Today’s Agenda

Sinsuoidal AC Signals

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• 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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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.

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• Generating a Sine Wave

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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

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• Cycle Time (Period)– The time required to complete one cycle of a signal

ms20div

ms5div4 T

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In-Class Activity 1

Calculate T in ms Calculate T in ms

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• 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

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• 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)

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• Note that is not the

same thing as

• What is a radian?

Hzs

cyclesf ][

s

radians][

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• 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

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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

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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

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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?