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: ure/acdc.html Loss of DC power over long distance. AC power transport is more efficient. AC power transport is more efficient

4 Generating a Sine Wave

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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

8 In-Class Activity 1 Calculate T in ms

9 Frequency – the rate at which the cycles repeat themselves – Unit of Measure – Hertz (Hz) = cycles/second T = 200 ms = 0.2s f = 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 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)

11 Note that is not the same thing as What is a radian?

12 1 Radian – the angle formed within a circle by two radii separated by an arc of length equal to the radii when r a = r 1

13 where V pk 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:

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?

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

In-Class Activity 4 Given the following oscilloscope display, express this signal as

How NOT to use an oscilloscope What’s wrong with this picture? How can I fix it?