Jitter Analysis: The dual-Dirac Model, RJ/DJ, and Q-Scale White Paper
31-December-2004
The dual-Dirac model is a tool for quickly estimating
total jitter defined at a low bit error ratio, TJ(BER). The
deterministic and random subcomponents of the jitter
signal are separated within the context of the model to
yield two quantities, root-mean-square random jitter
(RJ) and a model-dependent form of the peak-to-peak
deterministic jitter, DJ(δδ). The total jitter of a system is
then estimated from RJ and DJ(δδ).
This paper provides a complete description of the
dual-Dirac model, how it is used in technology standards
and a summary of how it is applied on different types of
test equipment. The Q-scale formulation is described in
detail and is used to provide a simple visual description
of the model’s features and to show how different
implementations of the model can lead to different
results. For an introduction to jitter analysis please
see reference [1].
Section one is a short self-contained summary. The
succeeding sections provide the complete reference
material for understanding the summary. This format
provides both the story-in-a-nutshell and the details-in-full
so that you can, hopefully, access the information you
need as quickly as possible – if you have comments or
suggestions, accolades or criticisms, please send me a
note: ransom_stephens@https://www.doczj.com/doc/d713277423.html,.
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three regions: at the crossing-point the distribution is dominated by DJ, at time-delays farther from the
crossing-point the distribution is increasingly dominated by RJ until, far from the crossing point, in the asymptotic limit, the tails follow the Gaussian RJ distribution. The asymptotic tails of the distribution usually cause errors at the level of BER < 10–8. The ideal way to determine the behavior of the tails, and hence, TJ(BER) would be o deconvolve RJ and DJ. But without knowing the DJ distribution beforehand, there is no practical way to deconvolve the distribution
The dual-Dirac model, Figure 1, provides the simplest possible distribution: the crossing-point is separated into two Dirac-delta functions positioned at μL and μR , the DJ dominated region, followed by an artificially abrupt transition to the RJ dominated tails. There are many ways to implement the dual-Dirac model, in all of them estimating TJ(BER) is a matter of describing the tails of the jitter distribution with the tails of two Gaussians of width σseparated by a fixed amount DJ(δδ) ≡|μL – μR |:The dual-Dirac model is a Gaussian approximation to the outer edges of the jitter distribution displaced by DJ(δδ).
Conceptually, think of DJ closing the eye a fixed amount,DJ(δδ), and the Gaussian RJ tails closing the eye an amount that depends on the bit error ratio of interest.Once σand DJ(δδ) are measured the eye closure at any BER can be estimated with:
TJ(BER)?2Q BER x σ+ DJ(δδ),
(1)
where Q BER is calculated from the complementary error function, as given in Table 2. Since σis multiplied by 2 Q BER , the accuracy of TJ(BER) depends first on the accuracy of the RJ measurement, σ, and second on the accuracy of the DJ(δδ) measurement.
1. What The dual-Dirac Approximation Is And What It Is Not
The dual-Dirac model is universally accepted for its utility in quickly estimating total jitter defined at a bit error ratio,TJ(BER), and for providing a mechanism for combining TJ(BER) from different network elements. It relies on the five assumptions given in Table 1.
Table 1: The dual-Dirac model assumptions.1.Jitter can be separated into two categories, random jitter (RJ) and deterministic jitter (DJ).
2.
RJ follows a Gaussian distribution and can be fully described in terms of a single relevant parameter, the rms value of the RJ
distribution or, equivalently, the width of the Gaussian distribution, σ.3.DJ follows a finite, bounded distribution.
4.
DJ follows a distribution formed by two Dirac-delta functions. The time-delay separation of the two delta functions gives the dual-Dirac model-dependent DJ, as shown in Figure 1.
5.
Jitter is a stationary phenomenon. That is, a measurement of the jitter on a given system taken over an appropriate time interval will give the same result regardless of when that time interval is initiated.
A measurement of TJ(BER) at low BER can only be
performed on a Bit Error Ratio Tester (BERT) and takes as long as is necessary to transmit about 10/BER bits 2(e.g., to measure TJ(10–12) would take about 70 minutes).The first two assumptions in Table 1, that jitter is caused by a combination of random and deterministic processes whose distributions can be separated and that RJ follows a Gaussian, are standard industry-wide assumptions; they are the key to how the dual-Dirac model is used to estimate TJ(BER) from measurements of comparatively low statistics.
The components of jitter combine through convolution. We can think of the jitter distribution, e.g., the histogram of the crossing-point of an eye diagram, as having
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Figure 1: The convolution of the sum of two delta functions separated by DJ
and a Gaussian RJ distribution of width σ. The underlying assumption of the dual-Dirac approximation is that any jitter distribution can be modeled this way.
Table 2: Values of Q BER , the multiplicative constant for determining eye closure due to RJ, for different BER values.
Q BER BER
6.4 10–106.710–11
7.010–127.310–137.610–14
While DJ(δδ) can always be measured, DJ(p-p) can only be measured in special cases. For example, when DJ is composed exclusively of data-dependent jitter (DDJ) it can be measured by comparing the average transition times of a repeating data pattern [Ref.5]. The inequality, Eq. (2), can be confusing when DJ(δδ) is mistaken as an estimate of DJ(p-p); for example DJ(δδ) may be smaller than a subcomponent of DJ, but DJ(p-p) cannot be smaller than one of its subcomponents.
The inequality, Eq. (2), is a consequence of the dual-Dirac model but does not detract from the model’s utility. On the contrary, DJ(δδ) meets the two necessary requirements of a quantity of interest for a standards body:
DJ(δδ) is both well defined and observable
DJ(δδ) can also be measured on a variety of different types of test equipment. The true peak-to-peak DJ, DJ(p-p), on the other hand can only be measured in special circumstances, is not useful for estimating
TJ(BER), and doesn’t provide any benefit in diagnosing problems.
Different implementations of the dual-Dirac model can give widely varying results in σand DJ(δδ) and hence TJ(BER). There are two different categories types of dual-Dirac implementations, those that determine σby fitting some type of Gaussian expression (e.g., the complementary error function) to a jitter distribution and those that measure the timing noise spectrum and equate it to σ. In both cases problems can occur when DJ is mistaken for RJ. Agilent Technologies solved this problem when we introduced the 86100C DCA-J. The DCA-J measures the timing noise that is independent of the bounded deterministic jitter to obtain an accurate value for σ. As shown in Figure 2 [details in Ref.3], extensive tests of all the available techniques on a
precision jitter transmitter [Ref.4] show that the DCA-J technique (described in Ref. 5) is the most accurate, sensitive, and repeatable jitter analysis tool available.Most of the confusion surrounding the application of the dual-Dirac model is caused by the fact that the dual-Dirac DJ is a completely different quantity than the peak-to-peak DJ. To distinguish the two, we’ll use the notation DJ(p-p) and DJ(δδ). The distinction is easy to understand: real DJ never follows the simple dual-Dirac distribution and so it is unreasonable to expect the DJ extracted from the dual-Dirac model to approximate the actual peak-to-peak DJ. DJ(δδ) is a model dependent quantity that must be derived under the assumption that DJ follows a distribution formed by two Dirac-delta functions, as shown in Figure 1. Generally,
DJ(δδ) < DJ(p-p)
(2)
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Figure 2: Comparison of different jitter analysis techniques in estimating TJ(10–12) for a variety of different combinations of random, periodic, and data-dependent jitter.The heavy solid line indicates the actual TJ(10–12) and the other lines give results from different test sets. The DCA-J (heavy dotted line) gives the most accurate results. For the details of the analysis, see ref. 3.
It’s not hard to show that for bounded DJ(x ) the
asymptotic behavior of J (x ) is the same as that of a Gaussian,
(7)
where ξL and ξR are constants that depend on DJ(x ).
In the dual-Dirac model ξL = μL and ξR = μR as in Figure 1.
The asymptotic behavior of the jitter distribution, Eq. (7),is the reason that the dual Dirac model can be used to represent a jitter distribution like that shown in Figure 3b.
When well-considered standards refer to DJ, it is DJ(δδ) to which they refer, either explicitly or implicitly.Once values for DJ(δδ) and σare obtained for a given network element, the values for combinations of elements can be estimated with these rules:
σT otal = √σ21 +σ22 + . . . +σ2n
(3)
DJ T otal (δδ)≈DJ 1(δδ)+DJ 2(δδ)+ . . . + DJ N (δδ)The simple rules, Eqs. (1) and (3), provide standards
committees an easy way to divide a BER budget among a systems’ components. Notice in Eq. (3) that σTotal is equal to the sum of the squares but DJ(δδ)Total is an approximation to the sum of DJ(δδ)i , the distinction is explained in Section 3.3.
