Transcript Transformers - La Salle University

Alternating Current: Modulation
and Transformers
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DC
In direct current (DC), the charge carriers
(usually electrons) flow in one direction
only.
The size of the current (number of amps)
may vary with time, but the flow direction
does not.
A voltage that would cause a direct current
in simple resistor circuit is called a DC
voltage.
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Voltage needs
Most computer hardware needs DC voltage,
requiring between 1.5 and 13.5 volts.
A typical monitor, a cathode ray tube CRT
display, requires much higher voltages.
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AC/DC
Direct current is produced by batteries.
In contrast, the electricity available from the
standard wall socket is alternating current
(AC).
Less power is lost in transmitting highvoltage AC than in transmitting the
corresponding amount using lower-voltage
DC.
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Tesla versus Edison
Thomas Alva Edison had “invented” the light bulb but he
needed to deliver power to the homes to light the lights.
Edison had in mind to use DC. But DC power had a lot of
problems: it could not travel long distances, it required
very thick wires, its voltage could not be easily, etc.
Nikola Tesla, who worked for Edison at one time,
proposed using AC transmission.
Edison used his fame and power to discredit Tesla and AC
at every opportunity.
Eventually Tesla convinced George Westinghouse of the
superiority of AC and AC became the transmission scheme
of choice.
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AC
Alternating current (AC) occurs when the
charge carriers periodically reverse their direction.
Household current is AC with a frequency of 60
Hertz (cycles per second).

In some countries it is 50 Hz and a different voltage
The radio-frequency (RF) current in antennas and
transmission lines is another example of AC.
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Converting
AC can be converted to DC by a computer’s
power supply.
A power supply consists of
a transformer (reduces voltage)
 a rectifier (makes voltage positive only)
 a filter (smoothes out voltage)

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Waveform
The waveform is the shape of the voltage
as a function of time.
Typical AC waveforms can be
sinusoidal
 square
 sawtooth
 ramped
 triangular

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Sinusoidal
AC Voltage
Peak voltage
Voltage (V)
200
100
0
0
0.01
0.02
0.03
0.04
-100
-200
Time (s)
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Square wave
Square
1.5
1
0.5
0
-0.5 0
-1
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-1.5
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Saw Tooth
Saw Tooth
1.5
1
0.5
0
-0.5 0
-1
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-1.5
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Ramp
Ramp
1.5
1
0.5
0
-0.5 0
-1
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-1.5
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Triangular
Triangular
2
1.5
1
0.5
0
-0.5 0
-1
-1.5
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0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
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Irregular
Ideally what comes out of a wall socket is a sine
wave.
Square or sawtooth waves may be produced by
some low-end uninterruptible power supplies
when operating from the battery.
Some AC waveforms are irregular, particularly
those carrying information.
AC waves are produced by audio amplifiers that
deal with analog voice signals and/or music.
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Carriers and Modulation
One way to transmit information is to send it
along with an AC current.
A simple sine wave conveys little to no
information but serves as carrier.
But one can modulate (change) the time
dependence to send information



Amplitude modulation (AM) changes the peak value.
Frequency modulation (FM) changes the frequency.
Phase shift keying (PSK) changes the phase of the
wave.
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Amplitude: how big is the disturbance (esp.
at its maxima)
The two waves shown above have different amplitudes.
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Frequency: how many cycles (one unit of
repeated disturbance) go by in a second
The two waves shown above have different frequencies.
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Phase: what part of the cycle the wave is
in at a particular time
The above waves are “out of phase.”
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Amplitude modulation
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Amplitude modulation
(4 states/2 bits)
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Frequency modulation
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Phase modulation
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QAM (Phase and Amplitude)
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Measuring AC voltage
An AC voltage is always changing with
time.
The effective voltage of an AC power
source is the DC voltage that would produce
the same power dissipation (i.e amount of
heat) for a simple resistor circuit.
This voltage is also known as the rootmean-square voltage.
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RMS Versus Peak Voltages
Another way to characterize AC supplies is by
their peak voltage, that is, the highest voltage in
the shape.
The rms voltage is not equal to the peak voltage.
For a sine wave, the rms voltage is 0.707 times the
peak voltage.

