What is the average peak RMS voltage

AC quantity measurements

AC quantity measurements

Chapter 1 - Basics of AC Theory

So far we know that alternating voltage changes polarity and alternating current changes direction. We also know that alternating current can alternate in different ways, and by tracing its course over time we can represent it as a "waveform". We can measure the rate of change by measuring the time it takes for a wave to develop, it repeats itself (the "period") and expresses this as cycles per unit of time or "frequency". In music, frequency is the same as pitch, which is the essential property that distinguishes one note from another.

However, a measurement problem arises when we try to express how large or small an AC quantity is. With direct current, where voltages and currents are generally stable, we have little difficulty in expressing how much voltage or current we have in any part of a circuit. But how do you give a single size measurement to something that is constantly changing? "// www.allaboutcircuits.com/textbook/alternating-current/chpt-1/ac-waveforms/">AC waveform: FigureBelow

Peak voltage of a waveform.

Another option is to measure the total height between opposing peaks. This is known as the peak-to-peak (PP) value of an AC waveform

Peak-to-peak voltage of a waveform.

Unfortunately, one of these waveform amplitude terms can be misleading when comparing two different types of waves. For example, a square wave that peaks at 10 volts is obviously a greater amount of voltage for a greater period of time than a triangular wave that peaks at 10 volts. The effects of these two AC voltages driving a load would be quite different: FigureBelow

A square wave produces a greater heating effect than the same peak voltage triangle wave.

One way to express the amplitude of various waveforms in a more equivalent way is to mathematically average the values ​​of all points on the graph of a waveform into a single aggregate number. This measure of amplitude is known simply as the average value of the waveform. If we algebraically average all the points on the waveform (i.e., their sign either positive or negative), the average for most waveforms is technically zero because all positive points cancel out all negative points over a full cycle: Figure below

The average value of a sine wave is zero.

This is of course true for any waveform that has areas of equal area above and below the "zero" line of a graph. However, as a practical measure of the total value of a waveform, "average" is commonly defined as the mathematical mean of all the absolute values ​​of the points over a cycle. In other words, we compute the practical average of the waveform by considering all the points on the wave to be positive quantities, as if the waveform looked like this: FigureBelow

Waveform seen by AC "average responsive" meter.

Polarity-insensitive mechanical meter movements (meters that are designed to react evenly to the positive and negative half-waves of an alternating voltage or an alternating current) are registered proportionally to the (practical) average value of the waveform, since the inertia of the pointer averages against the tension of the spring of course the force generated by the varying voltage / current values ​​over time. Conversely, polarity-sensitive meter movements vibrate uselessly when exposed to AC voltage or current, with their needles rapidly oscillating around the zero mark, indicating the true (algebraic) average of zero for a symmetrical waveform. In this text, when reference is made to the "average value" of a waveform, it is believed that the "practical" definition of the average is intended unless otherwise specified.

Another method of deriving a total waveform amplitude value is based on the waveform's ability to do useful work when applied to a load resistor. Unfortunately, an AC voltage measurement based on some work performed by a waveform is not the same as the "average" value of that waveform, since the power (per unit of time) delivered by a given load is not directly proportional to the magnitude of the voltage or impressed with current . Rather, the power is proportional to the square of the voltage or current applied to a resistor (P = E 2 / R and P = I 2 R). While the math of such an amplitude measurement can't be straightforward, its usefulness is.

Consider a band saw and a puzzle, two pieces of modern woodworking equipment. Both types of saws are cut with a thin, serrated, motorized metal blade to cut wood. But while the bandsaw uses a continuous movement of the blade to cut, the puzzle uses a back-and-forth motion. The comparison of alternating current (AC) to direct current (DC) can be compared with the comparison of these two types of saw: FigureBelow

Bandsaw puzzle analogy of DC versus AC.

The problem of describing the changing quantities of alternating voltage or current in a single total measurement is also present in this saw analogy: How can we express the speed of a jigsaw blade? // www.allaboutcircuits.com/textbook/direct -current / chpt-1 / resistance / "> Resistance: FigureBelow

An RMS voltage produces the same heating effect as a DC voltage

In the two circuits above, we have the same amount of load resistance (2Ω) giving off the same amount of energy in the form of heat (50 watts) with one powered by AC and the other powered by DC. Since the AC power source pictured above is equivalent to a 10 volt DC battery (in terms of the power delivered to a load), we would call this a "10 volt" AC power source. More precisely, we would call its voltage value 10 volts RMS. The "RMS" qualifier stands for Root Mean Square, the algorithm used to get the DC equivalent value of points on a graph (essentially the process is to square all the positive and negative points on a waveform graph and then to average these squared values) take the square root of that average to get the final answer). The alternate terms equivalent or DC equivalent are sometimes used in place of "RMS", but the amount and principle are both the same.

RMS amplitude measurement is the best way to relate AC quantities to DC quantities or other AC quantities of different waveform shapes when it comes to measuring electrical power. For other considerations, peak or peak-to-peak measurements may be best to use. For example, when determining the correct wire size (ampacity) for conducting electrical energy from a source to a load, it is best to use RMS current measurement because the main problem with current is overheating of the wire, which is a function of power dissipation caused by current through the resistance of the wire. However, when evaluating insulators for use in high voltage AC applications, peak voltage measurements are best because the main problem here is insulator "flashover" caused by brief voltage spikes regardless of time.