The full story is given in the rest of this note. We start in section 2, with some background material defining bit error ratio and TJ(BER). Section 3 gives a precise
description of the dual-Dirac model, including the Q-scale representation, and how the model provides a simple technique for combining the TJ(BER) of different network elements to estimate TJ(BER) of a system, Eq. (3). In Section 4 we discuss different implementations of the model, identify common pitfalls and show, for a specific system, the relationship between DJ(δδ) and DJ(p-p) and how accurately σand TJ(BER) are estimated in a na?ve dual-Dirac implementation. In Section 5, we conclude with a discussion of the veracity of the standard industry wide assumptions and a bulleted summary.
2. Total Jitter Defined At a Bit Error Ratio
Uncorrelated jitter distributions combine through convolution. The industry-wide assumption is that random jitter (RJ) follows a Gaussian distribution that is independent of all sources of DJ. The probability
density function, or jitter distribution, can be measured by making a histogram of an eye-diagram crossing point,Figure 3a. The jitter distribution, J (x ) Figure 3b, can then be described as RJ(x )_DJ(x ) where the functional form of DJ(x ) is not generally known or even observable, but RJ(x ) is given by a Gaussian distribution whose width is σand x is the time-delay, or horizontal axis of the eye diagram. If we write the jitter distribution as
J(x ) = RJ(x )*DJ(x )(4)
with
(5)
then
(6)
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RJ(x ) = exp [– ] x 22σ22πσ
√1J (x ) = ∫ DJ(x ')exp [
– ]
dx '.(x – x ')22σ22πσ
√1lim J (x ) exp [–
](x – ξL )22σ2
X –∞lim J (x ) exp [–
]
(x – ξR )2
2σ
2
X ∞Figure 3: (a) An eye diagram measured an Agilent 86100C DCA-J and,
(b), the jitter distribution, J (x ).
The eye opening at a given BER, t (BER), is given by the separation of the left and right BER curves at a given BER. For example, in Figure 4, the eye opening at BER =10–12, is given by the difference of x L and x R – those points where BER = 10–12. Formally, if we invert BER(x )to get x (BER), then
t (BER) = x R (BER) – x L (BER).
(11)
TJ(BER) is defined as the amount of eye closure due to jitter at a given BER; that is, TJ(BER) is the difference in the bit period and the eye opening:
TJ (BER) ≡T B – ι(BER).
(12)
The value of the dual-Dirac model is in its ability to provide a technique to quickly estimate total jitter at a given bit error ratio, TJ(BER). Since TJ(BER) is defined in terms of the bit error we need to back up a bit and define a few other things to make sense of it. The BER is defined as
(8)
where (x, V ) is the position of the sampling point and N err (x, V ) is the number of errors that would be detected from a total of N transmitted bits. An error is detected, for example, on a logic ‘0’ bit if the observed potential (or, for differential signals, the difference of the two potentials on the differential lines) is greater than V at the sampling time-delay x . In this document, we assume that all errors result from timing errors alone – that is,from jitter – which means that we can measure the dependence of the BER on the time-delay, x , without being concerned about amplitude noise.
The dependence of BER on x is the heart of how TJ(BER)is defined. By scanning the time-delay position of the sampling point across the eye a bathtub plot, BER(x ), as shown in Figure 4, can be measured on a bit error ratio tester. BER(x ), can also be derived from the jitter distribution, J (x ). Since BER(x ) is given by the probability for a logic transition fluctuating across the sampling point time position, x , if we consider the left edge of Figure 3a then the probability of a transition fluctuating across the point x is given by
BER L (x ) = ρT ∫∞
x J (x ′)dx ′
(9)
where ρr is the ratio of the number of logic transitions to the total number of bits, the transition density. Similarly,on the right side of the eye diagram, near x = T B ,
BER R (x ) = ρT ∫x
–∞J (x ′)dx ′
(10)
so that BER(x ) = BER L (x ) + BER R (x )[6].
Figure 4: A bathtub plot or BERTscan; the bit error ratio as a function of sampling point delay, x .
BER(x,V ) ≡ lim N err (x,V )N
X ∞
Figure 5a the dashed DJ distribution is given by a single frequency of sinusoidal jitter and, in Figure 5b, by a flat, bounded DJ distribution. The DJ distributions are convolved with a Gaussian resulting in the smooth solid curves. The effect of the convolution is to smooth the sharp edges of the DJ distribution and J (x ) obtains its Gaussian tails. Notice how the smoothing effect of the convolution brings the sharp DJ edges inward. The
vertical lines in Figure 5 are set at μR and μL demonstrating the inequality, DJ(δδ) = |μR – μL | < DJ(p-p). The two Gaussian curves (dash-dot) give the dual-Dirac
approximation to the solid curve. It doesn’t matter that the central part of the dual-Dirac distribution doesn’t match the actual distribution; the important feature is that the Gaussian tails match the tails of the true jitter distribution as in Eq. (7) so that TJ(BER) can be estimated using Eqs. (9) through (12).
3.1 Q-scale
To fully understand the dual-Dirac model it is useful to study a linearized version of the bathtub plot, Figure 4. We introduce a variable Q , instead of BER, for the vertical axis. The advantage of the “Q -scale” is that a Gaussian jitter distribution is a straight line in Q (x ) which makes it easier to see how the dual-Dirac model really works in estimating TJ(BER) and why DJ(δδ) < DJ(p-p).
If we set the time-delay sufficiently far from the DJ
distribution so that J(x ) can be described by a Gaussian,then BER L (x ), using Eqs. (5) and (9), is given by
(13)Now let
(14)
so that Eq. (13) becomes
The complementary error function is given by
(15)
so that Eq. (14) can be written
(16)
3. The dual-Dirac Model In Action
The fundamental assumption behind the dual-Dirac
approximation is that any deterministic jitter distribution can be approximated by two delta functions separated by DJ, as shown in Figure 1. In this special case, DJ(δδ) =DJ(p-p). A jitter distribution that closely follows a
dual-Dirac could result from pure duty cycle distortion (DCD) or square wave phase modulation but in practical applications it is much more complicated.
Separate jitter components combine through convolution – the mathematical process of folding one distribution over another, Eq. (6) – it is important to understand the process of convolution. To illustrate how RJ and DJ con-volve, think of the smooth Gaussian RJ as a smearing
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Figure 5: Application of the dual-Dirac model to two ideal cases.
In (a) the dashed DJ distribution is caused by a single frequency of sinusoidal jitter and in (b) the dashed bounded, constant (square wave)DJ distribution could be caused by triangle-wave phase modulation. In these examples, σ= 0.15xDJ(p-p), the solid curve is the convolved jitter distribution and the dash-dot lines are the dual-Dirac approximation.The vertical lines indicate where the dual-Dirac model sets the means of Gaussians, μR and μL .
BER L (x ) = ρT ∫ exp [– ]
dx '.(μL – x ')22σ2∞X
√2πσ1Q =
(if J (x ) is Gaussian) μL – x
σ
BER L (Q ) = ρT ∫ exp ()
dQ ' Q '2
∞
Q .
2
erfc(x ) = ∫ exp [– ]
dx '
x '22σ2∞X
2πσ√1BER L (Q ) = ρT erf (
) Q
2
√= ρT ( 1 – erf (
) )
Q
2
√
Notice the difference between DJ(p-p) and DJ(δδ) in Figure 6: they are completely separate quantities. While the accuracy of the dual-Dirac model is improved by inserting a value for σof greater accuracy, the accuracy is degraded by replacing DJ(δδ) with DJ(p-p); the dashed lines in Figure 6a would be displaced inward from μL to DJL and μR to DJ R resulting in a considerable overestimate of TJ(BER). Once again, DJ(δδ) does not estimate of DJ(p-p).
Given Eqs. (13) through (18) we can see where the values for Q BER in Table 2 come from. The BER due solely to the Gaussian tails is given by Eq. (16) with Q given by Eq.(14). For transition density, ρr = 1/2, BER = 10–11corre-sponds to Q = 6.7, for BER = 10–12, Q = 7.0, and so on.Equation (1) gives TJ(BER) due to the Gaussian tails,2Q BER x σ, plus a fixed displacement given by DJ(δδ):TJ(BER) ?2Q BER x σ+ DJ(δδ).
n the last step, I substituted the error function, erf(x ), for the complementary error function, erfc(x ); the two are related by erfc(x ) = 1 - erf(x ).
