畢業(yè)設計說明書外文翻譯---時間和頻率的基本原理

1、<p><b>　　畢業(yè)設計說明書</b></p><p><b>　　英文文獻及中文翻譯</b></p><p>　　學 院： 信息與通信工程 </p><p>　　專 業(yè)： 電子信息科學與技術 </p><p><b&g

2、t;　　2011年 6月</b></p><p><b>　　外文文獻原文</b></p><p>　　Fundamentals of Time and Frequency</p><p>　　Introduction</p><p>　　Time and frequency standards supply

3、 three basic types of information： time-of-day， time interval， and frequency. Time-of-day information is provided in hours， minutes， and seconds， but often also includes the date (month， day， and year). A device that dis

4、plays or records time-of-day information is called a clock. If a clock is used to label when an event happened， this label is sometimes called a time tag or time stamp. Date and time-of-day can also be used to ensure tha

5、t events are synchronized</p><p>　　Time interval is the duration or elapsed time between two events. The standard unit of time interval is the second(s). However， many engineering applications require the me

6、asurement of shorter time intervals， such as milliseconds (1 ms = 10 -3 s) ， microseconds (1 μs = 10 -6 s) ， nanoseconds (1 ns = 10 -9 s) ， and picoseconds (1 ps = 10 -12 s). Time is one of the seven base physical quanti

7、ties， and the second is one of seven base units defined in the International System of Units (SI). The defin</p><p>　　Frequency is the rate of a repetitive event. If T is the period of a repetitive event， th

8、en the frequency f is its reciprocal， 1/T. Conversely， the period is the reciprocal of the frequency， T = 1/f. Since the period is a time interval expressed in seconds (s) ， it is easy to see the close relationship betwe

9、en time interval and frequency. The standard unit for frequency is the hertz (Hz) ， defined as events or cycles per second. The frequency of electrical signals is often measured in multiples </p><p>　　Of cou

10、rse， the three types of time and frequency information are closely related. As mentioned， the standard unit of time interval is the second. By counting seconds， we can determine the date and the time-of-day. And by count

11、ing events or cycles per second， we can measure frequency. </p><p>　　Time interval and frequency can now be measured with less uncertainty and more resolution than any other physical quantity. Today， the bes

12、t time and frequency standards can realize the SI second with uncertainties of ≈1×10-15.Physical realizations of the other base SI units have much larger uncertainties.</p><p>　　Coordinated Universal Ti

13、me (UTC) </p><p>　　The world’s major metrology laboratories routinely measure their time and frequency standards and send the measurement data to the Bureau International des Poids et Measures (BIPM) in Sevr

14、es， France. The BIPM averages data collected from more than 200 atomic time and frequency standards located at more than 40 laboratories， including the National Institute of Standards and Technology (NIST). As a result o

15、f this averaging， the BIPM generates two time scales， International Atomic Time (TAI)， and C</p><p>　　UTC runs at the same frequency as TAI. However， it differs from TAI by an integral number of seconds. Thi

16、s difference increases when leap seconds occur. When necessary， leap seconds are added to UTC on either June 30 or December 31. The purpose of adding leap seconds is to keep atomic time (UTC) within ±0.9 s of an old

17、er time scale called UT1， which is based on the rotational rate of the earth. Leap seconds have been added to UTC at a rate of slightly less than once per year， beginning in 1972. </p><p>　　Keep in mind that

18、 the BIPM maintains TAI and UTC as ‘‘paper’’ time scales. The major metrology laboratories use the published data from the BIPM to steer their clocks and oscillators and generate real-time versions of UTC. Many of these

19、laboratories distribute their versions of UTC via radio signals which section 17.4 are discussed in.</p><p>　　You can think of UTC as the ultimate standard for time-of-day， time interval， and frequency. Cloc

20、ks synchronized to UTC display the same hour minute， and second all over the world (and remain within one second of UT1). Oscillators simonized to UTC generate signals that serve as reference standards for time interval

21、and frequency. </p><p>　　Time and Frequency Measurement</p><p>　　Time and frequency measurements follow the conventions used in other areas of metrology. The frequency standard or clock being me

22、asured is called the device under test (DUT). A measurement compares the DUT to a standard or reference. The standard should outperform the DUT by a specified ratio， called the test uncertainty ratio (TUR). Ideally， the

