Agilent 33120A User's Guide

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Chapter 7 TutorialAttributes of AC SignalsAC Attributes(continued)The magnitude of a sine wave can be described by the RMS value(effective heating value), the peak-to-peak value (2 x zero-to-peak),or the average value. Each value conveys information about the sinewave. The table below shows several common waveforms with theirrespective peak and RMS values.Waveform Shape Crest Factor (C.F.)AC RMSAC+DC RMSV –0 –1.414V1.414V1.414V –01.732V1.732V1.732V –0tTT» tVC.F.»X 1 - Ë 1 ÛÌÍC.F. ÜÝ2VC.F.Each waveshape exhibits a zero-to-peak value of “V” volts.Crest factor refers to the ratio of the peak-to-RMS value of the waveform.284
Chapter 7 TutorialAttributes of AC SignalsRMS The RMS value is the only measured amplitude characteristic of awaveform that does not depend on waveshape. Therefore, the RMS valueis the most useful way to specify ac signal amplitudes. The RMS value(or equivalent heating value) specifies the ability of the ac signal todeliver power to a resistive load (heat). The RMS value is equal to thedc value which produces the same amount of heat as the ac waveformwhen connected to the same resistive load.For a dc voltage, this heat is directly proportional to the amount ofpower dissipated in the resistance. For an ac voltage, the heat in aresistive load is proportional to the average of the instantaneous powerdissipated in the resistance. This has meaning only for periodic signals.The RMS value of a periodic waveform can be obtained by taking thedc values at each point along one complete cycle, squaring the values ateach point, finding the average value of the squared terms, and takingthe square-root of the average value. This method leads to the RMSvalue of the waveform regardless of the signal shape.Peak-to-Peak and Peak Value The zero-to-peak value is themaximum positive voltage of a waveform. Likewise, the peak-to-peakvalue is the magnitude of the voltage from the maximum positivevoltage to the most negative voltage peak. The peak or peak-to-peakamplitude of a complex ac waveform does not necessarily correlate tothe RMS heating value of the signal. When the specific waveform isknown, you can apply a correction factor to convert peak or peak-topeakvalues to the correct RMS value for the waveform.Average Value The average value of an ac waveform is the average ofthe instantaneous values measured over one complete cycle. For sinewaves, the average amplitude is zero since the waveform has equalpositive and negative half cycles. Since the quantity of interest is theheating value of the signal, the average value of a sine wave is taken tomean the average of the full-wave rectified waveform. The RMS value ofa sine wave is equal to 1.11 times the sine wave average amplitude.This relationship does not hold true for other waveshapes.7285
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