The reason we’re doing this is to map BER(x ) as shown in the bathtub plot of Figure 5 to Q (x ) where Gaussian distributions are straight lines. Next, we invert Eq. (16)from BER(Q ) to Q (BER),
(17)
where erf –1indicates the inverse of the error function (there are several good approximations to erf –1, but no closed form solution). To this point we have assumed a Gaussian distribution. But now that we have Q (BER) we can generalize to any case. Remember, BER(x) describes the dependence of the BER on the time-delay position of the sampling point. Similarly, by replacing BER with BER(x ) in Eq. (17) we get a definition of Q that does not rely on the form of the jitter distribution.
(18)
The important distinction is that Eq. (14) gives Q in the special case where J (x ) follows a Gaussian distribution,but Eq. (18) is true for any jitter distribution.
Finally, turning to Figure 6 we can decipher how the dual-Dirac distribution models the actual distribution. In Figure 6a the solid line gives Q (x ) and the dashed line gives the dual-Dirac approximation to Q (x ).
The statement – the dual-Dirac model is a Gaussian
approximation to the outer edges of the jitter distribution displaced by a fixed amount, DJ(δδ) – is demonstrated in Figure 6. In the absence of DJ, J(x ) would be purely Gaussian, the dual-Dirac model would give μL = 0 and μR = T B giving DJ(p-p) = DJ(δδ) = 0.
In Figure 6a the convolution of a bounded DJ distribution with a Gaussian RJ distribution results in Q (x) whose tails asymptotically approach the Gaussian tails as described by Eq. (7) with slope 1/σas required by Eq. (14). Figure 6b shows all of the parameters of the dual-Dirac model explicitly, it presents Q (x ) centered about a crossing point rather than about the center of the eye; the same symmetry as the jitter distributions shown in Figure 3a and Figure 5. Figure 6b is made by moving the right slope of Q (x ) – due to eye closure from the right crossing point – across the left slope and joining it at x = 0. The advantage of Figure 6b is that TJ(10–12),DJ(p-p), and DJ(δδ) can all be shown explicitly.
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Figure 6: (a) The Q -scale version of a bathtub plot – Q (x ) rather than BER(x )– where Gaussian effects are straight lines of slope 1/σ. The dashed line gives the dual-Dirac approximation to Q (x ). (b) The same plot, but with the right side of the bathtub plot shifted over to the left to explicitly show TJ(10–12) and emphasize the difference between DJ(p-p) and DJ(δδ).
Q (BER) = 2 erf –1
[1 – BER ]
,√1ρT
Q (x ) ≡ 2 erf –1
[
1 – BER (x )]
(general definition)
√
1
ρT
The peak-to-peak DJ of a convolution of uncorrelated distributions is the sum of the peak-to-peak DJs of the components. But, unlike for RJ, we have no assurance that the DJ sources are uncorrelated. For example, if a transmitter sends a signal with ISI into a channel, the response of the channel – its filtering effects and so forth – will be different than it would were there no ISI from the transmitter. In this case DJ(p-p) emitted from the channel is at most the sum of the DJ(p-p) of the transmitter and the channel,
DJ T otal (p-p) ≤DJ 1(p-p) + DJ 2(p-p) + … + DJ N (p-p).
Of course what we really need is DJ Total (δδ), not
DJ Total (p-p). It is not necessarily the case that the sum of DJ i (δδ) gives DJ Total (δδ); hence the approximate relationship denoted by “≈“ in Eq. (3). Still the approximation should be reasonably accurate.
As more DJ sources are convolved the resulting DJ
distribution is smoother about the edges. The difference between DJ(p-p) and DJ(δδ) is larger for smother distributions – for example, compare DJ(δδ) between Figure 5a and b. It is therefore reasonable to expect that DJTotal(δδ) resulting from the convolution of the DJ distributions of each network element should be smaller than that given by the na?ve sum in Eq. (3), rendering Eq. (3) a conservative estimate of the combined RJ and DJ(δδ) of the system. In some cases the estimate for DJ(δδ) given in Eq. (3) can give an appreciable overestimate that could lead you to believe that a system would fail its BER requirement when it would actually pass. The best way to determine how the effects combine is to study the data-dependent jitter of the system. For example, a measurement of DDJ vs bit can be performed quite accurately and provide concise information of how the DJ of different sources interferes.From the perspective of interoperability – whose
assurance is the primary role of a technology specification – Eq. (3) is a conservative way to combine σand DJ(δδ)for use in Eq. (1) to estimate TJ(BER).
3.2 Application of the dual-Dirac model
Once μR , μL , and σare obtained, TJ(BER) can be
estimated by using Eqs. (9) and (10) with the dual-Dirac jitter distribution in place of J(x ) to calculate x L (BER)and x R (BER) and then TJ(BER) as in Eq. (12), or just use Eq. (1), TJ(BER) = 2Q BER x σ+ DJ(δδ). Ultimately this process is the extrapolation of the tails of the observed distribution to the BER of interest. It can be a huge extrapolation. In most cases J (x ) is measured from the transitions of about 106bits, corresponding to a BER of more than 10–6; extending the tails down to 10–12is an extrapolation of at least six orders of magnitude.The dual-Dirac model is applied in many different ways on different types of test equipment. Real-time oscilloscopes from different vendors use vastly different techniques that frequently yield widely varying results. A concise analysis of the major differences of the techniques is provided below in Section 4.
3.3 Combining the jitter of different elements in a system
The jitter for a system of network elements can be combined according to Eq. (3), repeated below, under the assumption that the jitter of different network elements is uncorrelated.
σT otal = √σ1 +σ2 + . . . +σn
(3)
DJ T otal (δδ)≈DJ 1(δδ)+DJ 2(δδ)+ . . . + DJ N (δδ)
Remember that uncorrelated jitter distributions are
combined by convolution, Eqs. (4) and (6). Since the convolution of two uncorrelated Gaussian distributions gives a Gaussian distribution whose width is the RSS of the individual widths, the Gaussian RJ of each component can be combined through RSS as in Eq. (3).
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The accuracy of the fitting techniques is extremely sensitive to the region of the distribution to which the fit is applied. The fit should be performed on only the tails of the distribution that truly follows the underlying RJ Gaussian given by Eq. (7), but it is difficult to determine where this asymptotic behavior begins.
Consider Q (x ) in Figure 7. When Gaussian tails are fit to the region Q (x ) > 5, where Q (x ) is linear, the fit matches the asymptotes (i.e., the green dashed lines) and the slope gives an accurate estimate of 1/σ. But if the fit is applied to the region 2 < Q (x ) < 4 then a line with a smaller slope (larger σ) results (i.e., the red dot-dashed lines) and yields an overestimate of TJ(BER). In this
example, the fitting technique would indicate that the eye is completely closed at BER = 10–12(which corresponds to Q = 7.0). Whether or not the fit is applied low enough on the slopes depends on the statistical significance of the measurement. That is, the more data acquired, the farther down the slopes one can fit. The problem is that the effect of convolving the RJ Gaussian and the bounded DJ distribution yields a distribution whose tails are well parameterized by a Gaussian with a larger value of σthan that of the actual underlying RJ Gaussian even very close to the DJ dominated part of the curve. As a result,goodness-of-fit estimators (e.g., fit confidence levels or correlation values) are rarely useful indicators of where the distribution genuinely follows the underlying RJ Gaussian. The only way to be certain that the fitting technique is accurate is to acquire a generous statistical sample and appreciable increases in the sample size require exponentially longer test times.
While there is no way to be certain that the fit is performed far enough down the tails, you can at least assure that the fit doesn’t contradict itself with some simple convergence criteria. By repeating the fit for successively larger statistical samples to get to lower values of Q, DJ(δδ) should converge to a constant value.The slopes on the left and right edges should also
converge to a common value (for electrical systems [7]).Depending on the test device, it may not be possible to acquire enough data to meet these convergence
requirements – remember, only a BERT can realistically provide data well down the slopes to BERs of 10–9and lower. To make it worse, convergence doesn’t guarantee that your fit is far enough down the asymptotes; convergence is necessary but not sufficient.
4. Different Implementations Of The dual-Dirac Model
The dual-Dirac model is applied in two fundamentally different ways:
?The fitting techniques analyze J (x ) or BER(x ) to determine both σand DJ(δδ).
? The independent -σtechniques determine σwith a direct measurement of timing noise and then derive DJ(δδ) with a variety of techniques [3].The fitting techniques are used to estimate TJ(BER)
quickly on BERTs, oscilloscopes, and TIAs. There are two distinct approaches to the fitting techniques that operate in nearly equivalent ways. They both fit separate Gaussian distributions to the left and right edges of the distribution to yield four parameters σR , σL , μR , and μL ; they both average σR and σL and assign σ= 1/2(σR + σL ). In one approach a simple Gaussian Eq. (5) is used to fit a
fraction of the tails of the jitter distribution, J (x ). In the other approach the Gaussian inspired complementary error function, Eq. (15), is fit to the tails of a bathtub plot,BER(x ) or Q (x ). In ideal conditions the two techniques are equivalent. In ordinary conditions, the fit to the bathtub plot tends to be more repeatable because it is less affected by random fluctuations.