23、TUR should be 10：1 or higher. The higher the ratio， the less averaging is required to get valid measurement results. </p><p>　　The test signal for time measurements is usually a pulse that occurs once per se

24、cond (1 ps). The pulse width and polarity varies from device to device， but TTL levels are commonly used. The test signal for frequency measurements is usually at a frequency of 1 MHz or higher， with 5 or 10 MHz being co

25、mmon. Frequency signals are usually sine waves， but can also be pulses or square waves if the frequency signal is an oscillating sine wave. This signal produces one cycle (360∞ or 2π radians of phase)</p><p>

26、;　　This section examines the two main specifications of time and frequency measurements—accuracy and stability. It also discusses some instruments used to measure time and frequency.</p><p><b>　　Accura

27、cy </b></p><p>　　Accuracy is the degree of conformity of a measured or calculated value to its definition. Accuracy is related to the offset from an ideal value. For example， time offset is the differe

28、nce between a measured on-time pulse and an ideal on-time pulse that coincides exactly with UTC. Frequency offset is the difference between a measured frequency and an ideal frequency with zero uncertainty. This ideal fr

29、equency is called the nominal frequency. </p><p>　　Time offset is usually measured with a time interval counter (TIC). A TIC has inputs for two signals. One signal starts the counter and the other signal sto

30、ps it. The time interval between the start and stop signals is measured by counting cycles from the time base oscillator. The resolution of a low cost TIC is limited to the period of its time base. For example， a TIC wit

31、h a 10-MHz time base oscillator would have a resolution of 100 ns. More elaborate Tics use interpolation schemes to detect p</p><p>　　Frequency offset can be measured in either the frequency domain or time d

32、omain. A simple frequency domain measurement involves directly counting and displaying the frequency output of the DUT with a frequency counter. The reference for this measurement is either the counter’s internal time ba

33、se 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 9-digit frequency counter can detect </p>&

34、lt;p>　　Where fmeasur is the reading from the frequency counter， and fnominal is the frequency labeled on the oscillator’s nameplate， or specified output frequency. </p><p>　　Frequency offset measurements

35、in the time domain involve a phase comparison between the DUT and the reference. A simple phase comparison can be made with an oscilloscope. The oscilloscope will display two sine waves. The top sine wave represents a si

36、gnal 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 os

37、cilloscope display. Since the </p><p>　　Measuring high accuracy signals with an oscilloscope is impractical， since the phase relationship between signals changes very slowly and the resolution of the oscillo

38、scope display is limited. More precise phase comparisons can be made with a TIC. If the two input signals have the same frequency， the time interval will not change. If the two signals have different frequencies， the tim

39、e interval wills change， and the rate of change is the frequency offset. The resolution of a TIC determines the s</p><p>　　Since standard frequencies like 5 or 10 MHz are not practical to measure with a TIC，

40、 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 accommodate different f

41、requencies. Mixer systems are more expensive， require more hardware including an additional reference oscillator， and can often measure only one input frequency (e.g.， 10 MHz) ， but they have a hi</p><p>　　I

42、f 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 ca

43、n estimate frequency offset as follows：</p><p>　　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 measureme

44、nt period of 24 h. The unit used for measurement period (h) must be converted to the unit used for phase deviation (μs). </p><p>　　The equation becomes</p><p>　　As shown， a device that accumulat

45、es 1 μs of phase deviation/day has a frequency offset of 1.16 × 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

46、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 informa

47、tion is usually presented as a p</p><p>　　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

48、a nominal frequency of 5 MHz and a frequency offset of +1.16 ′ 10 -11. To find the frequency offset in hertz， multiply the nominal frequency by the offset： (5 ×106) (+1.16×10 -11) = 5.80×10 -5 =+0.0000580

49、Hz Then， add the offset to the nominal frequency to get the actual frequency： 5，000，000 Hz + 0.0000580 Hz = 5，000，000.0000580 Hz </p><p>　　Stability </p><p>　　Stability indicates how well an osc

50、illator can produce the same time or frequency offset over a given time interval. It doesn’t indicate whether the time or frequency is “right” or “wrong，” but only whether it stays the same. In contrast， accuracy indicat

