View of A REVIEW ON PHASE DIFFERENCE MEASUREMENT OF SINUSOIDAL SIGNALS

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ACCENT JOURNAL OF ECONOMICS ECOLOGY & ENGINEERING Peer Reviewed and Refereed Journal, ISSN NO. 2456-1037

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A REVIEW ON PHASE DIFFERENCE MEASUREMENT OF SINUSOIDAL SIGNALS

Surendra Kumar Rai M. Tech Scholar, JEC Jabalpur

Prashant Kumar Jain Prof. JEC Jabalpur

Abstract - The phase measurement of sine wave signals is important in several applications, such as electric and electronic instrumentation and telecommunications. The uncertainty of the phase measurement has an essential role in ensuring the suitable performance of the devices and systems used by the relevant application. Some highly accurate phase measurement methods have been developed and implemented in different instrument types that are currently available on the market or have been proposed in the scientific literature, each capable of covering very different frequency ranges. This article presents an overview of these methods and instruments in order to highlight the characteristics in terms of the measurement uncertainty of the main methods and instruments that are used, by taking into account a varying operative frequency range. The standard deviations considered in the surveyed literature are used to identify a phase measurement method that is capable of covering a large high-frequency range, simultaneously maintaining a low value of measurement uncertainty.

1 INTRODUCTION

The measurement of phase difference between sinusoidal signals plays an important role in communication, electric power, geological exploration, fault diagnosis, aerospace and other fields. For instance, in an AC power system, fast and accurate measurement of phase difference between voltage and current signals is an important prerequisite to calculate its precise power factor. The most common way is to use a general purpose oscilloscope in measuring phase difference between two sinusoidal signals.

But the measurement accuracy of the general purpose oscilloscope is generally low.

A signal is a function that conveys information about a phenomenon. In electronics and telecommunications, it refers to any time varying voltage, current, or electromagnetic wave that carries information. A signal may also be defined as an observable change in a quality such as quantity. Signals are classified as analog and discrete signals. Analog signal is a continuous signal which delivers information at every moment of time whereas discrete signal can only give information at defined time instants.

Analog signals are continuous in time. A continuous-time signal is an infinite and uncountable sequence of numbers, as are the possible values each number can have. A discrete-time signal is a finite

sequence of numbers, with finite possible values for each number.

The current and voltage signals are periodic analog signals. These signals are first discritized. This means that the original continuous signal is discritized in to samples.

Discrete Fourier series is applicable only in discrete signals. A discrete time signal can be expanded using DFS to recover the phase angle and amplitude of the signal. Let x(n) is a discrete time signal then Fourier coefficients for this signal are expressed as:

ak = ²

𝑁 ^𝑁_𝑛=0cos⁡(2 ∗ 𝜋 ∗ 𝑛 ∗ 𝑘 𝑁 ). xn

bk = ²

𝑁 ^𝑁_𝑛=0sin⁡(2 ∗ 𝜋 ∗ 𝑛 ∗ 𝑘 𝑁 ). xn

The practical signals are impure sinusoids. This means that they contain some harmonics also. To ensure faithful recovery of signal in the presence harmonics a separate simulation study has been carried out. Desired amplitude of harmonic of specific order is added to the original signal. This corrupt signal is then discritized at different sampling frequencies. The amplitude and phase of fundamental now is extracted again. Here a study is carried out as what should be minimum sampling frequency that will render the recovery process with required accuracy.

Process of taking values of the analog waveform at regularly spaced time

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ACCENT JOURNAL OF ECONOMICS ECOLOGY & ENGINEERING Peer Reviewed and Refereed Journal, ISSN NO. 2456-1037

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intervals is termed as sampling. Number

of samples taken per second is known as sampling rate and the time interval between samples is known as sampling period. Sampling period is reciprocal of frequency. An analog signal is continuous in time and it is necessary to convert this to a flow of digital values.

It is therefore required to define the rate at which new digital values are sampled from the analog signal. The rate of new values is called the sampling rate or sampling frequency of the converter.

An ADC converts a continuous- time and continuous-amplitude analog signal to a discrete-time and discrete- amplitude digital signal. The conversion involves quantization of the input, so it necessarily introduces a small amount of error or noise. Furthermore, instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input, limiting the allowable bandwidth of the input signal.

A harmonic is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called the 1st harmonic, the following harmonics are known as higher harmonics.

2 WORK STUDY

Tianxiang Wang et al [1] explain a digital correlation method to measure the phase difference between two sinusoidal signals is presented. In order to meet the requirements of real-time in practice application, a FPGA is employed to implement the measurement algorithm. In the correlation analysis by FPGA, a CORDIC algorithm is adopted to solve inverse trigonometric function, and thereby the phase difference can be conveniently derived. The experimental results show that the arctangent approach based on CORDIC can measure the real-time phase difference accurately.

Feng Pan et al [2] in their research paper have reported a new method for the testing of instrument transformers.

Measurement of ratio error and phase error are the important parameters to be measured. The transformer under test is compared against a standard transformer whose ratio error and phase error are

known. Generally, the errors are detected by comparing the output of the reference transformer and the output of the transformer which is under test when the same signal is applied to the primary windings of both the transformers.

D. Kang et al [3] reported their research in the paper. This paper explains a method to correct the phase difference.

An effective method is developed to correct the phase and frequency of spectrum. The continuous time domain signal is divided into two segments and fast Fourier transform is employed for them, respectively. The phase and frequency are corrected using the phase difference of matching discrete spectral lines.

Jon Ivar Juvik [4], in his solo authored research paper discussed the calibration of instrument transformers is.

Calibration of instrument transformers with digital output requires knowledge of the time delay that occurs in the system.

The delay-time of the reference systems should be exactly known. A time delay to the signals is produced by the entire analog to digital converters during the process of data processing and digital filtering.

XIA Weijian et al [5], in their paper explained a method for power harmonic analysis and phase difference correction.

According to this paper it is much complex to understand the synchronous sampling and when fast Fourier transforms (FFT) is used for harmonic analysis of power system. This paper presents an enhanced method for the harmonic analysis of power system which is based on phase-shifted difference correction and Blackman window technique.

3 CONCLUSION

Literature over the phase difference measurement has been studied thoroughly. Several authors worked on it.

It is concluded that phase difference measurement of analog signals is a need of signal engineering and it is not very easy in case when there is a very small phase difference o the order of few seconds. It is a big challenge to measure such difference between two sinusoidal signals. Phase difference between primary and secondary windings of transformers is an application of this task. It is also

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ACCENT JOURNAL OF ECONOMICS ECOLOGY & ENGINEERING Peer Reviewed and Refereed Journal, ISSN NO. 2456-1037

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concluded that harmonics present in the

signals affect the phase difference measurement process.

REFERENCES

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2. Feng Pan, Ruimin Chen, Yong Xiao and Weiming Sun, “Electronic Voltage and Current Transformers Testing Device”, Sensors, January 2012.

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