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Figure 7: A plot of Q (x ) demonstrating how fitting techniques can overestimate RJ if the fit is applied to regions of Q above the
asymptotes. The dashed (green) lines indicate the properly applied dual-Dirac model, the dot-dash (red) lines indicate a fit that
over-estimates RJ and underestimates DJ resulting in the mistaken impression that the eye is completely closed at BER=10–12(i.e., Q ~ 7).
It is interesting to contrast the fitting and independent-σtechniques. In the fitting techniques one assumes that RJ follows a Gaussian distribution before the measurement and in the independent-σtechniques the assumption is made after it is measured. In practice, the fitting techniques break down when a set of DJ components
convolve to form a DJ distribution with smoothly decaying tails. The central limit theorem of statistics says that the convolution of an infinite number of small uncorrelated processes, regardless of their individual distributions, follows a Gaussian distribution. This means that the more DJ components are included, the more that the resulting total DJ distribution resembles a Gaussian and the larger the statistical sample required of the fitting techniques.The effect is easy to observe by introducing data-dependent jitter with a backplane or by increasing the length and complexity of the test pattern; the fitting techniques give larger values for σunless the region included in the fit is appropriately adjusted. The fitting techniques cannot discriminate the bounded DJ from the unbounded RJ and end up overestimating σ. Since σhas a greater effect on TJ(BER) than does DJ(δδ), an apprecia-ble overestimate of σcan give a substantial overestimate of TJ(BER).
To illustrate the biases introduced by a fitting technique consider Figure 8. Figure 8a, the ratio of the RJ fit results,σfit , to the actual RJ, σtrue , as a function of σtrue /DJ(p-p),shows how RJ tends to be overestimated. Notice that in the limit of low and high RJ, σfit converges to σtrue . Figure 8b, the ratio of the DJ(δδ) results from a fitting technique to the actual DJ(p-p) as a function of σtrue
/DJ(p-p), shows that DJ(δδ) and DJ(p-p) are very different quantities; only in the limit of zero RJ does DJ(δδ)
approach DJ(p-p). Figure 8b is an excellent demonstration of the relationship DJ(δδ) < DJ(p-p). Figure 8c, the ratio of TJ(10–12) from a fitting technique to the true TJ(10–12)as a function of σtrue /DJ(p-p), shows how fitting techniques tend to overestimate TJ. Since the data in this example is from a simulation, there are no statistical fluctuations; hence, the results are more accurate than one should reasonably expect from actual data.
When σis measured independently, for example by
measuring the rms timing noise in the frequency domain,an accurate value can be obtained from a much smaller data set than by fitting. The slopes of BER(x ), or Q (x ), are then fixed and the sum of two Gaussians can be matched to the tails with only the centers of the Gaussians, μR and μL , allowed to vary.
11
Figure 8: Implementation of a fitting technique to the dual-Dirac model for different simulated RJ/DJ ratios.The fit is applied to simulated data from 10–6< BER < 10–3. In (a) the dual-Dirac estimate of RJ is typically overestimated by 5% but varies with the ratio RJ/DJ; (b) demonstrates that DJ(δδ) and DJ(p-p) are different quantities; and in (c), the resulting over-estimate of TJ(10–12) is shown. DJ in this example is dominated by ISI from a backplane model and the data pattern is a pseudo-random binary sequence of length 27–1 at 2.5 Gb/s.
The BERT measurements in Figure 9 were performed by transmitting 3x109bits in 1 ps steps of time-delay; the complementary error function, Eq. (15), was fit to the bathtub plots in the region BER < 10–4in all cases. You can see how the fitting technique over-estimate σand TJ(10–12) as the complexity of the DJ distribution increases.
The advantages of the BERT fitting technique compared to fitting techniques implemented on oscilloscopes and time interval analyzers are:
1. It’s easy to understand the simple implementation of the dual-Dirac model.
2. There is a lot of freedom in setting the region of the curve that is included in the fit because the statistical sample can be increased at the full data rate.
3. And, most importantly, fast estimates of TJ(BER) can be confirmed by performing a measurement of TJ(BER) when in doubt [2].
To see how different implementations give different
results, consider Figure 9. The precision jitter transmitter described in Ref. [4] was used to generate jitter signals on a 2.5 Gb/s, 27–1 pseudo-random binary sequence.
Measurements from real-time oscilloscopes, time interval analyzers, the Agilent N4901B SerialBERT, and the Agilent 86100C DCA-J equivalent-time sampling oscilloscope are shown – only the measurements performed by Agilent equipment are labeled – the details of the study are given in Ref. [3]. The data in Figure 9 is separated by column. Each column includes data from a given jitter condition described by the bars at the bottom. You can see that all of the test sets perform adequately when only periodic jitter is applied and, to a lesser extent when only RJ is applied. But as data dependent jitter is introduced – by introducing different lengths of backplane – the test sets give wildly disparate results. Figure 9b shows that every test-set except the DCA-J mistake DDJ for RJ. The situation deteriorates for most test-sets as the number and magnitude of different jitter sources are introduced.
Figure 9 demonstrates that the Agilent 86100C DCA-J is the only jitter analysis system that provides consistent,accurate measurements of TJ(10–12) and its sub-components. The Agilent N4901B SerialBERT is the only other test-set that gives consistently accurate
estimates of TJ(10–12). The BERT performs the simplest form of the fitting technique implementation of the
dual-Dirac model described in Section 4. The other fitting techniques include algorithmic variations beyond the simple dual-Dirac model that make their results more difficult to understand. It is ironic that the real-time oscilloscopes and TIAs use more complicated algorithms for estimating TJ(BER) and RJ, but yield less accurate results.
12
One of the real-time oscilloscope techniques also uses an independent-σtechnique but consistently mistakes DDJ for RJ anyway. The DCA-J technique is described in detail in Ref. [5]. For several years the real time oscilloscopes and TIAs have delivered inconsistent measurements of RJ,PJ, DDJ, and estimates of TJ(10–12) but it is only with the introduction of the DCA-J that reliable measurements in this field have been realized.
The reasons that the DCA-J gives the most accurate results are simple. The DCA-J’s first step is to separate jitter that is correlated to the test pattern (i.e., data dependent jitter) by using it’s built in pattern trigger and trigger divider to analyze each edge of the pattern independently. The hardware-based DDJ separation
technique immediately prevents DDJ from being confused for RJ. RJ is then measured from just a data set whose DDJ has been removed with an independent-σtechnique.
13
Figure 9: Comparison of jitter test-set results for TJ(10–12) and σ(i.e., RJ). Each column of the graphs corresponds to a jitter condition indicated by the bars at the bottom of the column. The left most data-point in each column is the calibrated level of jitter from the precision jitter transmitter described in Ref. [4]. The error bars on the calibrated values indicate the systematic uncertainty of the calibration. The unlabeled measurements were performed on common jitter test-sets such as real-time oscilloscopes and time interval analyzers; one of these measurements
is off the scale in the rightmost column. The data from the Agilent equipment is labeled.
The discrimination of timing and amplitude noise is another difficulty. Crosstalk between neighboring data paths causes errors by changing the crossing point position in time and is frequently referred to as non-periodic bounded uncorrelated jitter (BUJ). But cross-talk is amplitude noise, not timing noise - it’s not jitter, though it causes errors the same way that jitter does. None of the jitter test-sets on the market are capable of reliably analyzing BUJ simply because it can take on too many forms. But without a more comprehensive technique for analyzing amplitude and timing noise BUJ interferes with the implementation of the dual-Dirac model on all test equipment.
The finite bandwidth of a receiver can cause amplitude noise to timing noise conversion. The jitter properties of a receiver are usually tested with some type of jitter tolerance measurement – a test of the level of jitter that a receiver can tolerate. A jitter test-set with a receiver of limited bandwidth can experience the same amplitude noise to jitter conversion and overestimate the jitter
on a signal. However, a receiver’s intrinsic noise increases with bandwidth. The conflict is another case where the DCA-J is the best solution. Receivers with very high
bandwidth are available and the noise floor of the DCA-J is significantly lower than that of real-time oscilloscopes or TIAs.
In most cases noise is noise. The separation of jitter and amplitude noise is not always transparent or performed independently. For example, inter-symbol interference contributes to both. ISI affects the slew rate and amplitudes of different bits in a signal as well as the transition time. Generally, in diagnosing the problems of a system, it is wise to keep in mind the complexity of the signal.