51、es how well an oscillator has been set on time or on frequency. To understand this difference， consider that a stable oscillator that needs adjustment might produce a frequency with a large offset. Or， an unstable oscill

52、ator that was just adjust</p><p>　　Stability is defined as the statistical estimate of the frequency or time fluctuations of a signal over a given time interval. These fluctuations are measured with respect

53、to a mean frequency or time offset. </p><p>　　Short-term stability usually refers to fluctuations over intervals less than 100 s. Long-term stability can refer to measurement intervals greater than 100 s， bu

54、t usually refers to periods longer than 1 day. </p><p>　　Stability estimates can be made in either the frequency domain or time domain， and can be calculated from a set of either frequency offset or time int

55、erval measurements. In some fields of measurement， stability is estimated by taking the standard deviation of the data set. However， standard deviation only works with stationary data， where the results are time independ

56、ent， and the noise is white， meaning that it is evenly distributed across the frequency band of the measurement. Oscillator data i</p><p>　　where yi is a set of frequency offset measurements containing y1， y

57、2， y3， and so on， M is the number of values in the yi series， and the data are equally spaced in segments τ seconds long. Or </p><p>　　Where xi is a set of phase measurements in time units containing x1， x2，

58、 x3， and so on， N is the number of values in the xi series， and the data are equally spaced in segments τ seconds long. Note that while standard deviation subtracts the mean from each measurement before squaring their su

59、mmation， the Allan deviation subtracts the previous data point. This differencing of successive data points removes the time dependent noise contributed by the frequency offset. An Allan deviation graph is sh</p>

60、<p>　　Practically speaking， a frequency stability graph also tells us how long we need to average to get rid of the noise contributed by the reference and the measurement system. The noise floor provides some indica

61、tion of the amount of averaging required to obtain a TUR high enough to show us the true frequency where xi is a set of phase measurements in time units containing x1，x2，x3，and so on is the number of values in the xi ser

62、ies， and the data are equally spaced in segments τ seconds long. Note t</p><p>　　Practically speaking， a frequency stability graph also tells us how long we need to average to get rid of the noise contribute

63、d by the reference and the measurement system. The noise floor provides some indication of the amount of averaging required to obtain a TUR high enough to show us the true frequency offset of the DUT. If the DUT is an at

64、omic oscillator (section 17.4) and the reference is a radio controlled transfer standard (section 17.5) we might have to average for 24 h or longer to hav</p><p>　　Identifying and eliminating sources of osci

65、llator noise can be a complex subject， but plotting the first order differences of a set of time domain measurements can provide a basic understanding of how noise is removed by averaging. Figure 17.10 was made using a s

66、egment of the data from the stability graph in Fig. 17.8. It shows phase plots dominated by white phase noise (1 s averaging) ， white frequency noise (64 s averages) ， flicker frequency noise (256 s averages)， and random

67、 walk frequency (</p><p><b>　　外文文獻中文翻譯</b></p><p>　　時間和頻率的基本原理</p><p><b>　　介紹</b></p><p>　　時間和頻率標準應用于三種基本信息類型：時間，時間間隔和頻率.時間信息有小時，分，秒.通常還包括日期 (年，

68、月，日).用來顯示和記錄時間的器件叫做鐘表，如果鐘表標記了一件事的發(fā)生，那么這個標記叫做時間標簽或時間印記.日期和時間能確保事情的同步或同時發(fā)生.</p><p>　　時間間隔是兩個事件持續(xù)或斷續(xù)的時間，時間間隔的標準單位是秒，然而許多工程上應用要求更短的時間間隔，像毫秒，微秒，納秒，和皮秒，時間是七個基本物理量之一，并且秒是國際單位體制制定七個基本單位之一.許多區(qū)其他物理量的定義是依靠秒而定義的.秒曾經定義根據(jù)

69、地球回轉率.原子時代正式開始在1967年目前SI定義秒為： 秒是銫133原子(Cs133)基態(tài)的兩個超精細能級之間躍遷所對應的輻射的9，192，631，770個周期所持續(xù)的時間。 頻率是一個事件的重復次數(shù)，如果T一個重復事件的周期，那么頻率f是它的倒數(shù)，1/T.反過來說頻率的倒數(shù)是周期，T=1/f.周期是時間間隔用秒表示.很容易看出頻率和時間間隔關系很密切.頻率的標準單位是赫茲，定義為每秒發(fā)生的事件次數(shù)或循環(huán)次數(shù)，電信號的頻率通常用不

