What is Phase Angle?
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.
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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
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The above image shows the two different waveforms with the same frequency but different amplitudes.
FAQs on Phase Angle
1. Why does a Difference in Path Length Between the Waves Cause a Phase Shift in them?
Path difference refers to the difference in the path traversed by the waveforms. There is a direct relationship between the path difference and phase difference. If two waves travel different lengths to reach a point, then one of them has to go more distance than the other. Hence, if these waves were in phase in the beginning, then they will be out of phase after reaching the destination. The difference can be the number of wavelengths that fit in their path difference. Hence, we can say that the phase difference and the path difference are directly proportional to each other.
2. What are the two Different Conditions for the Out of Phase Wave?
Two waveforms are in-out of phase if they have the same frequency but different phase. The phase difference in these types of waves is not zero. There are two conditions in these types of waveforms, namely leading phase and lagging phase. When two waveforms are traveling along the same axis with the same frequency, and one is ahead of second, then this condition is known as the leading phase wave. Similarly, when one is behind the second, then this condition is known as lagging phase wave.
3. What is Phase Angle?
The term "Phase Angle" refers to a specific point in the time of a cycle that is measured from some arbitrary zero and expressed as an angle. Furthermore, one of the most crucial aspects of a periodic wave is its Phase Angle. A periodic wave is one whose displacement varies in a predictable pattern in proportion to distance, time, or both.
The periodic wave's amplitude, period, and frequency may all be calculated using its continuous repeating pattern. In addition, Phase Angle denotes the angular component of a periodic wave. Furthermore, it is a complicated quantity that is measured in angular units such as degrees or radians.
4. How to measure Phase Angle?
When dealing with a periodic wave, the following steps can be used to calculate the Phase Angle:
The number of units of angular measure that exist between the reference point and the point on the wave can be used to calculate the Phase Angle. In addition, the reference point can be on the same wave or on a different wave.
The reference point must be selected from the projection of the rotation vector onto the real axis of the Argand diagram.
The Phase Angle of a point on the wave is determined by the value of the point on the abscissa corresponding to that point.
The graphing of the wave can be done on any standard coordinate system in general. Furthermore, in the Cartesian plot, one complete wave cycle has a 360o Phase Angle.
In electronics, where voltage and other sinusoidal waves are involved, the Phase Angle is extremely essential. The amount of electrical degrees of lag or lead between the voltage and current waveforms in an ac circuit is referred to as Phase Angle in electronics.
5. What is the importance of Phase Angle?
Students already know that Phase Angle is important when it comes to electrical engineering. The term Phase Angle is not only important in electrical engineering.
Learn that linear time-invariant systems can be abstracted into blocks from the perspective of "signals and systems," which are mathematical abstractions of many systems, such as mechanical, electrical, and economic, and examine relationships. Between inputs (by dividing the output by the input, this is the so-called transfer function). This transfer function describes the amplification of the system as a mathematical abstraction.
6. What is a Phase Shift?
A "Phase Shift" is a small variation between two waveforms. In both electronics and mathematics, a Phase Shift is the delay that exists between these two waveforms with the same frequency or period. In summary, the Phase Shift is expressed as an angle. Angles are measured in positive or negative radians or degrees.
For example, a 90° positive Phase Shift corresponds to a quarter of a complete cycle. In this case, the second wave is 90° ahead of the first wave. The time delay between them and the frequency of the waveform can be used to calculate the Phase Shift.
7. What is the need of Phase Angle measurement?
The needs are-
Phase attitude meters are used to confirm the right connection of three-phase transformer banks which need to be paralleled with an current electric bus or high voltage line. The procedure of creating those measurements is understood as “phasing-out” and is executed earlier than the tie-in is made.
Phase attitude dimension is likewise hired to investigate the operation of AC synchronous mills and synchronous cars to confirm the right operation of discipline regulators and synchronizing system.
The Phase attitude dimension is used for verifying the right set up of medium and high-voltage number one metering system and complex protecting relays that receive enter from Potential and Current Transformers.