5. Conclusion
5.1 The reality of the standard, industry-wide assumptions
The assumptions of the dual-Dirac model, Table 1, can be debated. The Gaussian RJ assumption is based on the idea that RJ is caused by the thermal behavior of a Fermi gas of electrons in a conductor that induces timing fluctua-tions that follow a Gaussian distribution [8]. The debate over the Gaussian RJ assumption centers on whether the observed RJ levels are consistent with the levels one should expect from purely thermal processes. The argument is that thermal processes, in most cases, can only account for one or two picoseconds of rms RJ, but we frequently see three or four times that. The central limit theorem begs the possibility that many small DJ sources could convolve into a distribution that follows a Gaussian that is truncated and could easily be mistaken for RJ.
The last assumption, that jitter is a stationary phenomena, is nearly intractable. All jitter test-sets that estimate TJ(BER) sample the data. None of them analyze a
continuous data stream. Real-time oscilloscopes capture finite lengths of data and post-process them; even when separate captures are combined there is a long trigger re-arm time between data captures. BERTs analyze every bit as a digital stream with a given sampling point position, and equivalent time sampling oscilloscopes build statistical distributions by repetitively sampling the time-delay and voltage of a signal. None of these techniques analyze a continuous data stream; none of them can reliably detect nonstationarity of a jitter
signal. The only jitter analysis technique that analyzes a continuous data stream is phase-noise analysis of clock signals commonly used in SONET/SDH jitter analysis. The SONET/SDH jitter analysis is band limited and does not relate timing-noise to BER; Ref. [9] provides a comprehensive description of SONET/SDH jitter analysis.
14
1
To learn about the basics of jitter analysis, see Ransom Stephens, “The rules of jitter analysis,”
https://www.doczj.com/doc/d713277423.html,/nett0927.pdf, 2004; Ransom Stephens, “Analyzing Jitter at High Data Rates,”IEEE
Communications Magazine, vol. 42, no. 2, February 2004, pp. 6-10; Agilent Technologies’ Application Note, “Jitter Fundamentals: Agilent 81250 ParBERT Jitter Injection and Analysis Capabilities,” Literature Number AN-5988-9756EN, available from https://www.doczj.com/doc/d713277423.html,, 2003.
2
Marcus Müller, Ransom Stephens, and Russ McHugh, “Total Jitter Measurement at Low Probability Levels, Using Optimized BERT Scan Method,”DesignCon 2005,
https://www.doczj.com/doc/d713277423.html,/conference/7-ta4.html.3
Ransom Stephens et al., “Comparison of jitter analysis techniques with a precision jitter transmitter,”Agilent Technologies Whitepaper, 2005. Available from https://www.doczj.com/doc/d713277423.html,.
4
Jim Stimple and Ransom Stephens, “Precision Jitter Transmitter,” DesignCon 2005,
https://www.doczj.com/doc/d713277423.html,/conference/7-wa1.html.
5
Agilent Technologies Product Note, 86100C-1, “Precision jitter analysis using the Agilent 86100C DCA-J,”Agilent Literature Number 5989-1146EN,
https://www.doczj.com/doc/d713277423.html,/litweb/pdf/5989-1146EN.pdf . 6
Strictly speaking, Eqs. (9) and (10) are only valid if the observed jitter distribution, J (x ), is bounded with a peak-to-peak value less than one bit period. To posit a bounded J (x ) contradicts the unbounded nature of RJ. In practice the contradiction is not a problem because, in those systems where the tails of J (x ) from the left and right overlap the eye is closed, TJ(BER) = TB. Thus there is no practical problem using Eqs. (9) and (10) to derive BER(x ) from distributions measured on oscilloscopes.7
For optical systems nonlinearities in the laser transmitter can cause the left and right slopes to have different slopes, but in electrical systems, the thermal noise should give the same values for δon the left and right.
https://www.doczj.com/doc/d713277423.html,ndau and E.M.Lifshitz, Statistical Physics, Part 2, 3rd ed., Pergamon Press, 1980.
9
Agilent Tutorial, “Understanding Jitter and Wander Measurements and Standards, Second Edition,”Agilent Literature number 5988-6254EN, 2003. Available from https://www.doczj.com/doc/d713277423.html,.
5.2 Summary
The dual-Dirac model:
?Provides a useful way to quickly estimate TJ(BER) at low BER.
