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Chapter 8: Average and RMS Values, Complex Power, and Instruments
By Steven T. Karris
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From Circuit Analysis I with MATLAB Computing and Simulink/SimPowerSystems Modeling
This chapter defines average and effective values of voltages and currents, instantaneous and average power, power factor, the power triangle, and complex power. It also discusses electrical instruments that are used to measure current, voltage, resistance, power, and energy. 8.1 Periodic Time FunctionsA periodic time function satisfies the expression
 where n is a positive integer and T is the period of the periodic time function. The sinusoidal and sawtooth waveforms of Figure 8.1 are examples of periodic functions of time.
 Figure 8.1: Examples of periodic functions of time Other periodic functions of interest are the square and the triangular waveforms. 8.2 Average ValuesThe average value of any continuous function f (t) such as that shown in Figure 8.2 over an inter-val a ?t ?b,
 Figure 8.2: A continuous time function f(t) is defined as
 The average value of a periodic time function f(t) is defined as the average of the function over one period. Example 8.1 Compute the average value of the sinusoid shown in Figure 8.3, where V p denotes the peak (maximum) value of the sinusoidal voltage.
 Figure 8.3: Waveform for Example 8.1 Solution: By definition,  as expected since the net area of the positive and negative half cycles is zero. Example 8.2 Compute the average value of the half-wave rectification waveform shown in Figure 8.4.
 Figure 8.4: Waveform for Example 8.2 Solution: This waveform is defined as
 Then, its average value is found from
 In other words, the average...
Copyright Orchard Publications 2009 under license agreement with Books24x7
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