Phase Difference

3 Key excerpts on "Phase Difference"

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  eBook - ePub

  Introduction to Microwave Remote Sensing

  • Iain H. Woodhouse(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  1 , will travel a distance that can be divided up into some number of whole wavelengths, plus some additional fraction of a wavelength.

  FIGURE 3.6 Measuring the Phase Difference measured at the two detectors B1 and B2 gives you information on the separation distance, d. In this case, a Phase Difference of 3π/2 equates to a path length difference of 3/4 of the wavelength. Knowing the wavelength then gives a value for d, as long as d < λ.

  If the phase of the received wave is measured at the detector it does not tell us about the absolute distance (it does not count all the whole wavelengths) but it does tell us something about the remaining fraction of a wavelength.

  Unfortunately, unless you know the initial phase of the emitted wave at A, and the absolute number of whole waves, there is nothing useful you can actually do with this phase information on its own. However, imagine that we have another detector at a second location B2 , a small (<1 wavelength) distance, d, closer to the emitter at A (see Figure 3.6 ). In this case, we will measure a different phase at B1 compared to B2 , and this difference in phase is a direct measure of the difference in the length of the path from A to B1 , versus A to B2 , i.e. the distance d. A Phase Difference of 3π/2 (270°) for instance, indicates a path length difference of three quarters of a wavelength (whatever that may be for the particular frequency of waves being used). In this case it does not matter what the initial phase is at A, since it is the same wave that both detectors measure – it is the phase difference that is the key piece of information that tells you about the different path lengths and hence the distance, d.

  Notice that I specified that d

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  eBook - ePub

  Basic AC Circuits

  • Clay Rawlins(Author)
  • 2000(Publication Date)
  • Newnes

    (Publisher)

  in phase .

  Figure 4.26 Waveforms A and B In Phase

  If generator B waits until generator A has gone through one-half cycle before it starts, a 180-degree Phase Difference will exist as shown in Figure 4.27 . In this case, whenever wave A swings positive, wave B swings negative, and vice versa. Since both waves are always exactly the opposite, they are said to be inverted from each other, or 180 degrees out of phase .

  Figure 4.27 Waveforms A and B 180 Degrees Out of Phase

  Now, up to this point, we’ve only specified that one wave leads another. This situation is much like two runners in a race as shown in Figure 4.28 . You can say runner A is in the lead, but you could just as well say that runner B is lagging behind. Both mean the same thing; both are correct. Similarly, when describing the phase relationship of the two waveforms shown in Figure 4.22 you can say A leads B by 90 degrees or you can just as correctly say, B lags A by 90 degrees. Both statements mean the same thing. The 90-degree Phase Difference is a common one, and it will be studied in more detail in later chapters. Therefore, it is important that you are able to recognize Phase Differences.

  Figure 4.28 Runners A and B Are Similar to Waveforms A and B

  Determining Phase Difference for Partial Waveforms

  In oscilloscope patterns, you may often have two waveforms shown and not really see the beginning of either wave. One of the simplest methods you can use to determine the Phase Difference is to first choose a point at which both waveforms are of the same instantaneous value of voltage or current. A convenient level to choose is the zero reference level. In Figure 4.29 , waveform A and waveform B are the same value at all points where they cross the zero reference: zero volts. But, you must choose two points which are side by side and where waveform A is moving in the same direction

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  eBook - ePub

  Interferogram Analysis For Optical Testing

  • Zacarias Malacara, Manuel Servín(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  Smythe and Moore (1983, 1984) proposed an alternative heterodyne interferometric system in which the beats are not measured; instead, by means of an optical procedure (not described here) that utilizes polarizing optics, two orthogonal bias-free signals are generated. Each of these two signals comes from each of the two arms of the interferometer. The Phase Difference between these two orthogonal signals is the Phase Difference between the two interferometer optical paths. If we represent these two orthogonal signals in a polar diagram, one along the vertical axis and the other along the horizontal axis, the path described in this diagram when the phase is continually changed is a circle. The angle with respect to the optical axis is the phase. This heterodyning procedure can be easily implemented to measure wavefront deformations in two dimensions.

  7.5    PHASE-LOCK DETECTION

  In the phase-lock method for detecting a signal, the phase reference wave is phase modulated with a sinusoidally oscillating mirror (Moore, 1973; Moore et al., 1978; Johnson et al., 1979; Moore and Truax, 1979). Two phase components — δ0 and δ1 sin(wt) — are added to the signal phase, φ(x,y). One of the additional phase components being added has a fixed value and the other a sinusoidal time oscillation. Both components are independent and can have any desired value. Omitting the x,y dependence for notational simplicity, the total time-dependent phase is:

  ϕ   +   δ 0 + δ 1   cos ( 2 π f t )

  (7.6)

  thus, the signal is:

  s ( t ) = a + b   cos ( ϕ + δ 0 + δ 1 cos ( 2 π f t ) )

  (7.7)

  The phase modulation is carried out only in an interval smaller than π, as illustrated in Figure 7.6 . The output signal can be interpreted as the phase-modulating signal, after being harmonically distorted by the signal to be detected. This harmonic distortion is a function of the phase (φ), as shown in Figure 7.7 . This function is periodic and symmetrical; thus, to find the harmonic distortion using Equations 2.6 and 2.7

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