Download Energy Storage Elements - RPI ECSE

SMART LIGHTING
Energy Storage Circuit
Elements (aka L & C)
K. A. Connor
Mobile Studio Project
Center for Mobile Hands-On STEM
SMART LIGHTING Engineering Research Center
ECSE Department
Rensselaer Polytechnic Institute
Intro to ECSE Analysis
Examples of Periodic Motion
•
•
•
•
•
Pendulum
Bouncing ball
Vibrating string (stringed instrument)
Circular motion (wheel)
Cantilever beam (tuning fork)
K. A. Connor
15 September 2015
Other Periodic Phenomena
•
•
•
•
•
•
•
Daily cycle of solar energy
Annual cycle of solar energy
Daily temperature cycle
Annual temperature cycle
Monthly bank balance cycle
Electronic clock pulse trains
Line voltage and current
K. A. Connor
15 September 2015
Daily Ave Temperature in Troy
90
80
70
60
50
Series1
Series2
40
30
20
10
2850
2773
2696
2619
2542
2465
2388
2311
2234
2157
2080
2003
1926
1849
1772
1695
1618
1541
1464
1387
1310
1233
1156
1079
1002
925
848
771
694
617
540
463
386
309
232
155
-10
78
1
0
• Data (blue) covers 1995-2002
• Note the sinusoid (pink) fit to the data
K. A. Connor
15 September 2015
Tank Circuit
A Classical Method Used to Produce
an Oscillating Signal
• A Tank Circuit is a combination of a
capacitor and an inductor
• Each are energy storage devices
1
1 2
2
WE  WC  CV
WM  WL  LI
2
2
K. A. Connor
15 September 2015
Tank Circuit
TOPEN = 0
TCLOSE = 0
1
U1
1
U2
2
2
V
How Does it Work?
• Charge capacitor to 10V.
At this point, all of the
energy is in the capacitor.
• Disconnect voltage source and connect
capacitor to inductor.
• Charge flows as current through inductor until
capacitor voltage goes to zero. Current is then
maximum through the inductor and all of the
energy is in the inductor.
V1
10V
C1
1uF
0
K. A. Connor
15 September 2015
L1
10uH
Tank Circuit
TOPEN = 0
TCLOSE = 0
1
U1
1
U2
2
2
V
V1
L1
10V
C1
1uF
• The current in the inductor
then recharges the capacitor
until the cycle repeats.
• The energy oscillates between the
capacitor and the inductor.
• Both the voltage and the current are
sinusoidal.
K. A. Connor
0
15 September 2015
10uH
Tank Circuit V & I
4.0A
Current
0A
-4.0A
I(L1)
10V
Voltage
0V
SEL>>
-10V
0s
10us
20us
30us
40us
50us
60us
70us
80us
90us
100us
V(C1:1)
Time
K. A. Connor
15 September 2015
Tank Circuit
4.0A
Current
0A
-4.0A
I(L1)
10V
Voltage
0V
SEL>>
-10V
0s
10us
20us
30us
40us
50us
60us
70us
80us
90us
100us
V(C1:1)
Time
• There is a slight decay due to finite wire
resistance.
1
• The frequency is given by f 
2 LC
(period is about 10ms)
K. A. Connor
15 September 2015
Tank Circuit
• Tank circuits are the basis of most oscillators. If
such a combination is combined with an op-amp,
an oscillator that produces a pure tone will result.
• This combination can also be used to power an
electromagnet.
• Charge a capacitor
• Connect the capacitor to an electromagnet (inductor).
A sinusoidal magnetic field will result.
• The magnetic field can produce a magnetic force on
magnetic materials and conductors.
K. A. Connor
15 September 2015
Tank Circuit Application
• The circuit above uses the electronics from
a disposable camera. (From earlier course)
• We can also use this type of camera as a
power source for an electromagnet.
K. A. Connor
15 September 2015
Disposable Camera Launcher
This device can launch paperclips a small
distance using a coil of wire.
K. A. Connor
15 September 2015
Disposable Camera Flash Experiment/Project
• A piece of a paperclip is placed part way into the electromagnet.
• The camera capacitor is charged and then triggered to discharge
through the electromagnet (coil).
• The large magnetic field of the coil attracts the paperclip to move
inside of the coil.
• The clip passes through the coil, coasting out the other side at
high speed when the current is gone.
K. A. Connor
15 September 2015
K. A. Connor
15 September 2015
Conservation Laws
Deriving Fundamental Equations
Energy stored in capacitor plus inductor
Energy  WTOTAL
1 2 1
 LI  CV 2
2
2
• Total energy must be constant, thus
dWTOTAL
1
dI 1
dV
 0  L2 I
 C 2V
dt
2
dt 2
dt
K. A. Connor
15 September 2015
Conservation Laws
• Simplifying
dWTOTAL
dI L
dVC
0L
IL  C
VC
dt
dt
dt
• This expression will hold if
dI L
VL  L
dt
dVC
IC  C
dt
• Noting that
VC  VL
K. A. Connor
IC  I L
15 September 2015
Conservation Laws
I
VC
+
+
VL
• Note that for the tank circuit
• The same current I flows through both
components
• The convention is that the current enters the
higher voltage end of each component
K. A. Connor
15 September 2015
Conservation Laws
• Experimentally, it was also determined that
the current-voltage relationship for a
dVC
capacitor is
IC  C
dt
• Experimentally, it was also determined that
the current-voltage relationship for an
inductor is
dI L
VL  L
K. A. Connor
dt
15 September 2015
Conservation Laws
• Applying the I-V relationship for a capacitor
to the expressions we saw before for
charging a capacitor through a resistor
 t 
 t
dVC

IC  C
V  Vo 1  e 
I  Ioe
dt
• We see that
dVC
 t
 t 

IC  Ioe  C
 CVo  0   1 e 
dt

K. A. Connor

15 September 2015
Conservation Laws
• Simplifying
 
dVC
 t 

IC  Ioe  C
 CVo  1 e 
dt
• Which is satisfied if
 t
  RC
Vo
Io 
R
• The latter is the relationship for a resistor,
so the results work.
K. A. Connor
15 September 2015
K. A. Connor
15 September 2015