【正文】 interpolation schemes to detect parts of a time base cycle and have much higher resolution—1 ns resolution is monplace， and 20 ps resolution is available. Frequency offset can be measured in either the frequency domain or time domain. A simple frequency domain measurement involves directly counting and displaying the 中北大學(xué) 2021 屆畢業(yè)設(shè)計(jì)說明書 第 5 頁(yè) 共 16 頁(yè) frequency output of the DUT with a frequency counter. The reference for this measurement is either the counter?s internal time base oscillator， or an external time base. The counter?s resolution， or the number of digits it can display， limits its ability to measure frequency offset. For example， a 9digit frequency counter can detect a frequency offset no smaller than Hz at 10 MHz (1108). The frequency offset is determined as m easure nom inalnom inal(f f )f= f Where fmeasur is the reading from the frequency counter， and fnominal is the frequency labeled on the oscillator?s 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(xué) 2021 屆畢業(yè)設(shè)計(jì)說明書 第 6 頁(yè) 共 16 頁(yè) 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(xué) 2021 屆畢業(yè)設(shè)計(jì)說明書 第 7 頁(yè) 共 16 頁(yè) As shown， a device that accumulates 1 μs of phase deviation/day has a frequency offset