Waveforms of Voltages and Currents

2 Waveforms of Voltages and Currents Since f is a complex value, it can be expressed as 

The figure illustrates as the observation point shifts in the positive direction, the amplitude of the voltage decreases due to exp(-otx), and the angle of the voltage lags due to exp(- p x). 

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It is important to realize the difference between the AC Sweep and the Transient Analysis discussed in Part 6. The AC Sweep is used to find the magnitude and phase of voltages and currents. The Transient Analysis is used to look at waveforms versus time. An example of a waveform versus time is ... 

This graph shows us a voltage versus time. If you want to look at the magnitude and phase of voltages and currents, use the AC Sweep. The magnitude of the above waveform is 5 V and the phase is zero degrees—in phasor notation, 5Z0°. The AC Sweep will give a result such as 5Z0°. 

The Transient Analysis is used to look at plots of voltages and currents versus time. This simulation displays waveforms as you would see them on an oscilloscope screen. 

For comparison with the schematic drawings in Figure 19.7, the distribution of voltages and currents in the 1-cm simulated fiber is shown in Figure 19.8. The figure shows the transmembrane potential Vm and the total membrane current fm- Both are shown as a function of axial distance z along the strand at time t = 3 msec after the stimulus. (This spatial plot came from the same simulation as the set of waveforms... 

Total harmonic distortion (THD) Term used to quantify distortion as a percentage of the fundamental (pure sine) of voltage and current waveforms. 

In an alternating current system the voltage and current components travel in the shape of a sinusoidal waveform (Figure 17.9) and oscillate through their natural zeros, 100 times a second for a 50 Hz system. 

Figure 19.27 Approximate representation of assumed voltage and current waveforms illustrating a current-chopping effect and its attenuation while interrupting a circuit having 0,3 p.f.

The basic principle of this relay is the sensing of the phase displacement between the fundamental waveforms of the voltage and current waves of a power circuit. Harmonic quantities are filtered out when present in the... 

The conduction loss ( 2) is measured as the product of the switch terminal voltage and current waveforms. These waveforms are typically quite linear and the power loss during this period is given in Equation 4.1. 

A second type of quasi-resonant converter is the zero voltage switching (ZVS) quasi-resonant family. A ZVS QR buck converter and its waveforms are shown in Figure 4-11. Here the power switch remains on most of the time and performs resonant off periods to decrease the output power. Actually, the ZCS and the ZVS families mirror one another. If you were to compare the switch voltage and current waveforms between the two families, and if one inverts both the voltage and current waveforms in order to reference them to the power switch, the waveforms would have a striking resemblance to one another. 

Power factor (total) — Ratio of the total active power (watts) to the total apparent power (voltamperes) of the composite wave, including all harmonic frequency components. Due to harmonic frequency components, the total power factor is less than the displacement power factor, as the presence of harmonics tends to increase the displacement between the composite voltage and current waveforms. 

So far we have treated harmonics as stand-alone entities working to produce waveform distortion in AC voltages and currents. This approach is valid if we are looking at single-phase voltages or currents however, in a three-phase power system, the harmonics of one phase have a rotational and phase angle relationship with the... 

The terms displacement and true power factor, are widely mentioned in power factor studies. Displacement power factor is the cosine of the angle between the fundamental voltage and current waveforms. The fundamental waveforms are by definition pure sinusoids. But, if the waveform distortion is due to harmonics (which is very often the case), the power factor angles are different than what would be for the fundamental waves alone. The presence of harmonics introduces additional phase shift between the voltage and the current. True power factor is calculated as the ratio between the total active power used in a circuit (including harmonics) and the total apparent power (including harmonics) supplied from the source ... 

We know that voltages and currents reflect across the boundary by getting either multiplied or divided by the turns ratio. In fact, the reflected output voltage, Vor, is one of the most important parameters of a flyback, as we will see. As the name indicates, Vor is effectively the output voltage as seen by the primary side. In fact, if we compare the switch waveform of the flyback in Figure 3-1 with that of a buck-boost, we will realize that to the switch, it seems as if the output voltage is really Vor-... 

In traditional ac analysis in the complex plane, the voltages and currents were complex numbers. But the frequencies were always real. However now, in an effort to include virtually arbitrary waveforms into our analysis, we have in effect created a complex frequency plane too, (a + jco). This is called s-plane, where s = a + jco. Analysis in this plane is just a more generalized form of frequency domain analysis. 

Active query methods measure cell impedance, which is then correlated to SoC. The technique often superimposes an active signal (a low amplitude, characteristic high-frequency square or sinusoidal current pulse) onto the battery and then uses a transfer function on the response waveform to determine the ohmic polarization or a direct correlation to SoC. One permutation of this technique uses the voltage response to indigenous current spikes to map impedance in a similar way. This method provides reasonable results, but if hardware is involved it is often complex and expensive even sensors will require a relatively high-speed data acquisition bus to minimize the slew between voltage and current. 

Here Vo and /q are the amplitudes of the measured voltage and current waveforms, assumed sinusoidal. 

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