【文章內容簡介】 nameplate， or specified output frequency. Frequency offset measurements in the time domain involve a phase parison between the DUT and the reference. A simple phase parison can be made with an oscilloscope. The oscilloscope will display two sine waves. The top sine wave represents a signal from the DUT， and the bottom sine wave represents a signal from the reference. If the two frequencies were exactly the same， their phase relationship would not change and both would appear to be stationary on the oscilloscope display. Since the two frequencies are not exactly the same， the reference appears to be stationary and the DUT signal moves. By measuring the rate of motion of the DUT signal we can determine its frequency offset. Vertical lines have been drawn through the points where each sine wave passes through zero. The bottom of the figure shows bars whose width represents the phase difference between the signals. In this case the phase difference is increasing， indicating that the DUT is lower in frequency than the reference. Measuring high accuracy signals with an oscilloscope is impractical， since the phase relationship between signals changes very slowly and the resolution of the oscilloscope display is limited. More precise phase parisons can be made with a TIC. If the two input signals have the same frequency， the time interval will not 中北大學 2021 屆畢業(yè)設計說明書 第 6 頁 共 16 頁 change. If the two signals have different frequencies， the time interval wills change， and the rate of change is the frequency offset. The resolution of a TIC determines the smallest frequency change that it can detect without averaging. For example， a low cost TIC with a singleshot resolution of 100 ns can detect frequency changes of 1 10 7 in 1 s. The current limit for TIC resolution is about 20 ps， which means that a frequency change of 2 10 11 can be detected in 1 s. Averaging over longer intervals can improve the resolution to 1 ps in some units [6]. Since standard frequencies like 5 or 10 MHz are not practical to measure with a TIC， frequency dividers or frequency mixers are used to convert the test frequency to a lower frequency. Divider systems are simpler and more versatile， since they can be easily built or programmed to acmodate different frequencies. Mixer systems are more expensive， require more hardware including an additional reference oscillator， and can often measure only one input frequency (.， 10 MHz) ， but they have a higher signaltonoise ratio than divider systems. If dividers are used， measurements are made from the TIC， but instead of using these measurements directly， we determine the rate of change from reading to reading. This rate of change is called the phase deviation. We can estimate frequency offset as follows： tf=T? Where △ t is the amount of phase deviation， and T is the measurement period. To illustrate， consider a measurement of +1 μs of phase deviation over a measurement period of 24 h. The unit used for measurement period (h) must be converted to the unit used for phase deviation (μs). The equation bees 11t 1 u sf o ffs et = = = 1 . 1 6 1 0T 8 6 4 0 0 0 0 0 0 0 0 u s ?? ?（ ） ， ， ， 中北大學 2021 屆畢業(yè)設計說明書 第 7 頁 共 16 頁 As shown， a device that accumulates 1 μs of phase deviation/day has a frequency offset of 10 11 with respect to the reference. This simple example requires only two time interval readings to be made， and △ t is simply the difference between the two readings. Often， multiple readings are taken and the frequency offset is estimated by using least squares linear regression on the data set， and obtaining △ t from the slope of the least squares line. This information is usually presented as a phase plot， as shown in Fig. . The device under test is high in frequency by exactly 110 9， as indicated by a phase deviation of 1 ns/s. Dimensionless frequency offset values can be converted to units of frequency (Hz) if the nominal frequency is known. To illustrate this， consider an oscillator with a nominal frequency of 5 MHz and a frequency offset of + ′ 10 11. To find the frequency offset in hertz， multiply the nominal frequency by the offset： (5 106) (+ 10 11) = 10 5 =+ Hz Then， add the offset to the nominal frequency to ge