70、同的赫茲測量，包括千赫茲，兆赫茲，千兆赫茲.1KHz相當于每秒發(fā)生一千次事件，1MHz相當于每秒發(fā)生一百萬次事件.1GHz相當于每秒發(fā)生十億次事件.產生頻率的裝置叫做振蕩器，設置不同振蕩器具有相同的頻率叫做同步。</p><p>　　三種類型的時間和頻率信息是相似的，時間間隔的標準單位是秒通過計數(shù)秒我們知道時間和日期，通過計數(shù)每秒的事件數(shù)或循環(huán)數(shù)，我們能測量頻率于其他物理量相比時間間隔和頻率的測量具有誤差小，易于

71、分析的優(yōu)點.目前最好的時間和頻率標準是SI誤差為10-15 其他基本SI單位有更大的誤差如表17.1所示。</p><p>　　協(xié)調全世界時間(UTC)</p><p>　　世界的主要度量學實驗室測量時間和頻率標準，并發(fā)送的BIPM，法國BIPM收集至少40個實驗室的200多個原子時間和頻率標準包括來自國際標準和技術協(xié)會(NIST).通過這些平均結果由BIPM產生兩個時間標準，國際原子時間

72、(TAI)和協(xié)調全世界時間(UTC)，這些時間標準盡可能地與SI標準接近。</p><p>　　UTC與TAI執(zhí)行相同的頻率，然而它有區(qū)別的TAI 是整數(shù)秒，這個不同處總在增長隨著皮秒的跳變.皮秒增加到UTC的每年6月30日或12月31日.增加跑秒的目的在于是原子時間的誤差在+/-0.9S老的時間標準叫UT1，它根據(jù)地球的回轉率。皮秒作為一個小量增加到UTC每年一次從1972年開始的。</p>&l

73、t;p>　　BIPM包括UTC和TAI正規(guī)的時間標準，主要的度量學實驗室使用來自BIPM控制它們時鐘和振蕩器產生的數(shù)據(jù)并產生真正的UTC時間.許多實驗室描述他們的UTC信號是由射頻信號傳輸?shù)?，這點將在17.4節(jié)討論。</p><p>　　大家認為UTC將作為最終時間，時間間隔，頻率標準，時間同步使UTC在全世界范圍顯示相同的時，分，秒.振蕩器同步使UTC產生應用于時間間隔和頻率參考標準的信號.</p&

74、gt;<p><b>　　時間和頻率測量</b></p><p>　　時間和頻率測量可以應用于度量學的其他領域.頻率標準或時鐘測量叫做終端測試測量把DUT當作標準或參考，標準用一個已知的DUT表示，叫做測試誤差率(TUR).理想情況下，DUT應該是10：1或更高有效的.測量結果要求有高比率，低均值</p><p>　　時間測量的測試信號是一個脈沖每秒一個

75、脈沖(1pps)，脈沖的寬度和極性從一個器件到另一個其間有差別的，TTL電平通常被使用.頻率測量信號用1MHz或更高的頻率，5到10MHz是常用的，頻率信號是正弦波，月可以是脈沖或方波.如果頻率信號是振蕩的正弦波，它像圖17.1所示，信號在一個周期產生一個循環(huán)，真服用伏特表示，并且和測量器件一致的.如果振幅太大，將會削弱或妨礙測量儀器的速度。</p><p>　　這部分主要說明時間和頻率測量的兩個特性：精度和穩(wěn)定

76、度，討論用于測量頻率和時間的儀器。</p><p><b>　　精度</b></p><p>　　精度是測量值或實際值的與真實值一致性的接近程度，精度是與真實值的差量.時差是在測量時間脈沖和實際時間脈沖的差值準確地和UTC同時發(fā)生，頻差是測量頻率和真實頻率的差值，真實的頻率叫做時間頻率。</p><p>　　用時間間隔計數(shù)器(TIC)測量時差，

