1. 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

2. K. A. Connor15 September 2015 Pendulum Bouncing ball Vibrating string (stringed instrument) Circular motion (wheel) Cantilever beam (tuning fork) Examples of Periodic Motion

3. K. A. Connor15 September 2015 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 Other Periodic Phenomena

4. K. A. Connor15 September 2015 Daily Ave Temperature in Troy Data (blue) covers 1995-2002 Note the sinusoid (pink) fit to the data

5. K. A. Connor15 September 2015 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 Tank Circuit

6. K. A. Connor15 September 2015 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. Tank Circuit

7. K. A. Connor15 September 2015 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. Tank Circuit

8. K. A. Connor15 September 2015 Tank Circuit V & I

9. K. A. Connor15 September 2015 There is a slight decay due to finite wire resistance. The frequency is given by (period is about 10ms) Tank Circuit

10. K. A. Connor15 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.

11. K. A. Connor15 September 2015 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. Tank Circuit Application

12. K. A. Connor15 September 2015 Disposable Camera Launcher This device can launch paperclips a small distance using a coil of wire.

13. K. A. Connor15 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.

14. K. A. Connor15 September 2015

15. K. A. Connor15 September 2015 Deriving Fundamental Equations Energy stored in capacitor plus inductor Total energy must be constant, thus Conservation Laws

16. K. A. Connor15 September 2015 Simplifying This expression will hold if Noting that Conservation Laws

17. K. A. Connor15 September 2015 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 I + + VCVC VLVL Conservation Laws

18. K. A. Connor15 September 2015 Experimentally, it was also determined that the current-voltage relationship for a capacitor is Experimentally, it was also determined that the current-voltage relationship for an inductor is Conservation Laws

19. K. A. Connor15 September 2015 Applying the I-V relationship for a capacitor to the expressions we saw before for charging a capacitor through a resistor We see that Conservation Laws

20. K. A. Connor15 September 2015 Simplifying Which is satisfied if The latter is the relationship for a resistor, so the results work. Conservation Laws

21. K. A. Connor15 September 2015