1. ECE410 Spring 2012 Lecture #26 Mutual Inductance

2. Homework Due 4/2/2012 • Chapter 6 – Problems 2,3,4,8,14,16,19,43 • PSpice – Simulate a 10V voltage source charging a 10uF capacitor through a 5k resistor. Use transient analysis to plot the charging curve (Voltage across the capacitor vs. time) and find the simulated time constant. Compare the simulated value to the theoretical value of RC.

3. Inductors • The inductance we have discussed so far with inductors is the self inductance… the voltage induced across the coil from its own magnetic field.

4. Mutual Inductance • However, separate inductive coils can be linked together through mutual inductance • This is the voltage induced in one coil due to the changing magnetic flux of another coil • The an example of mutual inductance is the transformer

5. Mutual Inductance in Circuits • L1 and L2 are the self inductances of the two inductive coils • M is the mutual inductance between the coils • This arrow notation allows you to see which coils have a given mutual inductance

6. Using mesh current with mutual inductance • Mesh current technique is the easiest to use An extra voltage appears in each mesh that is the mutual inductance, M, multiplied by the time rate of change of the current through the opposite inductor. WHAT IS THE SIGN OF THE M TERM?

7. Dot Convention • The dot convention is used to denote the polarity of the mutual induction component of the voltage Dot Convention: When the reference direction of a current enters the dotted terminal of an inductor, the reference polarity that it will produce in the opposite coil is positive at the dot

8. Dot Convention Example

9. Determining Dot Markings • Circuit schematics will typically show dot markings • If there are no dot markings you must determine them yourself • You must either be able to see the physical windings and their directions • Or.. You must be able to experimentally test the circuit

10. Determining dots by inspection • Arbitrarily select on terminal of one coil and mark it with a dot • Assign a current into the dotted terminal and label it • Use the right hand rule to determine the direction of the magnetic field produced by the current, mark and label it • Arbitrarily select a terminal on the second coil • Assign a second current into the selected terminal • Again, use the right hand rule to determine the direction of the magnetic field produced by the current, mark and label this second field • If the two fields are in the same direction then mark your second terminal with a dot… if they are opposite, mark the opposite terminal (where the test current leaves) with a dot.

11. Experimentally Testing a circuit to determine dot position • Connect a voltage source, resistor, and switch to one coil. • Mark the terminal that current will flow into with a dot • Connect the other coil to a voltmeter • Allow current to flow by closing the switch and watch the voltmeter • If the voltmeter registers an increase in voltage mark the terminal connected to the positive terminal of the voltmeter with a dot • If the voltmeter registers an decrease in voltage mark the terminal connected to the negative terminal of the voltmeter with a dot

12. Examples • Example 6.6 • Assessment 6.6 780Ω ig

13. Capacitive Proximity Switches • Changes in capacitance can be used to detect input from everything from lamps, to elevators, to iphones. • Your book talks about how a capacitive proximity switch works as a elevator button.

14. Basic Premise • An elevator switch has two electrodes separated by an insulator • This forms a basic capacitor • When you insert your finger into the cup of the proximity switch you are effectively putting a connection to ground (you) between the electrodes. C1, C2, and C3 vary between 10-50pF Assume they are all 25 pF

15. Button Schematic • The button is placed in series with a known capacitor With finger Without finger

16. Button without finger Write node voltage equation for node between C1 and C2: Integrate If C1=C2 as we assume, then: v(t) = 0.5vs(t) + v(0) If we ignore the initial voltage across C2, then: v(t) = 0.5vs(t)

17. Button with finger Write node voltage equation for node between C1 and C2: Integrate If C1=C2=C3 as we assume, then: v(t) = 0.333vs(t) + v(0) If we ignore the initial voltage across C2, then: v(t) = 0.333vs(t)

18. Summary • You can determine if someone has pressed the button by simply monitoring the circuit for changes in output voltage. • Touch sensitive screens like those on smart phones typically use capacitive means to detect if a person is touching the screen and where • This is why there is no effect if you touch the screen through a glove or non-conductive stylus… they don’t generate a change in the capacitance