77、如圖17.2所示，一個TIC輸入兩路信號一路信號開始技術另一路停止計數(shù)，通過計數(shù)時基振蕩器振蕩的次數(shù)來測量其實信號的時間間隔。一個廉價的時間計數(shù)器時基是有限的。例如，一個10MHz的時間計數(shù)器時基振蕩器具有100ns的分辨率，大多數(shù)更復雜的計數(shù)器時基回路有更高的分辨率1ns，一般的可達到20ps。</p><p>　　測量頻偏即可以在頻域也可以在時域，一個基本的頻域測量包括直接計數(shù)和用脈寬測量儀數(shù)器在DUT顯示頻

78、率，測量的參考即可以是計數(shù)器的內部時基振蕩器也可以是外部時基。計數(shù)器分辨率或是被顯示。極限偏置不超過10-8 頻偏定義為：</p><p>　　fmeasur是由脈寬測量儀讀出的，fnominal 是振蕩器銘牌上標注的，具體輸出頻率。</p><p>　　頻偏測量在時域包括DUT和參考之間的相差，基本的相差可由示波器顯示，示波器可以顯示兩個正弦波，上面的正弦波是來自于DUT的信號，下面的

79、是來自參考頻率的信號。如果兩個頻率非常相似，那么相位關系在同一臺示波器上的位置不變。兩個頻率差異較大時，參考位置和DUT有一定的移動。通過測量DUT信號的移動率我們可以得到頻偏。每個正弦波通過零點的點形成了豎線。圖像底部顯示不同信號的相差欄，在隨著相差增大的情況下，DUT顯示的頻率值比參考值小。</p><p>　　在信號緩慢變化和示波器的分辨率之間關系是有限的，測量高精度的信號用一臺示波器是不現(xiàn)實的，用TIC可

80、以清楚測出相位差，使用配置如17.2所示，如果兩個輸入信號有相同的頻率，時間間隔將不改變，如果兩個信號頻率不相同時間間隔將改變，稱改變率為頻偏，TIC的分辨率決定最小頻率的改變量，例如，一臺便宜的時間計數(shù)器發(fā)射信號的分辨率為100ns可以得到1s內頻率改變量為10-7。目前TIC的分辨率極限值為20ps，也就是說在1s內有2×10-11 的頻率變量被忽略。平均較長的間隔可以改進分辨率是小于1ps在一些單元。 標準頻率像5MHz

81、或10MHz不能用TIC測量，頻率分配器或頻率合成器使測試頻率轉換到底頻。分配系統(tǒng)比較便宜且功能多，它們更容易建立或編程使其適應于不同的頻率?；祛l系統(tǒng)比較貴要求更多的硬件包括一個附加的參考振蕩器和一個能測量的輸入頻率(如10MHz)但它們的信噪比比分頻系統(tǒng)更高。</p><p>　　如果使用分頻器，用時間間隔計數(shù)器測量取代直接測量我們可以從不斷的讀數(shù)據(jù)測得變化量，這種變化量可以稱為相偏，我們估算的頻偏如下：<

82、;/p><p>　　△t代表相偏，T代表周期。上式說明，周期為24小時有+1us的相偏，周期測量的單位應轉換為相偏的單位(us)，等式為：</p><p>　　一臺設備每天積累1us的相偏，就其參考而言頻偏為-1.16×10-11 ，這個簡單的例子說明兩個時間間隔均被掃描到，△t在兩次掃描之間是不同的，多采集在數(shù)據(jù)集使用最小平方的線性回歸估算頻偏，從最先的傾斜獲得△t。這些數(shù)據(jù)通常用

83、相線表示，如圖17.6所示終端測試相對于頻率精確到1×10-9 ，表示為1ns/s的相偏。如果實際頻率是已知的最小頻偏可以轉化成頻率單位。以下為例一個振蕩器實際頻率為5MHz頻偏為+1.16*10-11。用赫茲表示頻偏，是頻率與頻偏相乘：5×106×(+1.16×10-11)=5.80×10-5=+0.0000560 Hz。那么，把頻偏增加到實際頻率上就得到了真實的頻率值5，000，00

84、0 Hz +0.0000580 Hz =5，000，0000.0000580Hz.</p><p><b>　　穩(wěn)定性</b></p><p>　　穩(wěn)定性表示為在給定時間間隔的情況下振蕩器能產生一個相同的時間或頻偏，它不能說明時間或周期是否正確，僅僅說明一致性。相比之下，精確度則說明振蕩器按時間或頻率的配置如何，明白了這個不同點，穩(wěn)定的振蕩器需要調整可能纏身較大偏執(zhí)的

