ECE410 Spring 2012

Lecture #26Mutual 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.

dt

diLtv )(

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

•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

Using mesh current with mutual inductance

• Mesh current technique is the easiest to use

0

0

12222

21111

dt

diM

dt

diLiR

dt

diM

dt

diLiRvg

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

0

0

12222

21111

dt

diM

dt

diLiR

dt

diM

dt

diLiRvg

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

ig 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 10-50pFAssume they are all 25 pF

Button Schematic

• The button is placed in series with a known capacitor

With fingerWithout finger

Button without fingerWrite node voltage equation for node between C1 and C2:

dt

dv

CC

C

dt

dvdt

dvC

dt

dvCC

dt

dvC

dt

dvC

dt

dvC

dt

dvC

dt

vvdC

s

s

s

s

21

1

121

211

21

0

0)(

Integrate

)0()()(21

1 vtvCC

Ctv s

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)

Button with fingerWrite node voltage equation for node between C1 and C2:

dt

dv

CCC

C

dt

dvdt

dvC

dt

dvCCC

dt

dvC

dt

dvC

dt

dvC

dt

dvC

dt

dvC

dt

dvC

dt

vvdC

s

s

s

s

321

1

1321

3211

321

0

0)(

Integrate

)0()()(321

1 vtvCCC

Ctv s

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)

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