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# Phase Time And Frequency Measurement Pdf

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## Frequency and Phase Measurement

If the AC is being generated by an electromechanical alternator, the frequency will be directly proportional to the shaft speed of the machine, and frequency could be measured simply by measuring the speed of the shaft. If frequency needs to be measured at some distance from the alternator, though, other means of measurement will be necessary.

One simple but crude method of frequency measurement in power systems utilizes the principle of mechanical resonance. Every physical object possessing the property of elasticity springiness has an inherent frequency at which it will prefer to vibrate. The tuning fork is a great example of this: strike it once and it will continue to vibrate at a tone specific to its length.

Longer tuning forks have lower resonant frequencies: their tones will be lower on the musical scale than shorter forks. Imagine a row of progressively-sized tuning forks arranged side-by-side. They are all mounted on a common base, and that base is vibrated at the frequency of the measured AC voltage or current by means of an electromagnet.

Whichever tuning fork is closest in resonant frequency to the frequency of that vibration will tend to shake the most or the loudest. The user of this meter views the ends of all those unequal length reeds as they are collectively shaken at the frequency of the applied AC voltage to the coil.

The one closest in resonant frequency to the applied AC will vibrate the most, looking something like:. Vibrating reed meters, obviously, are not precision instruments, but they are very simple and therefore easy to manufacture to be rugged. They are often found on small engine-driven generator sets for the purpose of setting engine speed so that the frequency is somewhat close to 60 50 in Europe Hertz.

While reed-type meters are imprecise, their operational principle is not. See Figure below. One or both components are made adjustable, and a meter is placed in the circuit to indicate the maximum amplitude of the voltage across the two components. The adjustment knob s are calibrated to show resonant frequency for any given setting, and the frequency is read from them after the device has been adjusted for the maximum indication on the meter.

In frequency as in other types of electrical measurement, the most accurate means of measurement are usually those where an unknown quantity is compared against a known standard , the basic instrument doing nothing more than indicating when the two quantities are equal to each other.

If we have access to an accurate frequency standard a source of AC voltage holding very precisely to a single frequency , the measurement of an unknown frequency, by comparison, should be relatively easy.

For that frequency standard, we turn our attention back to the tuning fork, or at least a more modern variation of it called the quartz crystal. Quartz is a naturally occurring mineral possessing a very interesting property called piezoelectricity. Piezoelectric materials produce a voltage across their length when physically stressed, and will physically deform when an external voltage is applied across their lengths.

Quartz rock is elastic springy within that small range of bending which an external voltage would produce, which means that it will have a mechanical resonant frequency of its own capable of being manifested as an electrical voltage signal. Chips of quartz rock can be precisely cut for desired resonant frequencies, and that chip mounted securely inside a protective shell with wires extending for connection to an external electric circuit.

The schematic symbol is shown in the figure below. Electrically, that quartz chip is equivalent to a series LC resonant circuit. Figure below The dielectric properties of quartz contribute an additional capacitive element to the equivalent circuit. The capacitance shown in parallel due to the wire connections across the dielectric insulating quartz body is real, and it has an effect on the resonant response of the whole system.

Because the resonant frequency is solely dependent on the physical properties of quartz a very stable substance, mechanically , the resonant frequency variation over time with a quartz crystal is very, very low. This is how quartz movement watches obtain their high accuracy: by means of an electronic oscillator stabilized by the resonant action of a quartz crystal.

For laboratory applications, though, even greater frequency stability may be desired. To achieve this, the crystal in question may be placed in a temperature stabilized environment usually an oven , thus eliminating frequency errors due to thermal expansion and contraction of the quartz. For the ultimate in a frequency standard though, nothing discovered thus far surpasses the accuracy of a single resonating atom. This is the principle of the so-called atomic clock , which uses an atom of mercury or cesium suspended in a vacuum, excited by outside energy to resonate at its own unique frequency.

The resulting frequency is detected as a radio-wave signal and that forms the basis for the most accurate clocks known to humanity. Now we get to the practical part: once we have a source of accurate frequency, how do we compare that against an unknown frequency to obtain a measurement? One way is to use a CRT as a frequency-comparison device. Cathode Ray Tubes typically have means of deflecting the electron beam in the horizontal as well as the vertical axis. If metal plates are used to electrostatically deflect the electrons, there will be a pair of plates to the left and right of the beam as well as a pair of plates above and below the beam as in the figure below.

Cathode ray tube CRT with vertical and horizontal deflection plates. These patterns are called Lissajous figures and are a common means of comparative frequency measurement in electronics.

If the two frequencies are the same, we will obtain a simple figure on the screen of the CRT, the shape of that figure being dependent upon the phase shift between the two AC signals. The first picture is of the Lissajous figure formed by two AC voltages perfectly in phase with each other:. If the two AC voltages are not in phase with each other, a straight line will not be formed. Lissajous figure: same frequency, 90 or degrees phase shift. When we are faced with signal frequencies that are not the same, Lissajous figures get quite a bit more complex.

