[Physics Class Notes] on Phase Angle Pdf for Exam

A periodic wave is the one whose displacement has a periodic variation with time or distance or even both. The continuous repeating pattern of this wave helps to determine its frequency, period, and amplitude. The Phase Angle is one of the crucial characteristics of a periodic wave. It is similar to the phrase in many properties. The angular component periodic wave is known as the Phase Angle. It is a complex quantity measured by angular units like radians or degrees. A representation of any pure periodic wave is as follows. 

 

A∠θ, where A is the magnitude and θ represents the Phase Angle of the wave. 

 

How can Phase Angle be measured?

The time delay between two periodic impulses is measured. The phase difference between two sinusoidal waveforms of the same frequency and without a dc component can be easily represented as illustrated in the diagram. As can be seen, the Phase Angle can be thought of as a percentage of the wave period measure of the temporal delay between two periodic signals. This fraction is usually stated in angle units, with a full cycle equaling 360 degrees. For example, in the figure, the voltage v1 leads by 360°/8 or 45° after passing through the zero cycle before a second voltage v2. Because Phase Angle is often calculated from the fundamental component of each waveform, distortion of either or both signals can result in mistakes, the magnitude of which varies depending on the nature of the distortion and the measuring method.

 

The majority of current phase-measuring devices are based on the usage of zero-crossing detectors. A squaring-up circuit (for example, an overdriven amplifier) is used to calculate the time at which each signal crosses the zero-voltage axis, which is then followed by a high-speed comparator. This generates a trigger pulse in each channel, which is used to drive a bistable flip-flop. The bistable produces a rectangular wave with a duty cycle proportionate to the phase difference between the two input signals. When this signal is integrated with a proper filter, a dc voltage is produced that represents the Phase Angle analogously. This voltage is then displayed on a panel meter (analogue or digital) with degrees or radians scaled appropriately. This principle-based instrumentation can measure phase deviations to within 0.05° over a wide range of amplitudes and frequencies.

 

Phase Difference

In the case of a sine wave, the phase difference refers to the time interval by which one wave is behind or ahead of the waveform. Hence, it is a relative property of more than one waveform. It is represented by a Greek Letter ‘ɸ’. In any waveform, the complete phase is 360 degrees or 2π radians. The leading phase represents that the wave is ahead of another one having the same frequency. The definitions of two important terms in this concept are as follows. 

 

Phase Quadrature: Two waves are said to be in phase quadrature if their phase difference is 90 degrees (positive or negative).

 

Phase Opposition: If the phase difference between two waves of the same frequency is 180 degrees (positive or negative), then they are in phase opposition with each other. 

 

Phase Angle Formula and its relation with Phase Difference

The equation of the phase difference of a sine wave using maximum amplitude and voltage is

 

A(t)  = Amax X sin(ωt ɸ) 

 

Where Amax is the amplitude of the sine wave, ωt represents the angular velocity, and ɸ represents the Phase Angle. 

 

If ɸ > 0, then the wave has a positive phase of the Phase Angle. Similarly, if ɸ < 0, then the wave has a negative phase of the Phase Angle. 

 

Measurement of a Phase Angle

Let’s consider a periodic wave. According to the Phase Angle definition, it is nothing but the angular component of the periodic wave. You can measure its value by following the below steps. 

• To measure the Phase Angle, we have to measure the number of units of angular measure between the point on the wave and reference point. It is important to note that the reference point can be present on the same waveform or another wave. 

• The projection of a rotating vector of an Argand diagram to the real axis is the reference point.

• The Phase Angle of a point is the value of the point on the abscissa with respect to the point on the wave. 

 

Generally, we can plot the wave on any standard coordinate system. There is also a crucial role of Phase Angle in electronics due to the presence of different sinusoidal waves and voltage. In electronics, Phase Angle refers to the lag or lead in the number of electric degrees between voltage and current waveforms in the circuit. 

 

Voltage and Current Phase Relationships to Resonance Circuit

The resonance circuit is popularly known as the RLC circuit, which consists of a resistor, inductor and capacitor. The explanation of the voltage and current behavior of the RLC circuit with respect to phase is as follows.

 

Resistor: The voltage and current in the same phase in a resistor. Hence, the phase difference between these quantities in a resistor is zero. 

 

Capacitor: The current and voltage in a capacitor are not in the same phase with each other. In this equipment, the current leads the voltage by 90 degrees. Hence, the phase difference between both of them is 90 degrees in a capacitor. 

 

Inductor: The voltage and current are not in the same phase with each other in the inductor too. In this device, the voltage is ahead of the current by 90 degrees. Hence, the phase difference between voltage and current is 90 degrees in an inductor. This nature is the opposite as compared to the capacitor.

 

 

The above image shows the phase difference between voltage and current in an inductor. Here, the voltage leads the current, as shown above. 

 

In Phase Sine Waveforms

Two alternating waves are in-phase with each other when their phase difference is zero. It can be possible if both the waves have the same frequency and same phase. It is important to note that there can be a difference in amplitude of two in-phase waveforms.  In these types of waveforms, the retardation of wavelengths is the whole number like 0, 1, 2, 3…etc

 

 

The above image shows the two different waveforms with the same frequency but different amplitudes.