1. Definitions

section TODO

  • instantaneous power

  • average power

  • energy vs power

  • inductor energy

  • capacitor energy

  • inductor equations

  • capacitor equations

2. Stored energy in reactive components

Reactive components (inductors and capacitors) store finite amounts of energy. This is different from an independent voltage or current source, which can supply power indefinitely (thus infinite amounts of energy).

In steady-state or periodic operation, a reactive component:

  • Must have zero average power.

  • May have a nonzero average stored energy.

The average change in energy must be zero (exactly the same as saying the average power, a.k.a. “change in energy”) must be zero, otherwise the system is NOT in steady-state nor periodic! Stated more simply or practically, an inductor can have average current that is ≠0, and a capacitor can have an average voltage that is ≠0 without any theoretical problems.

2.1. Relay coil driver

inductor recovery r
Figure 1. Inductor current paths through switches.
inductor recovery
Figure 2. Recovering energy stored in an inductor.

For each of the two figures Figure 1 and Figure 2 plot the following waveforms as a function of time (2 periods):

  • For all switches, MOSFETS and diodes

    • Switch state (0:OFF, 1:ON)

    • Switch current

    • Switch voltage

  • Inductor voltage

  • Inductor current

  • Inductor power (passive sign convention)

  • Vdd power (passive sign convention)

Your plots should include the following information or labeled points:

  • Peak (max+min) inductor current.

  • Peak inductor stored energy.

  • Average resistor power.

  • Average power supplied by Vdd.

Make T ≥ 3t1 and the L/R time constant short enough that the inductor current decays to nearly zero by the next switching cycle. Draw these in a similar manner as was done in class time, with a the plots vertically stacked having a common x-axis scaling.