?Is built on the assumption that RJ follows a Gaussian distribution that can be described by a single parameter, σ?Defines an observable DJ(δδ) that can be measured in a variety of different ways but should not be confused with the true peak-to-peak DJ, DJ(p-p). Generally, DJ(δδ) < DJ(p-p).
?Provides a transparent way to combine σand DJ(δδ) of different network elements to estimate TJ(BER) for a system.
?Provides observable, well defined quantities for use in technology standards.
?Can be applied in different ways that have different systematic uncertainties that can lead to different errors that make comparison of results difficult.
?Is most accurately implemented through the technique introduced on Agilent’s 86100C DCA-J that combines a hardware separation of jitter that is correlated to the test pattern from that which is uncorrelated with a direct measurement of timing noise, σ.
15
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PSS仿真的原理是什么 Q:我一直没有弄明白PSS仿真的原理是什么，只知道他叫做周期稳态仿真，貌似仿那种非线性很强的电路会遇到不收敛的问题。 很想知道这种仿真原理是什么，为什么一般是PSS加上另外一个一起仿真？？？？？ A1:我是这么理解的： PSS先假设你的信号是周期性的(1/beat frequency)，它寻找这个周期内的信号是否重复出现，如果电路非线性很强，可能导致周期性不强（两个周期内信号不完全重合），如果精度设定比较高，就会出现不收敛。一般向相位噪声，jitter 这种周期信号特有的特性，可以先做PSS找到周期信号，然后再分析每个周期内的相位差别，从而找到pnoise结果。 望高人指点。 A2:pss是针对时钟控制电路的稳定性分析，spectre使用一种overshooting 的算法持续计算n个（例如5个）时钟的电路dc工作点，然后比较，如果这n个周期算下来的结构都一致，说明电路稳定 A3:我认为PSS是一种比较精确的仿真方式。 我对他的理解是这样的： PSS,Periodic steady-state,其译名是稳态谐波仿真,就是电路以一个周期为节点，先仿第一个周期，然后第二个周期，进行比较，看电路是否进入稳态，否则，再仿真一个周期，与第二个周期作比较，看电路是否进入稳态。有点类似数值分析里面的迭代算法，看两次迭代的结果是否在误差允许范围内，通过这样的一种方式得到一个稳态的电路状态，然后进行时域到频域的变换，得到一些频域的电路状态。 A4:至于和其他的如PSP一起仿真，是因为别的仿真是基于PSS的。 至于设置问题，一般是设置它的仿真算法和误差容忍范围，即判决何时到达稳态。 A5:一般AC的是先DC找到DC工作点，再AC小信号， 同理，PSS是先找到周期性工作点，取决于大信号，然后做PAC等等是在PSS工作点上的小信号处理
电子分频器要注意的几点问题及故障排除网络摘编 电子分频器： 电子分频器的主要功能当然就是给不同的音箱分配好不同的工作频率了，当然还有保护音箱的功能，下面说下调整电子分频器时需要注意的几点问题及故障排除： 1、分频点： 在一个2分频的音响系统中，一般情况下分频点放在130Hz附近比较合适，但很多情况下，对分频点的调整实际上不是取决于低音音箱，而是要看中高音或全频音箱。因为低音音箱在300Hz以下工作都可以，但有些中高音和全频音箱由于扬声器口径太小，动态范围不够大，必须在200Hz以上工作才能保证它们的安全，如果此时分频点分在130Hz附近，那么这些中高音音箱工作起来就很危险了，因此在效果和安全当中还是要找一个平衡点。我觉得双15寸的全频主音箱最好不要经过电子分频器；单15寸的主音箱可灵活运用；而单12寸以下的主音箱最好要通过电子分频器，至少在180Hz以上工作才安全。 2、音量控制： 不管是输入电平还是输出电平，调整的时候都要有一个度，不要开的太大。如果是电子分频器上的各个音量旋钮都开到很大了，系统的声压还不够，那就要调整电子分频器前面设备的信号电平或者调整电子分频器下面功放的电平和音量开关了。 3、×10按钮： 有一些电子分频器上有一个： ×10的按钮，大家注意不要轻易按下它。 例如我们的分频点调整在200Hz的话，按下此按钮200×10就变成2000Hz 了，因此除非是需要，否则一般不要按下此按钮。
4、低音模式： 有些电子分频器后面板有一个低音模式的选择，它可以把2路立体声信号混合成1路单声道信号，这样可以减少低音音箱之间的声干涉。大家可以适当利用下。 当然要是低音分频点分的较高，那么低音音箱发出的声音就会有一定的指向性了，此时还是要在2路立体声信号的状态下工作较好。 5、立体声工作模式和单声道工作模式： 目前我们使用的大多数电子分频器都是2分频的居多，考虑到灵活性和多功能性，这些电子分频器的后面板一般会有一个立体声和单声道的工作模式转换开关，如果把此开关放在单声道工作模式下，那么此时这台电子分频器就从一台双通道2分频的电子分频器变成了一台单通道3分频的电子分频器了。因此除非必要，否则不要轻易转换此工作开关，要不然电子分频器后面信号输出口所输出的频率信号就会大不一样了！轻者恶化了音质，重者还会损坏设备！ 6、系统中低音信号的输出和中高音信号的输出一定不要搞混了，否则高音信号给了低音音箱，低音信号给了高音音箱，那样南辕北辙的做法音响系统中就真的没有声音出来了，因为频率不对呀！搞不好还会烧坏音箱呢！ 电子分频器故障例子： 1、05年朋友在长沙做了一个大型的酒吧，音响系统中共使用了单12寸全频主音箱16只，双18寸重低音音箱22只，还有其它20多只辅助音箱。但开业几天后发现主音箱的单12寸的喇叭坏了2只，开始那里的技术人员以为是正常损坏，更换了2只新的喇叭了事，但后来一个星期内陆陆续续的又坏了6只12寸的全频喇叭，这样就很不正常了，而且除了12寸主音箱发生故障外别的音箱都没有问题。后来我去帮忙检查了下系统，发现那里的电子分频器分的频率太低，我把分频器的分频点从130Hz调高到了230Hz，这样问题就解决了，而且低音效果也比以前好了很多。其实道理很简单： 这个系统中由于要兼顾人声演出，所以采用了对人声表现较好的12寸全频主音箱，开始时电子分频器的分频点在130Hz，这是什么概念呢？就是说系统中
相位噪声和抖动jitter的概念及估算方法 时钟频率的不断提高使和在系统时序上占据日益重要的位置。本文介其概念及其对系统性能的影响，并在电路板级、芯片级和单元模块级分别提供了减小相位噪声和抖动的有效方法。 随着通信系统中的时钟速度迈入GHz级，相位噪声和抖动这两个在模拟设计中十分关键的因素，也开始在数字芯片和电路板的性能中占据日益重要的位置。在高速系统中，时钟或振荡器波形的时序误差会限制一个数字I/O接口的最大速率，不仅如此，它还会增大通信链路的误码率，甚至限制A/D转换器的动态范围。 在此趋势下，高速数字设备的设计师们也开始更多地关注时序因素。本文向数字设计师们介绍了相位噪声和抖动的基本概念，分析了它们对系统性能的影响，并给出了能够将相位抖动和噪声降至最低的常用电路技术。 什么是相位噪声和抖动？ 相位噪声和抖动是对同一种现象的两种不同的定量方式。在理想情况下，一个频率固定的完美的脉冲信号(以1 MHz为例)的持续时间应该恰好是1微秒，每500ns有一个跳变沿。 但不幸的是，这种信号并不存在。如图1所示，信号周期的长度总会有一定变化，从而导致下一个沿的到来时间不确定。这种不确定就是相位噪声，或者说抖动。 抖动是一个时域概念 抖动是对信号时域变化的测量结果，它从本质上描述了信号周期距离其理想值偏离了多少。通常，10 MHz以下信号的周期变动并不归入抖动一类，而是归入偏移或者漂移。抖动有两种主要类型：确定性抖动和随机性抖动。确定性抖动是由可识别的干扰信号造成的，这种抖动通常幅度有限，具备特定的（而非随机的）产生原因，而且不能进行统计分析。造成确定性抖动的来源主要有4种： 1. 相邻信号走线之间的串扰：当一根导线的自感增大后，会将其相邻信号线周围的感应磁场转化为感应电流，而感应电流会使电压增大或减小，从而造成抖动。 2. 敏感信号通路上的EMI辐射：电源、AC电源线和RF信号源都属于EMI源。与串扰类似，当附近存在EMI辐射时，时序信号通路上感应到的噪声电流会调制时序信号的电压值。 3. 多层基底中电源层的噪声：这种噪声可能改变逻辑门的阈值电压，或者改变阈值电压的参考地电平，从而改变开关门电路所需的电压值。
NS-3网络仿真 一：实验要求 用NS-3仿真某个特定的网络环境，并输出相应的仿真参数（时延，抖动率，吞吐量，丢包率）。 二：软件介绍 NS-3 是一款全新新的网络模拟器，NS-3并不是NS-2的扩展。虽然二者都由C++编写的，但是NS-3并不支持NS-2的API。NS-2的一些模块已经被移植到了NS-3。在NS-3开发过程时，“NS-3项目”会继续维护NS-2，同时也会研究从NS-2到NS-3的过渡和整合机制。 三：实验原理及步骤 NS-3是一款离散事件网络模拟驱动器，操作者能够编辑自己所需要的网络拓扑以及网络环境，来模拟一个网络的数据传输，并输出其性能参数。 软件中包含很多模块：节点模块（创造节点），移动模块（仿真WIFI，LTE可使用），随机模块（生成随机错误模型），网络模块（不同的通信协议），应用模块（创建packet 数据包以及接受packet数据包），统计模块（输出统计数据，网络性能参数）等等； 首先假设一个简单的网络拓扑：两个节点之间使用点对点链路，使用TCP协议进行通信，假设随机错误率为0.00001，节点不可移动（因为不是无线网络），具体代码如下：
