3112021 1 Electronic Instrumentation Experiment 3 Part A

3/11/2021 1 Electronic Instrumentation Experiment 3 • Part A: Making an Inductor • Part B: Measurement of Inductance • Part C: Simulation of a Transformer • Part D: Making a Transformer

Review RLC and Resonance w 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/cgibin/getbig/ece/271/allie/labmanu als/1271 l 1 sp 03. doc 3/11/2021 Electronic Instrumentation 2

Review RLC and Resonance http: //ecow. engr. w isc. edu/cgibin/getbig/ece/271 /allie/labmanuals/1 271 l 1 sp 03. doc 3/11/2021 Electronic Instrumentation 3

Inductors & Transformers How do transformers work? w How to make an inductor? w How to measure inductance? w How to make a transformer? w 3/11/2021 Electronic Instrumentation ? 4

Part A Inductors Review w Calculating Inductance w Calculating Resistance w 3/11/2021 Electronic Instrumentation 5

Inductors-Review w General form of I-V relationship w For steady-state sine wave excitation 3/11/2021 Electronic Instrumentation 6

Determining Inductance Calculate it from dimensions and material properties w Measure using commercial bridge (expensive device) w 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. w 3/11/2021 Electronic Instrumentation 7

Making an Inductor w 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 2 rc 3/11/2021 Electronic Instrumentation 8

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) w For magnetic materials, we use instead, which can typically be 105 times larger for materials like iron w is called the permeability w 3/11/2021 Electronic Instrumentation 9

Some Typical Permeabilities w w w w Air 1. 257 x 10 -6 H/m Ferrite U M 33 9. 42 x 10 -4 H/m Nickel 7. 54 x 10 -4 H/m Iron 6. 28 x 10 -3 H/m Ferrite T 38 1. 26 x 10 -2 H/m Silicon GO steel 5. 03 x 10 -2 H/m supermalloy 1. 26 H/m 3/11/2021 Electronic Instrumentation 10

Making an Inductor w If the coil length is much smaller than the diameter (rw is the wire radius) Form Diameter =2 rc Coil Length (d) Such a coil is used in the metal detector at the right 3/11/2021 Electronic Instrumentation 11

Calculating Resistance All wires have some finite resistance. Much of the time, this resistance is negligible when compared with other circuit components. w Resistance of a wire is given by l is the wire length A is the wire cross sectional area (prw 2) s is the wire conductivity w 3/11/2021 Electronic Instrumentation 12

Some Typical Conductivities Silver 6. 17 x 107 Siemens/m w Copper 5. 8 x 107 S/m w Aluminum 3. 72 x 107 S/m w Iron 1 x 107 S/m w Sea Water 5 S/m w Fresh Water 25 x 10 -6 S/m w Teflon 1 x 10 -20 S/m Siemen = 1/ohm w 3/11/2021 Electronic Instrumentation 13

Wire Resistance w Using the Megaconverter at http: //www. megaconverter. com/Mega 2/ (see course website) 3/11/2021 Electronic Instrumentation 14

Part B: Measuring Inductance with a Circuit w 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. 3/11/2021 Electronic Instrumentation 15

In Class Problem #1 Vin w w w Vout What is ZLC (assuming R 2 is very small)? What does R 2 represent? What is its transfer function (equation)? What is H at low and high frequencies? What is H at the resonant frequency, ω0? 3/11/2021 Electronic Instrumentation 16

Determining Inductance Vin w Vout Reminder—The parallel combination of L and C goes to infinity at resonance. (Assuming R 2 is small. ) 3/11/2021 Electronic Instrumentation 17

Determining Inductance 3/11/2021 Electronic Instrumentation 18

3/11/2021 Electronic Instrumentation 19

w Even 1 ohm of resistance in the coil can spoil this response somewhat Coil resistance small Coil resistance of a few Ohms 3/11/2021 Electronic Instrumentation 20

Part C Examples of Transformers w Transformer Equations w 3/11/2021 Electronic Instrumentation 21

Transformers w Cylinders (solenoids) w Toroids 3/11/2021 Electronic Instrumentation 22

Transformer Equations Symbol for transformer 3/11/2021 Electronic Instrumentation 23

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 w The inductors work as expected, but they also couple to one another through their mutual inductance: M 2=k 2 LS LL w 3/11/2021 Electronic Instrumentation 24

Transformers w Assumption 1: Both Inductor Coils must have similar pr 3/11/2021 Electronic Instrumentation 25

Transformers Note Current Direction IS IL Let the current through the primary be w Let the current through the secondary be w The voltage across the primary inductor is w w The voltage across the secondary inductor is 3/11/2021 Electronic Instrumentation 26

Transformers w Sum of primary voltages must equal the source w Sum of secondary voltages must equal zero 3/11/2021 Electronic Instrumentation 27

Transformers w Assumption 2: The transformer is designed such that the 3/11/2021 Electronic Instrumentation 28

