# Passives

## Resistors

• Ohm’s law: V =IR, assuming everyone remembers this
• Everything is a resistor, ie. has an equivalent series resistance ESR. Look for this number on capacitors, mosfets, lengths of wire (also note that everything is a capacitor and an inductor as well…).

## Capacitors

• Capacitors Summary
• Two primary types of capacitors we use when designing power electronics, often we will use both in parallel:
• Ceramic - Not Polarized, High frequency but lower capacitances
• Electrolytic - Polarized, higher ESR and therefore suitable for lower frequencies but higher capacitances
• Capacitors are used in one of two ways
• Bypass capacitors - In parallel with a load, a capacitor will act like a short duration power supply capable of smoothing out voltage ripples and meeting immediate demand. Generally it’s a good idea to bypass everything. This concept is also integral to switching power supplies, RC filters for signal processing, and much more. Primarily what we will see today.
• Blocking capacitors - In series with a load a capacitor will “block” direct current and pass alternating current.
• A small reminder that current represents a flow of charge (1 amp = 1 coulomb/second), and integrating over current yields total charge across a capacitor.

The current through a capacitor is a function of the rate of change of voltage across it, and its capacitance (dielectric material / size + size of your conductors (commonly parallel plates)). When voltage is changing rapidly, (displacement) current will flow “in” or “out” of a capacitor. It’s useful to remember that current doesn’t actually flow through a capacitor, charges just collect on one side or the other (no continuity!).

## Inductors

• Inductors Summary
• Convert energy between electric and magnetic fields
• We will talk about inductors primarily in two ways:
• Energy storage for filtering switching power supplies
• Designing an inductor is a balancing act: Inductor Material and Size/Shape, turns required to achieve desired inductance at optimal cost and favorable saturation. The inductor is probably going to the costliest single component in an inexpensive power supply.
• Can be bought as surface mount components (bottom right of picture below).
• Electric motors and generators can most often be thought of as inductors
• Typically you will just be interested in the inductance of your motor, which will inform current rise time, and therefore peak RPM and torque of the motor

The rate of current through an inductor is a function of the voltage across it and its inductance (core geometry and material + number of turns). When current changes rapidly through an inductor (eg. when we flip a switch off in series) voltage will increase or decrease accordingly! Think what would happen in the equation below if we abruptly flipped the switch on an inductor (voltage will increase!). This is why you may have blown up an arduino trying to drive a small brushed motor directly off of I/O without a flyback diode. Electric inertia.

## Diodes

• Diodes Summary
• Diodes are the one-way valves of the electronics world and are used everywhere.
• They have a characteristic forward voltage drop, and won’t pass current until it is reached, so not lossless.
• There are a lot of different types of diodes with uses spanning much wider than controlling current direction.
• Silicon diodes are standard when looking at surface mount components, and usually what we mean when we just say “diode.” 0.7 V forward voltage drop is typical.
• Zener diodes allow current to flow in both directions, and so have a (different) forward and reverse voltage drop, which we will discuss exploiting later.
• Schottky diodes can have very low forward voltages (150mV - 450mV) and very fast switching times, so are useful for power electronics circuits. Downsides are comparatively low reverse voltage ratings and high leakage currents.
• LED’s are light emitting diodes, different wavelengths have different V_fs.
• We most often regulate current through an LED with a resistor in series. We can use ohm’s law to size that resistor…
• Using a resistor to limit current is not the most efficient way to accomplish. Later we will talk about DCM.