NodeContainer nodes; nodes.Create (2); 创建两个节点； PointToPointHelper pointToPoint; pointToPoint.SetDeviceAttribute ("DataRate", StringValue ("5Mbps")); pointToPoint.SetChannelAttribute ("Delay", StringValue ("2ms")); 设置链路的传输速率为5Mbps，时延为2ms； NetDeviceContainer devices; devices = pointToPoint.Install (nodes); 为每个节点添加网络设备 Ptr
专业电子分频器的使用技巧 在一套音响系统中提到分频器一般来说是指能将：20Hz--20000Hz频段的音频信号分成合适的、不同的几个频率段，然后分别送给相应功放，用来推动相应音箱的一种音响周边设备。由于它是一种用来处理、分配音频频率信号的电子设备，所以我们通常也叫它：电子分频器。电子分频器的详细功能和工作原理我就不多说了，这里我只是侧重于对一些大家比较重视或经常感到困惑的方面做一些通俗易懂的介绍，希望能对大家有所帮助！ 一、我们为什么要使用电子分频器 我们音响师研究电声和现在电声设备与技术的不断发展都是为了一个目的：就是要尽量忠实的再现各种音源，当然要把自然界里千奇百怪、各种各样的声音完全利用现在的电声技术再现是不太现实几乎做不到的。大家知道，声音的频率范围是在20Hz—20000Hz之间，现在大多数前级音频处理设备的频率范围是可以达到这样宽度的，但目前的扬声器却成了一个瓶颈部分，我们奢想使用一种或简单几只扬声器就能放送出接近20Hz--20000Hz这样宽频率的声音是很难做到的，因为现在单只喇叭的有效工作频率范围都不是很宽。鉴于此电声工程师们就设计出了在不同频率段内工作的音箱，如： 1、重低音音箱：让它在大约30-200Hz的频率范围内工作。 2、低中音音箱：让它在大约200-2000Hz的频率范围内工作。 3、高音音箱：让它在大约2000-20000Hz的频率范围内工作。 如此以来我们就可以利用在不同频率段工作的不同种类的音箱配置一套能最大限度接近声音真实频率（20Hz--20000Hz）的音响系统了。当然不同音箱设备的构成和参数是不同的，我上面说的是以一个三分频的系统为例，实际使用上还有其它诸如：2分频或4分频等系统，而且不同音响系统中由于采用的音箱会有区别，因此这些音箱的工作频率也不可能是固定相同的，但大体的原理和思路是一样的。 那么有一个问题就是： 我们如何给这些在不同频率段工作的、不同种类的音箱灵活分配音频频率呢？为了解决这个问题，电子分频器就应运而生了，它可以根据不同音箱工作频率的需要提供合适的频率段，例如： 1、我们可以用电子分频器将高频信号通过功放送到高音扬声器中. 2、可以用电子分频器将中频信号通过功放送到中音扬声器中。 3、可以用电子分频器将低频信号通过功放送到低音扬声器中。
超低相位噪声基于频梳的微波产生和性能 摘要——我们通过光电检测锁定于1.5um超窄线宽超稳定激光的基于铒掺杂光纤频梳相位的脉冲串来报告12GHz超低相位噪声微波信号的产生。拥有先进的光电检测技术和自制相位噪声计量器具，我们的实验证明了微波源的产生，具有10KHz以上且低于170dBc/Hz，源自一个12 GHz 载体的1Hz且低于100dBc/Hz的全相噪声，这将极大推进目前最好的记录结果。 关键字——光纤频梳，光电微波源，超低相位噪声 前言 诸如无线通讯，雷达，深空航行系统，精密微波光谱学的许多应用都需要超稳定微波信号。这种光纤信号通过光纤频梳产生是特别有趣的，因为它允许把无法超越的超稳定连续波激光的光谱纯度转变成微波领域（同光纤和太赫兹辐射波领域），潜在的引导记录低相位噪声微波源。 光纤到微波的转变由拥有超稳定光纤参考频率的飞秒激光器的重复率同步完成。通过光纤脉冲串的快速光电探测对微波信号进行更深入的提取。然而，光电产生微波信号的光谱纯度同时受到频梳重复率性能以及光电探测过程自身的限制。光电探测进程收到了影响，特别是振幅
相位转变（APC）的影响，它转变了微波信号相位噪声中飞秒激光的强烈噪声，同时，它还受到光电探测器的约翰逊·奈奎斯特定理和冲击的影响。 我们通过增加产生在重复率相关谐波的微波功率来克服后来基本原理的限制，并运用基于光纤的梳状滤波器，该滤波器增加脉冲串的有效重复率，并与高线性高处理功率的光电探测器结合。我们也发展了一套自动测量伺服装置来降低APC的水平，这种状态下就不会对我们生产的微波信号的相位噪声产生重大的影响。 对其自身而言，超低相位噪声微波的特性达到这种水平状态是一项有趣的挑战。我们已经发明了一套基于3光纤频梳的特殊装置（给基础参考频率额外加上一个作为参考），3超稳定激光，一个高质量微波电路以及一个基于现场可编程门阵列自制的外差法振荡器，在源自具有极低的振幅噪声敏感度的12Ghz载体的傅里叶频率大于1KHz的条件下，该振荡器与达到低于-180dBc/Hzd的测量噪声水平互相关。 II 实验装置 我们的实验装置由一些光纤频梳和超稳定连续波激光器。这些超稳定连续波激光器由波长为1.5um的半导体二极管激光器组成，激光器被超高精细度（典型~6 10）的超高真空法布里-珀罗空腔的调制技术伺服。
时序计算和Cadence仿真结果的运用 中兴通讯康讯研究所EDA设计部余昌盛刘忠亮 摘要：本文通过对源同步时序公式的推导，结合对SPECCTRAQuest时序仿真方法的分析，推导出了使用SPECCTRAQuest进行时序仿真时的计算公式，并对公式的使用进行了说明。 关键词：时序仿真源同步时序电路时序公式 一．前言 通常我们在时序仿真中，首先通过时序计算公式得到数据信号与时钟信号的理论关系，在Cadence仿真中，我们也获得了一系列的仿真结果，怎样把仿真结果正确的运用到公式中，仿真结果的具体含义是什么，是我们正确使用Cadence仿真工具的关键。下面对时序计算公式和仿真结果进行详细分析。 二．时序关系的计算 电路设计中的时序计算，就是根据信号驱动器件的输出信号与时钟的关系（Tco——时钟到数据输出有效时间）和信号与时钟在PCB上的传输时间（Tflytime）同时考虑信号驱动的负载效应、时钟的抖动（Tjitter）、共同时钟的相位偏移（Tskew）等，从而在接收端满足接收器件的建立时间（Tsetup）和保持时间（Thold）要求。通过这些参数，我们可以推导出满足建立时间和保持时间的计算公式。 时序电路根据时钟的同步方式的不同，通常分为源同步时序电路（Source-synchronous timing）和共同时钟同步电路（common-clock timing）。这两者在时序分析方法上是类似的，下面以源同步电路来说明。 源同步时序电路也就是同步时钟由发送数据或接收数据的芯片提供。图1中，时钟信号是由CPU驱动到SDRAM方向的单向时钟，数据线Data是双向的。 图1
图2是信号由CPU 向SDRAM 驱动时的时序图，也就是数据与时钟的传输方向相同时 的情况。 Tsetup ’ Thold ’ CPU CLK OUT SDRAM CLK IN CPU Signals OUT SDRAM Signals IN Tco_min Tco_max T ft_clk T ft_data T cycle SDRAM ’S inputs Setup time SDRAM ’S inputs Hold time 图2 图中参数解释如下： ■ Tft_clk ：时钟信号在PCB 板上的传输时间； ■ Tft_data ：数据信号在PCB 板上的传输时间； ■ Tcycle ：时钟周期 ■ Tsetup’：数据到达接收缓冲器端口时实际的建立时间； ■ Thold’：数据到达接收缓冲器端口时实际的保持时间； ■ Tco_max/Tco_min ：时钟到数据的输出有效时间。 由图2的时序图，我们可以推导出，为了满足接收芯片的Tsetup 和Thold 时序要求，即 Tsetup’>Tsetup 和Thold’>Thold ，所以Tft_clk 和Tft_data 应满足如下等式： Tft_data_min > Thold – Tco_min + Tft_clk （公式1） Tft_data_max < Tcycle - Tsetup – Tco_max + Tft_clk (公式2) 当信号与时钟传输方向相反时，也就是图1中数据由SDRAM 向CPU 芯片驱动时，可 以推导出类似的公式： Tft_data_min > Thold – Tco_min - Tft_clk （公式3） Tft_data_max < Tcycle - Tsetup – Tco_max - Tft_clk （公式4） 如果我们把时钟的传输延时Tft_clk 看成是一个带符号的数，当时钟的驱动方向与数据 驱动方向相同时，定义Tft_clk 为正数，当时钟驱动方向与数据驱动方向相反时，定义Tft_clk 为负数，则公式3和公式4可以统一到公式1和公式2中。 三．Cadence 的时序仿真 在上面推导出了时序的计算公式，在公式中用到了器件手册中的Tco 参数，器件手册中 Tco 参数的获得，实际上是在某一种测试条件下的测量值，而在实际使用上，驱动器的实际 负载并不是手册上给出的负载条件，因此，我们有必要使用一种工具仿真在实际负载条件下 的信号延时。Cadence 提供了这种工具，它通过仿真提供了实际负载条件下和测试负载条件 下的延时相对值。 我们先来回顾一下CADENCE 的仿真报告形式。仿真报告中涉及到三个参数：FTSmode 、
电子分频是什么 说到电子分频，首先要说分频器是什么。顾名思义，分频器是一种将不同频率的信号进行分割的电路装置。其本质就是信号中的各种滤波器。通常我们指的音频的频率范围在20Hz-20KHz，高音指的是频率较高的声音，低音指的的是频率较低的声音。而在HiFi音响中，分频器的作用就是将高、中、低音，按照需要频率进行分割。因此分频器也常被称为“分音器”。 为什么需要分频器呢？因为不同的喇叭单元各自的特性不同，它们都有最佳表现的频率范围。因此在要求较高的HiFi音响系统中，利用分频器将频率进行分割，再分别交给高、中、低音喇叭，使在它们仅在最佳表现的频率范围内工作，以达到音质更佳的目的。 那么分频器有哪些种类呢？根据分频器在音响系统中所处的位置不同，我们通常又将它们分为功率分频器和电子分频器。 功率分频器： 电子分频器：
