Average rectified value

The arithmetic mean of a change of size is zero and is therefore not suitable to characterize an alternating quantity. The metrological easiest way to obtain a quantitative statement about a change whose size is rectified value. This term is used in the electrical engineering is the average of the amount of this size ( engl. average rectified value (ARV ) ).

Preferably, the rectified value in alternating current or AC voltage is applied.

  • 4.1 For Sinus size
  • 4.2 For bleed sinusoidal voltage
  • 4.3 For pulsed voltage
  • 4.4 For alternating component of the pulsed voltage

Introduction

The rectified value of an alternating current indicates that the same DC current amount of charge transported as averaged over time, a rectified alternating current.

The mathematical definition is:

Can not the shape of the signal readily describe mathematically, one can apply the following to the calculation of standard value approximation method

Wherein sample and instantaneous values ​​, which are read in a more equal spacing for a period of the signal. It is

The order - only the amount, and form mean - must not be interchanged. Therefore, they must be connected to the notation (see above) be recognizable. To be avoided are the spellings (wrong order) and | | ( order unclear ).

For the most common case of a sinusoidal alternating quantity of rectified value is (2 / π ) times the maximum value ( peak value).

Application in metrology

Indicating Measuring Instruments to work so slowly that you can read the measured values. With rapid changes which can not detect the human eye, they show an average size of, for example, electro-mechanically averaged with moving coil movement, electronically averaged with dual-slope method, see also Digital measurement technology. The average value of an alternating quantity is equal to zero but ( according to the definition of an exchange size, see). The simplest way of measuring the size is to measure their direct guidance value. A more complex way is to measure its effective value. Physically, this is the DC equivalent in view of the active power of the size. In the art, the effective value is much more important; Change sizes gauges are designed to ensure that this value is displayed.

Nevertheless, the rectified value of visual instruments are widely used. But do not show the rectified value of, but the 1.11 -fold of it. This is in a sinus curve, the rms value, see below at " comparison ". This allows the devices indicate the RMS value - due to the detection of the direct guidance value. Sensible and correctly is the only sinusoidal for the course, which occurs however in many sizes change measuring tasks. For any other waveform, the use of such devices, however, is questionable to meaningless, see below under "Consequence ".

Also questionable is meaningless to the measurement of an AC signal, the signal is superimposed on a DC, see below under " mixed voltage ". Therefore, it is detected by a part of the measuring instruments, the alternating component alone.

Derivation

The average value is in a signal -time-diagram determined from the area, which extends in height between the signal line and the neutral line, and in width about the length of a full period. A rectangle having the same area and the same width, the average height of the surface; this height is the average. The area is determined by integration, the rectangle by multiplying.

Accordingly, the rectified value results from the area of the rectified signal; that means

Hence the formula

Result for sine size

A sinusoidal alternating quantity, short sine size, satisfies the equation

Since the surface is to be formed over a whole period of the function, this is independent of the starting point in time of the surface. A zero phase angle does not need to be taken into account; He is scheduled to simplify to 0.

As the picture shows, the rectified signal is after periodically so that the bill can be carried out with instead.

In, so that the amount sign can be omitted.

With is

By simplifying the to

Result for bleed sinusoidal voltage

The often produced by phase angle, shown in the picture to the left voltage is essentially a sinusoidal voltage, but after each zero crossing remains at zero, and only one time aT then the sine wave is turned back on. For this voltage results

With 0 ≤ a < ½.

Result for pulsed voltage

The voltage shown in the picture above u is a mixed voltage; it arises from a periodically for the duration aT off and off for the remainder of the period of positive DC voltage U. Since there are no negative instantaneous values ​​here, average rectified value and are the same size;

0 ≤ a ≤ 1, The boundary cases a = 0 and a = 1, the supply never switched on, and the always-on voltage.

Is the DC component of the mixed voltage which is superimposed on an alternating component.

Result for the alternating component

The alternating component of the pulsed voltage shows the picture below left. Here again is the mean = 0

Rectification is obtained the curve shown next; the rectified value is obtained from the mean value. The surface for the duration of one period is composed of two rectangles, each of which has the size. This is

Result for mixed voltage

For a mixed voltage, two cases must be distinguished.

1 In the accompanying picture on the left is the DC component ( in absolute value ) is greater than the peak value of the AC component. The curve does not intersect the zero line. In this case, the rectified value is equal to the magnitude of the DC component. For a discussion of the alternating component is not included.

2 In the picture, the DC component is right ( in absolute value ) is less than the peak value of the AC component. The curve intersects the zero line. In this case, the determination of a direct guideline value is not meaningful; it does not contain a statement to the dc component to ac component nor yet to their ratio.

Comparison with RMS rectified value

The ratio of the rms value for rectified value is referred to as the form factor

This allows the waveform of an alternating or mixed size judge. He is ≥ 1 and is greater, the " bizarre " of course.

For sine size

For bleed sinusoidal voltage

For pulsed voltage

The limiting case of a = 0, gives V = 0, and is excluded from the comparison.

For alternating component of the pulsed voltage

The limiting cases a = 0 and a = 1 do not contain alternating component and be excluded.

Metrological consequence

By the rectified value -forming instrument can result in a considerable error of measurement, as it is scaled and adjusted so that the displayed value should be an effective value.

When using these devices so caution is advised. The relative error of the waveform can easily exceed the range " a few percent ". The sinusoidal shape is still most likely to be found in the voltage in the power supply network; there is the area of ​​operation of these devices. But even the mains voltage is distorted by the variety of electronic, non-linear loads. A fortiori, the power consumption from the mains is often distorted so much that the measurement of the direct guidance value, no reasonable conclusion can be made about the current.

Documents

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  • Electromagnetic Theory
Form factor (electronics)
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