today’s agenda sinsuoidal ac signals. 2 one of the most important ac signals is the periodic...
Post on 21-Dec-2015
212 views
TRANSCRIPT
Today’s Agenda
Sinsuoidal AC Signals
2
• One of the most important AC signals is the periodic sinusoid, as shown below.– Electricity generating power plants.– Radios and radio stations.
3
Differences between AC & DC
• Demo: http://www.pbs.org/wgbh/amex/edison/sfeature/acdc.html
• Loss of DC power over long distance.• AC power transport is more efficient.
4
• Generating a Sine Wave
5
6
Insert Figure 9.3
• Alternations and Cycles– Alternations – the positive
and negative transitions– Cycle – the complete
transition through one positive alternation and one negative alternation
– Half-Cycle – one alternation
7
• Cycle Time (Period)– The time required to complete one cycle of a signal
ms20div
ms5div4 T
8
In-Class Activity 1
Calculate T in ms Calculate T in ms
9
• Frequency– the rate at which the cycles repeat themselves– Unit of Measure – Hertz (Hz) = cycles/second
T = 200 ms = 0.2sf = 1/0.2 = 5 cps = 5 Hz
10
• Relation between Cycle Time (Period) and Frequency
where T = the cycle time (period) of the waveform in seconds
fT
Tf
1or
1
Another way to describe periodicity of the wave is through theangular frequency defined as
2 f where
= angular velocity, in radians per second2 = the number of radians in one cycle f = the number of cycles per second (frequency)
11
• Note that is not the
same thing as
• What is a radian?
Hzs
cyclesf ][
s
radians][
12
• 1 Radian – the angle formed within a circle by two radii separated by an arc of length equal to the radii
1
1 arradr
when ra = r1
13
where Vpk is the magnitude of the voltage.
In terms of f,
Instantaneous Value • The value of a sinusoidal voltage or current at a
specified point in time can be expressed as:
)sin()( tVtv pk
)2sin()( ftVtv pk
14
In-Class Activity 2
• An AC voltage in volts is given by
• what are the units of the number 10?• what are the units of the number 377?• what is the angular frequency in rad/s?• what is the frequency in Hz or cps?• what is the period in ms?
)377sin(10)( ttv
15
In-Class Activity 3• A device emits a sinusoidal signal that has a magnitude of
2 volts and a frequency of 690 kHz.
• What is the period of the signal in ms?• What is the angular frequency in rad/s?• Express this signal as (i.e. fill in the values
for A and )
• Express this signal as
)sin()( tAtv
)2sin()( ftAtv
In-Class Activity 4• Given the following oscilloscope display,
express this signal as )2sin()( ftAtv
How NOT to use an oscilloscope
• What’s wrong with this picture? How can I fix it?
• What’s wrong with this picture? How can I fix it?