Design Realization lecture 14

John Canny/Dan Reznik

10/9/03

Last Time

Composites: Fiberglass, carbon fiber and kevlar.

Hierarchical materials.

Cellular materials, honeycomb and foam.

This time

Electronics

Voltage, Current, Ohm’s law

Voltage is analogous to pressure, and is measured naturally enough, in volts.

Current is analogous to flow, and is measure in amperes or amps for short.

Direct current (DC) is a constant voltage, e.g. a single C or D battery produces 1.5 volts.

Alternating Current (AC) is a voltage that reverse rapidly, at 60 cycles/second in the US. An electrical outlet gives 110 volts AC.

Voltage, Current, Ohm’s law

Resistors are used to produce desired voltage or current, independent of frequency.

Resistance is measured in ohms, and the current through a resistor satisfies Ohm’s law:

V = I R

I in amps

V in volts

Resistors

Resistors have a power rating as well, ½, ¼, 1/8 watt etc. (P = V I)

Resistors used to all look like this:(axial lead type):

But increasingly are surface-mount:

Or grouped in chip packages:

Resistors

Variable resistors are called potentiometers:

Here’s a simple circuit, avoltage divider:

Note the ground and power supply symbols:

A potentiometer can actas a variable voltage divider, to control a voltage.

AC and frequency

Alternating current most often has a sinusoidal shape over time:

The frequency is thenumber of completecycles per second.

Its measured in Hertz (Hz).

Waveform is

V = sin 2 f t

AC and Capacitors

Capacitors are charge storage devices, but don’t allow DC to flow.

AC can flow because a little charge is stored each cycle and returned.

The current flow increases with frequency.

Capacitor Construction

Capacitors are sandwiches of dielectric between two conductors.

The dielectric is an insulator, usually a polymer.

Performance determined by “dielectric constant” and electrical breakdown strength (kV/mm).

Capacitor Construction

Capacitor Reactance

A capacitor limits AC current rather like a resistor does.

The reactance Z of the capacitor determines how much current flows, V = Z I where:

C is the capacitance in Farads. A Farad is a huge unit. Most capacitors are

measured in micro-farads or pico-farads (10-12)

CfZ

2

1

Variable Capacitors

Capacitors can be variable. Used for tuning: Radios, antennas, crystal oscillators (to drive

computers).

Inductors

Inductors are coils of wire, sometimes around a ferrite or iron core.

The ferrite core is a composite with small magnetic particles. Works at high frequencies where iron doesn’t.

Transformer

Two coils of wire around the same magnetic core create a transformer.

An AC voltage in one coil induces a voltage in the other.

Ratio of voltages = ratio of turns.

(more turns = highervoltage).

A simple R/C circuit

This circuit is a voltage divider, with one leg which is a capacitor, one a resistor.

Discuss what “high-pass” and “low-pass” would mean in this circuit.

Amplifiers

Amplifiers are an important class of active component (resistors, capacitors and inductors are passive – they cant strengthen a signal).

Amplifiers boost small signals from radio antennas, microphones, sensors etc. to larger values.

Ex: stereo amplifier. There is a popular component for building

amplifiers called an Operational Amplifier (Op-Amp).

Inverting Amplifier

Here is a basic inverting amplifier. The gain (ratio of Vo to Vi) is - Rf / Ri The OpAmp has very high gain, which makes

it change output until its two inputs are nearly equal – you can assume they are.

Non-Inverting Amplifier

Here is a basic non-inverting amplifier. The gain (ratio of Vo to Vi) is (Rf + Rg) / Rg