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. What is meant by the term 'phase angle' in Physics?
In Physics, the phase angle represents the specific position of a point in time within a periodic waveform's cycle. It is an angular component, usually measured in degrees or radians, that describes the wave's starting position at time t=0 relative to a reference point. Essentially, it tells you at what point the cycle begins.
2. What is the general formula representing phase angle in a sinusoidal wave?
The general equation for a sinusoidal wave, such as voltage or displacement, is given by:
A(t) = Amax × sin(ωt + φ)
Where:
- A(t) is the instantaneous amplitude at time t.
- Amax is the maximum amplitude or peak value.
- ω is the angular frequency of the wave.
- φ (phi) is the phase angle, which shifts the wave horizontally along the time axis.
3. How does the phase angle relationship between voltage and current differ in a resistor, inductor, and capacitor?
In an AC circuit, the phase relationship between voltage (V) and current (I) is fundamental and varies across different components:
- Resistor (R): The voltage and current are in-phase. The phase angle difference is 0°, meaning they reach their maximum and zero values simultaneously.
- Inductor (L): The voltage leads the current by 90° (or π/2 radians). The voltage reaches its peak value a quarter cycle before the current does.
- Capacitor (C): The current leads the voltage by 90° (or π/2 radians). The current reaches its peak value a quarter cycle before the voltage does.
4. What is the significance of phase angle in Simple Harmonic Motion (SHM)?
In Simple Harmonic Motion (SHM), the phase angle, often called the phase constant or epoch, is crucial as it determines the initial conditions of the oscillating particle. Specifically, it defines the particle's position and direction of velocity at the starting time (t=0). A different phase angle means the oscillation starts from a different point in its cycle.
5. Why does a path difference between two waves lead to a phase difference?
A phase difference arises from a path difference because the two waves travel unequal distances to reach a common point. The wave that travels the longer path takes more time to arrive. This time lag means it has completed a different number of oscillations compared to the wave with the shorter path. This mismatch in the number of completed cycles at the point of observation is what creates a phase difference. The phase difference is directly proportional to the path difference.
6. What is the difference between phase angle and phase shift?
While related, phase angle and phase shift describe different aspects:
- Phase Angle: This is an absolute property of a single wave. It defines the wave's starting point or position on its cycle at t=0.
- Phase Shift: This is a relative measurement between two or more waves of the same frequency. It describes the amount by which one wave is displaced (leads or lags) in time with respect to another, and it's also known as the phase difference.
7. Why is understanding phase angle so important in real-world applications like AC circuits?
Understanding phase angle is critical for practical engineering. In AC power systems, the phase angle between voltage and current determines the power factor. A low power factor indicates inefficient power usage, which is why utility companies work to correct it. In electronics and telecommunications, phase angles are vital for designing filters, oscillators, and ensuring signals are synchronized correctly for accurate data transmission.
8. How are 'in-phase' and 'out-of-phase' conditions for waves defined?
These terms describe the relative timing of two waves with the same frequency:
- In-Phase: Two waves are in-phase when their phase difference is 0° or a full multiple of 360° (2π radians). They reach their maximum peaks, troughs, and zero-crossings at the exact same time. This leads to constructive interference.
- Out-of-Phase: This occurs when there is any non-zero phase difference. A special case is phase opposition, where the phase difference is exactly 180° (π radians). In this state, one wave's peak aligns with the other's trough, leading to destructive interference.