.707 1 / 2
For example, if the typical US rms voltage is 117
V, then the typical peak voltage is 165 V.
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Average Voltage
Sinusoidal AC voltage has the form
V(t) = Vpeak sin(2  f t), where
Vpeak is the peak voltage
 f is the frequency

The average voltage is zero,

Half the time it’s positive, half the time it’s
negative
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The Root Mean Square Average
The root mean square is a way to take a
meaningful average
Square: the voltage is half negative,half
positive. Square it so it will always be
positive
Mean: average over time
Root: take the square root so we get back to
voltage instead of voltage squared
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RMS Voltage for sine wave
Vrms
Vrms
Vrms
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 1/ f
  f  V peak sin( 2ft )
 0

1 2 
  V peak 
2

1

V peak
2
2 1/ 2




1/ 2
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Audio frequency
AC between 20 and 20,000 Hz is known as
audio frequency (AF).
If such current is fed into a speaker, it will
produce sound waves within the range of
human hearing.
All telephone circuits operate with AF
signals in a restricted range of
approximately 200 Hz to 3000 Hz.
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Modem
Modems convert data in binary form into
analog signals in the AF range that can be
transmitted over the telephone wire
Modems also receive the AF signals and
convert them back into binary form.
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Limitations
The phone system was designed to work over a
limited range of frequencies suitable to human
voices


Humans hear 20-20,000 Hz
Phone system uses up to 3000 Hz
This limitation in frequencies puts limitations on
bandwidth which is related to the rate of
information flow.
The baud rate of a modem is tied to the
frequencies phone lines were designed to handle.
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Radio Frequencies
Radio frequency (RF) refers to an AC
voltage that if applied to an antenna would
produce an electromagnetic wave of the sort
used in radio and other wireless
communications.
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Frequency range
These frequencies cover the portion of the
electromagnetic spectrum, starting at around
9 kHz, and going up to thousands of
gigahertz (GHz).
AM radio is between kHz and MHz.
FM radio is in the MHz range.
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Wireless
Many wireless devices make use of RF fields.




Cordless and cellular telephone
Radio and television broadcast stations
Satellite communications systems
Two-way radio services
Some wireless devices operate at higher
frequencies (Infrared IR or visible-light)
frequencies


most television-set remote-control boxes
some cordless computer keyboards and mice
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DSL
Digital Subscriber Line.
One choice to beat the limitations of
modems.
It works at higher frequencies and hence
higher bandwidths.
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Ranges of RF
The RF spectrum is divided into several
ranges, or bands.
The table shows the eight bands in the RF
spectrum, along with their frequency and
corresponding wavelengths.
The SHF and EHF bands are often referred
to as the microwave spectrum.
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RF Ranges
Name
Abbrev.
Freq.
Wavelength
Very low freq.
VLF
9kHz-30kHz
33 km - 10 km
Low Freq.
LF
30 kHz - 300 kHz
10 km - 1 km
Medium Freq.
MF
300 kHz - 3 MHz
1 km - 100 m
High Freq.
HF
3 MHz - 30 MHz
100 m - 10 m
Very High Freq.
VHF
30 MHz - 300 MHz
10 m - 1 m
Ultra High Freq.
UHF
300 MHz - 3 GHz
1 m - 100 mm
Super High Freq.
SHF
3 GHz - 30 GHz
100 mm - 10 mm
Extremely High Freq.
EHF
30 GHz - 300 GHz
10 mm - 1 mm
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Electricity and Magnetism
Changing electric fields cause magnetic
fields.
Changing magnetic fields cause electric
fields.
These effects lead to electromagnetic
radiation (radio, microwaves, infrared, light,
ultraviolet, x-rays).
They also lead to motors and transformers.
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Transformers
Wires from two independent AC circuits are
wound around a core (usually iron).

That’s why transformers are heavy.
A current is sent through the first (primary)
circuit, producing a magnetic field in the core

Magnetic fields are caused by currents and changing
electric fields.
That magnetic field is changing because the
current is changing.
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Transformers (Cont.)
The changing magnetic field in the core
causes and electric field around the core.
That electric field causes a current in the
other (secondary) circuit.
It too is an alternating current.
The voltages and currents are dependent on
the number of times each is wrapped around
the core.
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Transformers (Cont.)
In this way the transformer changes the
voltage.
Power=voltage current remains the same
for the two circuits.
If the secondary voltage is lowered, it is
known as a step-down transformer.
If the secondary voltage is raised, it is called
a step-up transformer.
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