Download Lecture 14

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=IR
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, a
voltage divider:
 Note the ground and
power supply symbols:
 A potentiometer can act
as a variable voltage
divider, to control a voltage.
AC and frequency
 Alternating current most often has a
sinusoidal shape over time:
 The frequency is the
number of complete
cycles 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:
1
Z
2 f C
 C is the capacitance in Farads.
 A Farad is a huge unit. Most capacitors are
measured in micro-farads or pico-farads (10-12)
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 = higher
voltage).
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 (OpAmp).
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