting Inductors Induction Heating 10/1/014 Electronic Instrumentation 34

35 ome Interesting Inductors Induction Heating in Aerospace 10/1/014 Electronic Instrumentation 35

36 ome Interesting Inductors Induction Forming 10/1/014 Electronic Instrumentation 36

37 ome Interesting Inductors Primary Coil econdary Coil Coin Flipper 10/1/014 Electronic Instrumentation 37

38 ome Interesting Inductors GE Genura ight 10/1/014 Electronic Instrumentation 38

39 ome Interesting Transformers A huge range in sizes 10/1/014 Electronic Instrumentation 39

40 ome Interesting Transformers High Temperature uperconducting Transformer 10/1/014 Electronic Instrumentation 40

41 Household Power 700V transformed to 40V for household use 10/1/014 Electronic Instrumentation 41

42 Wall Warts Transformer 10/1/014 Electronic Instrumentation 4

Electronic Instrumentation

10/15/01 1 Electronic Instrumentation Experiment 3 Part A: Making an Inductor Part B: Measurement of Inductance Part C: imulation of a Transformer Part D: Making a Transformer Review RC and Resonance How