Lissajous figure: Horizontal frequency is twice that of vertical. The more complex the ratio between horizontal and vertical frequencies, the more complex the Lissajous figure. Consider the following illustration of a frequency ratio between horizontal and vertical:. Lissajous figure: Horizontal frequency is three times that of vertical. If the two frequencies are locked in an exact integer ratio between each other, the Lissajous figure will be stable on the viewscreen of the CRT.

The physics of Lissajous figures limits their usefulness as a frequency-comparison technique to cases where the frequency ratios are simple integer values , , , , , etc. Despite this limitation, Lissajous figures are a popular means of frequency comparison wherever an accessible frequency standard signal generator exists. In Partnership with Infineon. In Partnership with Analog Devices. Don't have an AAC account? Create one now. Forgot your password? Click here. Latest Projects Education. Textbook Frequency and Phase Measurement.

Home Textbook Vol. An important electrical quantity with no equivalent in DC circuits is frequency. Method of Frequency Measurement Using the Principle of Mechanical Resonance One simple but crude method of frequency measurement in power systems utilizes the principle of mechanical resonance.

Using a form of Tank Circuit While reed-type meters are imprecise, their operational principle is not. Using Quartz Crystal For that frequency standard, we turn our attention back to the tuning fork, or at least a more modern variation of it called the quartz crystal.

This deformation is very, very slight in most cases, but it does exist. Crystal frequency determining element schematic symbol. Quartz crystal equivalent circuit. Practical Part Now we get to the practical part: once we have a source of accurate frequency, how do we compare that against an unknown frequency to obtain a measurement? Other frequency meters use electric resonant circuits LC tank circuits, usually to indicate frequency.

One or both components are made to be adjustable, with an accurately calibrated adjustment knob, and a sensitive meter is read for maximum voltage or current at the point of resonance. Frequency can be measured in a comparative fashion, as is the case when using a CRT to generate Lissajous figures. Reference frequency signals can be made with a high degree of accuracy by oscillator circuits using quartz crystals as resonant devices.

For ultra precision, atomic clock signal standards based on the resonant frequencies of individual atoms can be used. Published under the terms and conditions of the Design Science License. Log in to comment.

## We apologize for the inconvenience...

If the AC is being generated by an electromechanical alternator, the frequency will be directly proportional to the shaft speed of the machine, and frequency could be measured simply by measuring the speed of the shaft. If frequency needs to be measured at some distance from the alternator, though, other means of measurement will be necessary. One simple but crude method of frequency measurement in power systems utilizes the principle of mechanical resonance. Every physical object possessing the property of elasticity springiness has an inherent frequency at which it will prefer to vibrate. The tuning fork is a great example of this: strike it once and it will continue to vibrate at a tone specific to its length. Longer tuning forks have lower resonant frequencies: their tones will be lower on the musical scale than shorter forks. Imagine a row of progressively-sized tuning forks arranged side-by-side.

Frequency is generally defined as the number of cycles which occur in a given interval of time. This interval is usually chosen to be the second. The interdependence of frequency and time interval requires that a standard of one be also a standard of the other. Similarly, it can be said that the measurement of frequency is based upon time measurement. While certain instruments will measure either quantity with equal facility, many methods apply to the measurement of one or the other.

Resource Letter TFM Time and Frequency Measurement. Christine Hackman and puting the spectral density of either the phase or frequency fluctuations.

## We apologize for the inconvenience...

If the AC is being generated by an electromechanical alternator, the frequency will be directly proportional to the shaft speed of the machine, and frequency could be measured simply by measuring the speed of the shaft. If frequency needs to be measured at some distance from the alternator, though, other means of measurement will be necessary. One simple but crude method of frequency measurement in power systems utilizes the principle of mechanical resonance. Every physical object possessing the property of elasticity springiness has an inherent frequency at which it will prefer to vibrate.

### Time-Frequency Based Phase-Amplitude Coupling Measure For Neuronal Oscillations

Facebook Twitter. It is a very important oscilloscope used to analyse the waveform and measure them. Now here we will discuss how the measurement of waveform i. It is interesting to consider the characteristics of patterns that appear on the screen of a CRT when sinusoidal voltages are simultaneously applied to horizontal and vertical plates. These patterns are called 'Lissajous Patterns'.

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. Oscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory. The high temporal resolution provided by electroencephalography EEG enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Lack of symmetry in such a structure can result in oscillation in a standing wave rather than the travelling wave mode. In order to determine the mode of the signal, before going through the time consuming steps of time domain phase shift measurement, we have proposed a preliminary phase shift measurement technique in the frequency domain for a high frequency RTWO. This new technique was verified against direct phase measurements for a multiphase RTWO fabricated in a 0.

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Time and frequency measurements follow the conventions used in other areas where ∆t is the amount of phase deviation, and T is the measurement period.

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