85、頻率，或者不穩(wěn)定的</p><p>　　振蕩器僅僅調整接近實際值的頻率，圖17.7顯示了精確度與穩(wěn)定度的關系，穩(wěn)定的定義是統(tǒng)計估計的頻率或時間的波動信號，在一個特定的時間 區(qū)間. 這些波動是衡量對一個平均頻率或時間抵消。短期穩(wěn)定通常是指波動區(qū)間不到100，長期穩(wěn)定的可參考測量間隔大于100 s ，但通常是指時間超過1天 。</p><p>　　穩(wěn)定性估計可無論是在頻域或時間域，可以從任一頻

86、率偏移或時間間隔測量集計算。在測量一些領域，穩(wěn)定是估計到數(shù)據(jù)集的標準偏差。然而，標準偏差只適用于靜止的數(shù)據(jù)，其中的結果是時間獨立，噪音是白色的，這意味著它是均勻分布在測量頻帶分配。振蕩器數(shù)據(jù)通常非平穩(wěn)的，因為它包含了時間的相關噪聲頻率偏移所貢獻。靜止的數(shù)據(jù)，均值和標準差將收斂到更多的測量值，尤其是制成。隨著非平穩(wěn)數(shù)據(jù)，均值和標準差從未收斂到任何特定的值。相反，有一個可以改變移動平均每次我們增加一個測量?；谶@些原因，非經典統(tǒng)計往往是用來

87、估計在時域的穩(wěn)定。這一統(tǒng)計數(shù)字是有時被稱為Allan方差，但因為它是方差的平方根，其正確名稱是阿倫偏差。艾倫偏差為方程</p><p>　　其中yi是頻率偏移含y1，y2，y3等一系列值的數(shù)量，并把數(shù)據(jù)段同樣τ秒長的間隔?；蚩蓪憺椋?lt;/p><p>　　其中xi是一種含有單位相位的測量時間，為x1，x2，x3等等，N是在十一系列值數(shù)集，數(shù)據(jù)也同樣分部τ秒長的間隔。請注意，雖然標準差減去每次

88、測量前軋平其總和的平均值，在阿倫偏差減去以前的數(shù)據(jù)點。這種連續(xù)的數(shù)據(jù)點差分消除了時間相關的噪聲的頻率偏移貢獻。阿蘭偏差圖如圖17.8所示。它顯示了作為平均周期(τ)提高設備的穩(wěn)定性愈長，因為有些噪聲類型可通過平均刪除。在某些時候，然而，更多的平均不再提高的結果。這一點被稱為本底噪聲，或點剩余噪聲的非平穩(wěn)過程組成，如閃爍噪聲或隨機游動。該裝置測量圖17.8。τ=100?5×10 -11 s為本底噪聲。</p>&l

89、t;p>　　實際上，一個頻率穩(wěn)定度圖還告訴我們，我們需要多久平均得到的噪音消除由基準和測量系統(tǒng)作出了貢獻。本底噪聲提供了一些對平均需要獲得足夠高的TUR向我們展示了真實頻率金額跡象DUT的偏移。如果DUT是一個原子振蕩器(第17.4)和參考是無線電控制的傳輸標準(第17.5)，我們可以有24小時或更長的時間平均在測量結果的信心。五噪聲類型通常討論的時間和頻率文學：白色相，相閃爍，白頻率，閃爍頻率，隨機游動的頻率。在阿倫偏差的直線的

90、斜率可以幫助確定所需的平均消除這些噪聲類型(圖17.9)的金額。第一種類型的噪聲被刪除的平均相位噪聲，或快速，在信號的相位隨機波動。理想情況下，只能根據(jù)測試設備將有助于相位噪聲的測量，但在實踐中，一些從測量系統(tǒng)和參考相位噪聲需要通過平均刪除。請注意，阿倫偏差不區(qū)分白相位噪聲和閃爍的相位噪聲。表17.2顯示了用于估算穩(wěn)定和確定各種應用中的噪聲類型的其他幾個統(tǒng)計數(shù)字。</p><p>　　查明和消除噪聲源的振蕩器是一