ECE410 Spring 2012 Lecture #26 Mutual Inductance

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.

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.

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

Mutual Inductance in Circuits L 1 and L 2 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

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?

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

Dot Convention Example

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

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.

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

Examples Example 6.6 Assessment 6.6 igig 780Ω

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.

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

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

Button without finger Write node voltage equation for node between C 1 and C 2 : Integrate If C 1 =C 2 as we assume, then: v(t) = 0.5v s (t) + v(0) If we ignore the initial voltage across C 2, then: v(t) = 0.5v s (t)

Button with finger Write node voltage equation for node between C 1 and C 2 : Integrate If C 1 =C 2 =C 3 as we assume, then: v(t) = 0.333v s (t) + v(0) If we ignore the initial voltage across C 2, then: v(t) = 0.333v s (t)

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