1. Sinusoidal AC Signals
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2. One of the most important AC signals is the periodic sinusoid, as shown below.
Electricity generating power plants.
Radios and radio stations.
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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
Insert Figure 9.3
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4. Cycle Time (Period)
The time required to complete one cycle of a signal
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5. In-Class Activity 1
Calculate T in ms
Calculate T in ms
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6. Frequency the rate at which the cycles repeat themselves
Unit of Measure – Hertz (Hz) = cycles/second
T = 200 ms = 0.2s f = 1/0.2 = 5 cps = 5 Hz
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7. Relation between Cycle Time (Period) and Frequency
where T = the cycle time (period) of the waveform in seconds
Another way to describe periodicity of the wave is through the
angular frequency defined as
where
 = angular velocity, in radians per second
2 = the number of radians in one cycle
f = the number of cycles per second (frequency)
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8. Note that is not the same thing as
What is a radian?
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9. 1 Radian – the angle formed within a circle by two radii separated by an arc of length equal to the radii
when ra = r1
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10. Instantaneous Value
The value of a sinusoidal voltage or current at a specified point in time can be expressed as:
where Vpk is the magnitude
of the voltage.
In terms of f,
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11. 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?
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12. 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 ω)
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13. In-Class Activity 4
Given the following oscilloscope display, express this signal as
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14. How NOT to use an oscilloscope
What’s wrong with this picture? How can I fix it?
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15. How NOT to use an oscilloscope
What’s wrong with this picture? How can I fix it?
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