Transformers w k is the coupling coefficient • If k=1, there is perfect coupling. • k is usually a little less than 1 in a good transformer. w Assumption 3: Assume perfect coupling (k=1) We know M 2=k 2 LS LL= LS LL and Therefore, 3/11/2021 Electronic Instrumentation 29

Transformers The input impedance of the primary winding reflects t w It can be determined from the loop equations w • 1] • 2] w Divide by 1] IS. Substitute 2] and M into 1] 3/11/2021 Electronic Instrumentation 30

Transformers w Find a common denominator and simplify w By Assumption 2, RL is small compared to the impedanc 3/11/2021 Electronic Instrumentation 31

Transformers w 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. w Detailed derivation of transformer equations http: //hibp. ecse. rpi. edu/~connor/education/transformer_notes. pdf 3/11/2021 Electronic Instrumentation 32

Transformer Equations 3/11/2021 Electronic Instrumentation 33

In Class Problem #2 VGEN=120 V RL=20 Ω NL=1 NS=12 Ns: NL VGEN Vs 1. Find VL if RS~0 2. Find VL if Rs= 1 k Ω VL Is Zin Vs VL Hint: Is VGEN = VS? Under what conditions is this not true? How would you find VS? Need Zin 3/11/2021 Electronic Instrumentation 34

Part D Step-up and Step-down transformers w Build a transformer w 3/11/2021 Electronic Instrumentation 35

Step-up and Step-down Transformers Step-up Transformer Step-down Transformer Note that power (P=VI) is conserved in both cases. 3/11/2021 Electronic Instrumentation 36

Build a Transformer Wind secondary coil directly over primary coil w “Try” for half the number of turns w At what frequencies does it work as expected with respect to voltage? When is ωL >> R? w 3/11/2021 Electronic Instrumentation 37

Some Interesting Inductors w Induction Heating 3/11/2021 Electronic Instrumentation 38

Some Interesting Inductors w Induction Heating in Aerospace 3/11/2021 Electronic Instrumentation 39

Some Interesting Inductors w Induction Forming 3/11/2021 Electronic Instrumentation 40

Some Interesting Inductors w 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!) 3/11/2021 Primary Coil Secondary Coil Electronic Instrumentation 41

Some Interesting Inductors w GE Genura Light 3/11/2021 Electronic Instrumentation 42

Some Interesting Transformers w A huge range in sizes 3/11/2021 Electronic Instrumentation 43

Household Power w 7200 V transformed to 240 V for household use 3/11/2021 Electronic Instrumentation 44

Wall Warts Transformer 3/11/2021 Electronic Instrumentation 45

In Class Problem #1 Vin w w w Vout What is ZLC (assuming R 2 is very small)? What does R 2 represent? What is its transfer function (equation)? What is H at low and high frequencies? What is H at the resonant frequency, ω0? 3/11/2021 Electronic Instrumentation 46

In Class Problem #1 Vin 3/11/2021 Vout Electronic Instrumentation 47

In Class Problem #1 Vin 3/11/2021 Vout Electronic Instrumentation 48

In Class Problem #1 w What is H at low frequencies? This can be determined from the magnitude so w Remember these steps! w 1. Take the lowest power in the numerator and denominator of the equation 2. Write down x 1, y 1, x 2, and y 2 (can do this in your head) 3. Use the magnitude equation (square and square root numerator and denominator) 4. Simplify (this is the answer if approaching 0) 49 3/11/2021 Electronic Instrumentation 5. Take limit as it approaches 0 (this is the answer at 0)

In Class Problem #1 w What is H at low frequencies? Step 1: Take lowest power in numerator and denominator w Step 2: Find x 1, y 1, x 2, y 2 w 3/11/2021 Electronic Instrumentation 50

In Class Problem #1 w w 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 3/11/2021 Electronic Instrumentation 51

In Class Problem #1 w What is H at high frequencies? This can be determined from the magnitude so w Remember these steps! w 1. Take the highest power in the numerator and denominator of the equation 2. Write down x 1, y 1, x 2, and y 2 (can do this in your head) 3. Use the magnitude equation (square and square root numerator and denominator) 4. Simplify (this is the answer if approaching ∞) 52 3/11/2021 Electronic Instrumentation 5. Take limit as it approaches 0 (this is the answer at ∞)

In Class Problem #1 w What is H at high frequencies? Step 1: Take highest power in numerator and denominator w Step 2: Find x 1, y 1, x 2, y 2 w 3/11/2021 Electronic Instrumentation 53

In Class Problem #1 w What is H at high frequencies? Step 3: Use the magnitude equation w Step 4: Simplify w Step 5: Take limit as ω approaches ∞ w • Answer is that it becomes very small or 0 3/11/2021 Electronic Instrumentation 54

In Class Problem #1 w What is H at the resonant frequency, ω0? 3/11/2021 Electronic Instrumentation 55

In Class Problem #2 3/11/2021 Electronic Instrumentation 56

In Class Problem #2 3/11/2021 Electronic Instrumentation 57