THE SINEWAVE

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If the generated emf of the loop is measured and plotted as the loop rotates, the result will be as shown in the diagram below.

It can be seen that when the conductors are moving parallel to the lines of flux, and not cutting them, the induced emf is zero. When the conductors are cutting the lines of flux at right angles, maximum emf is induced in them. By convention, the part of the waveform above the zero line is labelled positive and the part below the line is labelled negative.

4.2 THE SINEWAVE

If the conductor is rotated at uniform speed in a uniform magnetic field, the output waveform is said to be ‘sinusoidal’ and we refer to this type of waveform as a sine wave. There are many other wave shapes that can be generated or

developed, but it is the sine wave that is used for main power supply systems. It is therefore necessary for the engineer to be very familiar with this particular

JAR 66 CATEGORY B1 MODULE 3 (part B)

ELECTRICAL FUNDAMENTALS

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4.2.1 PEAK AND PEAK-TO-PEAK VALUES

Amplitude values and their calculation apply equally to current and voltage measurement.

The Peak or Maximum Value. The maximum value attained by the wave in either direction is called the maximum value, or more usually, the peak value.

The Peak-to-Peak Value. The maximum value in one direction, to the maximum in the other direction is called the Peak-to-Peak value. It must not be confused with peak value, which is measured in one direction only. Peak-to-peak values are often used on oscilloscopes because it is easier to measure from top to bottom of the waveform, but the majority of calculations require the use of the peak value. It must be remembered to divide the peak-to-peak value by two in order to obtain the peak value for calculations.

The Instantaneous Value. As previously stated, the value at any instant can be calculated by multiplying the peak value by the sine of the angle (from 0º) through which the conductor has rotated.

4.2.2 AVERAGE VALUES

The amplitude of an ac waveform may be defined in terms of its average values.

Over one complete cycle, this would mathematically be zero (the wave goes as far positive as it does negative) If the pulses of voltage or current are always in one direction, the average value can be calculated from:

For single-phase full-wave rectification

Average Value = Peak Value × 0.637 For single-phase half-wave rectification

Average Value = Peak Value × 0.318

JAR 66 CATEGORY B1

Whilst the Peak and Average values of ac have their place and uses, they are not a lot of use for everyday work on ac. What is required is a value of ac which relates to an equivalent value of dc. Suppose an electric fire is operating with 5 amperes of d.c. current flowing through it and it is giving out a certain amount of heat. We want to know the value of a.c. which will produce the same amount of heat. Such a value is given by the Root Mean Square (rms) value of an a.c.

current.

For a sinusoidal waveform, the rms value = peak value × 0.707.

In other words, a sine wave of peak value ‘y’ produces a certain amount of heat when passed through a given resistor. To produce the same heating effect, in the same resistor using d.c., would require a d.c. with a steady current of only 0.707 of ‘y’.

By convention, it is not necessary to add ‘rms’ to a voltage or current value but, if peak or average values are being referred to, then the word ‘peak’ (Pk) or

‘average’ (Av) must be added after the value.

4.2.4 FORM FACTOR.

The form factor of a waveform is a number which indicates its shape:

Form Factor = rms value average value

For a sine waveform, this works out at 0.707 / 0.637 = 1.11. For any other waveform, the values will be different and so the Form Factor will be a different number. (This is given in these notes for information only as the aircraft engineer should not have to concern himself with the form factor).

4.2.5 PERIODIC TIME

The time taken to complete one cycle is called the ‘periodic time’ (t). It is measured in seconds or fractions of a second.

4.2.6 FREQUENCY

In electrical terms, frequency is the number of cycles completed in one second

JAR 66 CATEGORY B1

Periodic time and frequency are related.

T = 1/f and f = 1/T 4.2.7 ANGULAR VELOCITY.

The velocity at which a phasor rotates is very important and can be calculated from:

(A proper understanding of this formula is essential as it is used in other formulae).

Referring back to our simple loop it can be seen that, if the loop was rotating at 120 revolutions per second, the output frequency would be 120 Hz. It therefore follows, that the frequency of the output of an ac generator is directly proportional to its speed of rotation.

4.2.8 PHASE DIFFERENCE (ANGULAR DIFFERENCE).

If two conductors are caused to rotate at the same angular velocity, then two waves would be generated. Any angle between them is said to be their phase difference. In the following diagram, the phase difference is 90º. As the

conductors rotate in an anti-clockwise direction, the dotted wave is said to lead the solid wave by 90º.

When two waves are 90º apart, they are said to be in ‘quadrature’ with each other.

When two waves are 180º apart, they are said to be in ‘antiphase’ with each other.

JAR 66 CATEGORY B1