Peak and peak-to-peak measurements are best performed with an oscilloscope, which, due to the rapid action of the cathode ray tube in response to voltage changes, can capture the wave crests with great accuracy. For RMS measurements, analog movement movements (D'Arsonval, Weston, Eisenflügel, electrodynamometer) will work as long as they are calibrated in RMS numbers. Since the mechanical inertia and dampening effects of an electromechanical meter movement naturally make the deflection of the needle proportional to the average value of the AC current rather than the actual RMS value, analog meters need to be specially calibrated (or mis-calibrated) depending on how you're doing it on) to display voltage or current in RMS units. The accuracy of this calibration depends on an assumed waveform, usually a sine wave.

Electronic measuring devices specially developed for RMS measurement are best suited for this task. Some device manufacturers have developed ingenious methods to determine the RMS value of any waveform. One such manufacturer produces "true RMS" gauges with a tiny resistance heating element powered by a voltage proportional to that measured. The heating effect of this resistor element is measured thermally to give a true RMS value without any mathematical calculations, just the laws of physics that are in action in fulfilling the definition of RMS. The accuracy of this type of RMS measurement is independent of the waveform.

For "pure" waveforms, simple conversion coefficients exist to equate peaks, peaks, averages (practical, not algebraic), and RMS measurements:

Conversion factors for general waveforms.

In addition to RMS, average, peak (peak), and peak-to-peak measurements of an AC waveform, there are ratios that express the proportionality between some of these fundamental measurements. For example, the crest factor of an AC waveform is the ratio of its peak value (peak value) divided by its RMS value. The form factor of an AC waveform is the ratio of its RMS value divided by its average value. Rectangular waveforms always have a peak and shape factor of 1 because the peak is the same as the RMS and average value. Sinusoidal waveforms have an RMS value of 0.707 (the reciprocal of the square root of 2) and a shape factor of 1.11 (0.707 / 0.636). Triangle and sawtooth waveforms have RMS values ​​of 0.577 (the reciprocal of the square root of 3) and shape factors of 1.15 (0.577 / 0.5).

Note that the conversion constants shown here for peak, RMS, and average amplitudes of sine, square, and triangle waves only apply to pure shapes of those waveforms. The RMS and average values ​​of the distorted waveforms are not in the same proportion to each other: FigureBelow

Arbitrary waveforms do not have easy conversions.

This is a very important concept to understand when using an analog D'Arsonval meter movement to measure AC voltage or current. D'Arsonval analog motion calibrated to display sine wave RMS amplitude is only accurate when measuring pure sine waves. If the waveform of the voltage or current being measured is anything but a pure sine wave, the reading given by the meter will not be the true RMS value of the waveform, since the degree of needle deflection in an analog D'Arsonval meter movement is proportional to the average value the waveform, not the RMS. The RMS meter calibration is achieved by "twisting" the span so that it shows a small multiple of the average value, which is the RMS value for a particular waveform and only for a particular waveform.

Since the sinusoid is most common in electrical measurements, it is the waveform adopted for the analog calibration and the small multiple used in calibrating the meter is 1. 1107 (the form factor: 0.707 / 0.636: the ratio of divided RMS) on average for a sinusoidal waveform). Any waveform other than a pure sine wave will have a different ratio of RMS to mean values, and thus a meter calibrated for sinusoidal voltage or current will not display true RMS when reading a non-sinusoidal wave. Note that this restriction only applies to simple analog AC meters that do not use "True RMS" technology.

  • The amplitude of an AC waveform is its height as shown on a graph over time. An amplitude measurement can take the form of peak, peak-to-peak, average, or RMS size.
  • The peak amplitude is the height of an alternating current curve measured from the zero mark to the highest positive or lowest negative point on a graph. Also known as the ridge amplitude of a wave.
  • Peak-to-peak amplitude is the total height of an AC waveform measured from maximum positive to maximum negative peaks on a graph. Often abbreviated as "PP".
  • Average amplitude is the mathematical "mean" of all points on a waveform over the period of a cycle. Technically, the average amplitude of any waveform with areas of equal area above and below the "zero" line on a graph is zero. However, as a practical measure of amplitude, the average value of a waveform is often calculated as the mathematical mean of all the absolute values ​​of the points (taking all negative values ​​and considering them positive). For a sine wave, the average value so calculated is approximately 0.637 of its peak value.
  • "RMS" stands for Root Mean Square and is a way of expressing an AC amount of voltage or current in terms of functionally equivalent DC. For example, 10 volts AC RMS is the amount of voltage that would produce the same amount of heat dissipation across a resistor of a given value as a 10 volt DC power supply. Also known as the "equivalent" or "DC equivalent" value of an alternating voltage or current. For a sine wave, the RMS value is approximately 0.707 of its peak.
  • The crest factor of an AC waveform is the ratio between its peak value (crest) and its RMS value.
  • The form factor of an AC waveform is the ratio of its RMS value to its average value.
  • Analog, electromechanical counter movements react proportionally to the mean value of an alternating voltage or an alternating current. If an RMS display is desired, the calibration of the measuring device must be "distorted" accordingly. This means that the accuracy of an electromechanical meter's RMS display depends on the purity of the waveform: whether it is exactly the same waveform as the waveform used in calibration.