Electronic Instrumentation

Transcription

1 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

2 Review RC 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) o circuit is purely resistive at resonance H depends on the position of V out als/171l1sp03.doc Vs Ideal Inductor C Ideal Capacitor R Ideal Resistor 10/15/01 Electronic Instrumentation

3 Review RC and Resonance Voltage Transfer Function Vx=VR Vx=V Vx=VC Vx/Vs isc.edu/cgibin/getbig/ece/71 /allie/labmanuals/1 71l1sp03.doc Frequency KHz 10/15/01 Electronic Instrumentation 3

4 Inductors & Transformers How do transformers work? How to make an inductor? How to measure inductance? How to make a transformer?? 10/15/01 Electronic Instrumentation 4

5 Part A Inductors Review Calculating Inductance Calculating Resistance 10/15/01 Electronic Instrumentation 5

6 Inductors-Review General form of I-V relationship V di dt For steady-state sine wave excitation Z j V ji 10/15/01 Electronic Instrumentation 6

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. 10/15/01 Electronic Instrumentation 7

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 ( 0 N r d c ) Henries where this expression only holds when the length d is very much greater than the diameter r c 10/15/01 Electronic Instrumentation 8

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 10 5 times larger for materials like iron is called the permeability 10/15/01 Electronic Instrumentation 9

10 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 10/15/01 Electronic Instrumentation 10

11 Making an Inductor If the coil length is much smaller than the diameter (r w is the wire radius) 8rc N rc {ln( ) } Coil r uch a coil is used in the metal detector at the right w ength (d) Form Diameter =r c 10/15/01 Electronic Instrumentation 11

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 (r w ) is the wire conductivity R l A 10/15/01 Electronic Instrumentation 1

13 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 10/15/01 Electronic Instrumentation 13

14 Wire Resistance Using the Megaconverter at (see course website) 10/15/01 Electronic Instrumentation 14

15 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. 10/15/01 Electronic Instrumentation 15

16 In Class Problem #1 Vin R1 47 Vout R VOFF = 0 VAMP = 0. FREQ = 1kHz AC =. V1 C 1u 0 C1 1u 1 1 Z Z R C R Z 1 j C j What is Z C (assuming R is very small)? What does R represent? What is its transfer function (equation)? What is H at low and high frequencies? What is H at the resonant frequency, ω 0? C f 1 C 10/15/01 Electronic Instrumentation 16

17 Determining Inductance Vin FREQ = 1kHz VAMP = 0. VOFF = 0 AC =. V1 R1 47 C 1u C1 1u Vout R C f 1 C Reminder The parallel combination of and C goes to infinity at resonance. (Assuming R is small.) Z 0 j 1 jc j j C 1 1 jc 10/15/01 Electronic Instrumentation 17

18 10/15/01 Electronic Instrumentation 18 Determining Inductance 1,, ) 1( j j H resonance at small H H j C R j H Z R Z H O HI

19 V R1 47 V R VOFF = 0 VAMP = 0. FREQ = 1kHz AC =. V1 C 1u C1 1u mV 0 00mV 100mV 0V 100Hz 1.0KHz 10KHz 100KHz 1.0MHz V(V1:+) V(C1:1) Frequency 10/15/01 Electronic Instrumentation 19

20 Even 1 ohm of resistance in the coil can spoil this response somewhat 300mV 00mV Coil Resistance small 100mV Coil resistance small 0V 100Hz 1.0KHz 10KHz 100KHz 1.0MHz V(V1:+) V(C1:1) Frequency 300mV 00mV 100mV Coil resistance of a few Ohms 0V 100Hz 1.0KHz 10KHz 100KHz 1.0MHz V(V1:+) V(C1:1) Frequency 10/15/01 Electronic Instrumentation 0

21 Part C Examples of Transformers Transformer Equations 10/15/01 Electronic Instrumentation 1

22 Transformers Cylinders (solenoids) Toroids 10/15/01 Electronic Instrumentation

23 Transformer Equations ymbol for transformer a N N V V I I Z in R a 10/15/01 Electronic Instrumentation 3

24 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 10/15/01 Electronic Instrumentation 4

25 10/15/01 Electronic Instrumentation 5 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

26 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 ji jmi The voltage across the secondary inductor is ji jmi I I 10/15/01 Electronic Instrumentation 6

27 Transformers um of primary voltages must equal the source V R I j I jmi um of secondary voltages must equal zero 0 RI ji jmi 10/15/01 Electronic Instrumentation 7

28 Transformers Assumption : The transformer is designed such that the impedances Z j are much larger than any resistance in the circuit. Then, from the second loop equation j I 0 RI ji jmi jmi I I M I M I 10/15/01 Electronic Instrumentation 8

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 M =k = and a Therefore, I I M s 1 a 10/15/01 Electronic Instrumentation 9

30 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 j I jmi 1] ] Z Divide by 1] I. ubstitute ] and M into 1] Z IN 0 RI ji jmi V I R j in R total j 10/15/01 Electronic Instrumentation 30

31 Transformers Find a common denominator and simplify Z IN j R j R By Assumption, R is small compared to the impedance of the transformer, so Z IN R 10/15/01 Electronic Instrumentation 31 R a

32 Transformers It can also be shown that the voltages across the primary and secondary terminals of the transformer are related by NV Note that the coil with more turns has the larger voltage. Detailed derivation of transformer equations NV 10/15/01 Electronic Instrumentation 3

33 Transformer Equations a N N V V I I Z in R a 10/15/01 Electronic Instrumentation 33

34 In Class Problem # V GEN =10V R =0 Ω N =1 N =1 V GEN V s N s :N V a Z in N N R a V V 1. Find V if R ~0. Find V if R s = 1 k Ω Z in I s V s V Hint: Is V GEN = V? Under what conditions is this not true? How would you find V? Need Z in 10/15/01 Electronic Instrumentation 34

35 Part D tep-up and tep-down transformers Build a transformer 10/15/01 Electronic Instrumentation 35

36 10/15/01 Electronic Instrumentation 36 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 (P=VI) is conserved in both cases.

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 ω >> R? N V a N V 10/15/01 Electronic Instrumentation 37

38 ome Interesting Inductors Induction Heating 10/15/01 Electronic Instrumentation 38

39 ome Interesting Inductors Induction Heating in Aerospace 10/15/01 Electronic Instrumentation 39

40 ome Interesting Inductors Induction Forming 10/15/01 Electronic Instrumentation 40

41 ome Interesting Inductors Coin Flipper Flash camera circuits charge 6 capacitors arge current in primary coil arge current induced in coin (larger by ratio of turns) Current in coin creates electromagnet of opposite polarity (Repel!) Primary Coil econdary Coil 10/15/01 Electronic Instrumentation 41

42 ome Interesting Inductors GE Genura ight 10/15/01 Electronic Instrumentation 4

43 ome Interesting Transformers A huge range in sizes 10/15/01 Electronic Instrumentation 43

44 Household Power 700V transformed to 40V for household use 10/15/01 Electronic Instrumentation 44

45 Wall Warts Transformer 10/15/01 Electronic Instrumentation 45