Student: Gherghina Alexandru-Georgica

Proffesor: PhD. Eng. Zdzislaw Polkowski

Generation of a Sinusoidal Waveform

GENERATION OF A SINUSOIDAL WAVEFORM

Sine waves

The sinusoidal waveform (sine wave) is the fundamental alternating current (ac) and alternating voltage waveform.

Electrical sine waves are named from the mathematical function with the same shape.

Summary

A wave is a disturbance. Unlike water waves, electrical waves cannot be seen directly but they have similar characteristics. All periodic waves can be constructed from sine waves, which is why sine waves are fundamental.

Sine waves

Sine waves are characterized by the amplitude and period. The amplitude (A) is the maximum value of a voltage or current; the period (T) is the time interval for one complete cycle.

0 V

1 0 V

-1 0 V

1 5 V

-1 5 V

-2 0 V

t ( s )0 2 5 3 7 .5 5 0 .0

2 0 V

The amplitude (A) of this sine wave is 20 V

A

The period is 50.0 ms

T

Sine waves

The period of a sine wave can be measured between any two corresponding points on the waveform.

T T T T

T TA

By contrast, the amplitude of a sine wave is only measured from the center to the maximum point.

Frequency

Frequency ( f ) is the number of cycles that a sine wave completes in one second.

Frequency is measured in hertz (Hz).

Example

If 3 cycles of a wave occur in one second, the frequency is 3.0 Hz 1.0 s

Period and frequency

The period and frequency are reciprocals of each

other.

Tf

1 and f

T1

Thus, if you know one, you can easily find the other.(The 1/x key on your calculator is handy for converting between f and T.)

If the period is 50 ms, the frequency is 0.02 MHz = 20 kHz.

Generation of a sine wave

Sinusoidal voltages are produced by ac generators and electronic oscillators.

When a conductor rotates in a constant magnetic field, a sinusoidal wave is generated.

N S

M o tio n o f c o nd uc to r C o nd uc to r

B

C

D

A

When the loop is moving perpendicular to the lines of flux, the maximum voltage is induced.

When the conductor is moving parallel with the lines of flux, no voltage is induced.

A B C D

AC generator (alternator)

Generators convert rotational energy to electrical energy. A stationary field alternator with a rotating armature is shown. The armature has an induced voltage, which is connected through slip rings and brushes to a load. The armature loops are wound on a magnetic core (not shown for simplicity).

N S

slip ring s

a rm a tureb rushe s

Small alternators may use a permanent magnet as shown here; other use field coils to produce the magnetic flux.

AC generator (alternator)

By increasing the number of poles, the number of cycles per revolution is increased. A four-pole generator will produce two complete cycles in each revolution.

Function generators

Function selection

Frequency

Output level (amplitude)

DC offset CMOS output

RangeAdjust

Duty cycle

Typical controls:

Outputs

Readout

Sine Sq ua re Tria ng le

Bibliography

eecs.oregonstate.edu/.../3Phase_Presentation..pdf http://webshaker.ucsd.edu/homework/Creating_A_Sine_Wave.pdf http://1.bp.blogspot.com/-_

Wak_lTyZJM/UFTdaffDKNI/AAAAAAAAAik/58sQs6IN9rk/s1600/mixed+signal+oscilloscope+osciloscop+digital+2n.JPG

http://www.electronics-tutorials.ws/accircuits/sinusoidal-waveform.html Ioan D. LIŢĂ ,Circuite electronice pentru achiziția de date , MATRIX ROM,

Bucureşti, 2008..

http://oscilatii.blogspot.com/2008/03/un-generator-sinusoidal-simplu.html

Thank you for attention!