功率分频器是家庭HiFi音响中最常见的分频器，它处于功放之后、喇叭之前。正是因为它需要承受功放输出的巨大功率，所以称为功率分频器。功率分频器都是无源滤波器。 电子分频器则用来构成另一种音响系统。它处于音源之后，功放之前。经过它的音频信号较弱，所以通常用有源滤波器来实现。因此电子分频器也常被成为：有源分频器、主动分频器等。
功率分频器由于受元器件所限，所以在阻抗匹配、相位特性、插入损耗等方面和电子分频相比都不具优势。更重要的是，电子分频系统中，以多台功放分工合作的方式代替了功率分频系统中一台功放全力工作的方式，使得对功放的要求明显下降，但表现却能大大提升。 其实在专业音响上，电子分频系统早就被成熟运用。不过略有不同的是，专业音响中更多使用的电子分频器是DSP（数字信号处理器），它的最大特别是集成度高，功能强大，可以对曲线等进行各种调整。而在家用HiFi音响中，特别是对普通用户来说，笔者更推荐使用模拟的电子分频器。模拟的电子分频器没有很多功能和可调整的部分，但也因此能拥有更自然更优质的声音。 当然，不可否认，无论哪种音响系统如果设计合理，都可能发出好声音。 一家之言，仅供参考。
电子数字频率计测量方法毕业论文 1绪论 1.1研究背景及主要研究意义 频率是电子技术领域永恒的话题，电子技术领域离不开频率，一旦离开频率，电子技术的发展是不可想象的，为了得到性能更好的电子系统，科研人员在不断的研究频率，CPU就是用频率的高低来评价性能的好坏，可见，频率在电子系统中的重要性。 频率计又称为频率计数器，是一种专门对被测信号频率进行测量的电子测量仪器，其最基本的工作原理为：当被测信号在特定的时间段T的周期个数N时，则被测信号的频率f=N／T.电子计数器是一种基础测量仪器，到目前为止已有三十多年的发展历史。早期，设计师们追求的目标主要是扩展测量围，再加上提高测量精度、稳定度等，这些也是人们衡量电子计算机的技术水平，决定电子技术器价格高低的主要依据。目前这些技术日臻完善，成熟。应用现代技术可以轻松地将电子计数器的频率扩展到微波频段。 1.2数字频率计的发展现状 随着科学技术的发展，用户对电子计数器也提出了新的要求。对于低档产品要求使用操作方便，量程（足够）宽，可靠性高，价格低。而对中高档产品，则要求有较高的分辨率，高精度，高稳定度，高测量速率；除通常通用计数器所具有的功能外，还要有数据处理功能，统计分析功能等等，或者包含电压测量等其他功能。这些要求有的已经实现或者部分实现，但要真正地实现这些目标，对于生产厂家来说，还有许多工作要做，而不是表面看来似乎发展到头了。 由于微电子技术和计算机技术的发展，频率计都在不断地进步着，灵敏度不断提高，频率围不断扩大，功能不断增加。在测试通讯、微波器件或产品时，通常都市较复杂的信号，如含有复杂频率成分、调制的含有未知频率分量的、频率固定的变化的、纯净的或叠加有干扰的等等。为了能正确的测量不同类型的信号，必须了解待测信号特性和各种频率测量仪器的性能。微波技术器一般使用类型频谱分析仪的分频或混频电路，另外还包含多个时间基准、合成器、中频放大器等。虽然所有的微波计数器都是用来完成技术任务的，但各自厂家都有各自的一套复
本科生科研训练计划项目（SRTP）项目成果项目名称：航天器在轨运行的三维可视化仿真 项目负责人：林凡庆 项目合作者：曲大铭侯天翔杨唤晨孙洁 所在学院：空间科学与物理学院 专业年级：空间科学与技术2013级 山东大学（威海） 大学生科技创新中心
航天器在轨运行的三维可视化仿真 空间科学与物理学院空间科学与技术专业林凡庆 指导教师许国昌杜玉军摘要：航天器在轨运行的三维可视化程序设计是建立卫星仿真系统最基础的工作。航天器在轨运行的三维可视化仿真有着重要的意义：它既可以使用户对卫星在轨运行情况形成生动直观、全面具体的视觉印象，又可以大大简化卫星轨道的设计过程。本文首先构建了航天器在轨运行的三维可视化仿真程序的基本框架，然后对涉及到的关键理论与知识，如时间、坐标转换、卫星轨道理论、OpenGL图形开发库等也做了阐述，最后介绍了我们的主要工作和科研成果。我们的主要成果是实现了卫星在轨运行的三维可视化仿真并对原有程序进行了改进。 关键词：航天器在轨运行三维可视化程序设计 OpenGL Abstract：The programmer of three-dimensional visualization on satellite in-orbiting is the utmost foundational work in establishing satellite emulation system. The three-dimensional visual simulation on satellite is of great significance: it assures that users may receive a vivid and direct-viewing and it also can greatly simplify the design process of satellite orbit.The basic frame of three-dimensional visual simulation program on satellite in-orbiting has been set up firstly. then, related essential theory and knowledge such as time system, coordinate conversation, satellite orbit, OpenGL and etc also has been introduced. Lastly, our main work and research results has been introduced. Our main achievement is that we realized the program of three-dimensional visualization on satellite in-orbiting and we improve the original program. Key words：satellite In-orbit movement 3D visualization programming OpenGL 一、引言 当今社会是一个信息的社会，谁掌握了信息的主动权，就意味着掌握了整个世界。而人造卫星是当今人们准确、实时、全面的获取信息的重要手段，卫星的各项应用已经成为信息社会发展的强大动力。而人造卫星的应用是一项高投入、高风险、长周期的活动，仿真技术由于具有可控制、可重复、经济、安全、高效的特点，在人造卫星应用领域以至整个航天领域都起到了重大的作用。目前国际上较常用的卫星仿真软件主要有美国的Winorbit、美国Cybercom System公司研制的CPLAN和AGI公司的STK。其中以STK功能最为强大，界面最为友好，在卫星仿真领域占有绝对领先地位。STK功能虽然强大，但其价格昂贵，源码也不公开，无法自主扩展，并且该软件被限制了对中国的销售，所以中国不得不独立开发适于自己的卫星仿真系统[1]。而且国内目前卫星系统的仿真软件很少，主要有一些大学开发的小型的卫星系统仿真软件，还有北京航天慧海系统仿真科技有限公司开发的Vpp-STK航天卫星仿真开发平台V4.0。总体来说，国内目前在这个方面的技术还相当不成熟，因此研究和自主开发卫星仿真系统意义重大。 仿真可视化，就是把仿真中的数字信息变为直观的，以图形图像形式表示的，随时间和空间变化的仿真过程呈现在研究人员面前，使研究人员能够知道系统中变量之间、变量与参数之间、变量与外部环境之间的关系，直接获得系统的静态和动态特征[2]。 本文首先构建了航天器在轨运行的三维可视化仿真程序的基本框架，然后对涉及到的关键理论与知识，如时间、坐标转换、卫星轨道理论、OpenGL图形开发库等也做了阐述，最后介绍了我们的主要工作和科研成果。
4专业电子分频器的使用技巧 在一套音响系统中提到分频器一般来说是指能将：20Hz--20000Hz频段的音频信号分成合适的、不同的几个频率段，然后分别送给相应功放，用来推动相应音箱的一种音响周边设备。由于它是一种用来处理、分配音频频率信号的电子设备，所以我们通常也叫它：电子分频器。电子分频器的详细功能和工作原理我就不多说了，这里我只是侧重于对一些大家比较重视或经常感到困惑的方面做一些通俗易懂的介绍，希望能对大家有所帮助！ 一、我们为什么要使用电子分频器 我们音响师研究电声和现在电声设备与技术的不断发展都是为了一个目的：就是要尽量忠实的再现各种音源，当然要把自然界里千奇百怪、各种各样的声音完全利用现在的电声技术再现是不太现实几乎做不到的。大家知道，声音的频率范围是在20Hz—20000Hz之间，现在大多数前级音频处理设备的频率范围是可以达到这样宽度的，但目前的扬声器却成了一个瓶颈部分，我们奢想使用一种或简单几只扬声器就能放送出接近20Hz--20000Hz这样宽频率的声音是很难做到的，因为现在单只喇叭的有效工作频率范围都不是很宽。鉴于此电声工程师们就设计出了在不同频率段内工作的音箱，如： 1、重低音音箱：让它在大约30-200Hz的频率范围内工作。 2、低中音音箱：让它在大约200-2000Hz的频率范围内工作。 3、高音音箱：让它在大约2000-20000Hz的频率范围内工作。 如此以来我们就可以利用在不同频率段工作的不同种类的音箱配置一套能最大限度接近声音真实频率（20Hz--20000Hz）的音响系统了。当然不同音箱设备的构成和参数是不同的，我上面说的是以一个三分频的系统为例，实际使用上还有其它诸如：2分频或4分频等系统，而且不同音响系统中由于采用的音箱会有区别，因此这些音箱的工作频率也不可能是固定相同的，但大体的原理和思路是一样的。 那么有一个问题就是： 我们如何给这些在不同频率段工作的、不同种类的音箱灵活分配音频频率呢？为了解决这个问题，电子分频器就应运而生了，它可以根据不同音箱工作频率的需要提供合适的频率段，例如： 1、我们可以用电子分频器将高频信号通过功放送到高音扬声器中. 2、可以用电子分频器将中频信号通过功放送到中音扬声器中。 3、可以用电子分频器将低频信号通过功放送到低音扬声器中。 这样高、中、低频信号独立输出、互不干涉，因此可以尽可能发挥不同扬声器的工作频段优势，使音响系统中各频段声音重放显得更加均衡一些，使声音更具层次感，使音色更加完美。
V ol 38No.4 Aug.2018 噪 声与振动控制NOISE AND VIBRATION CONTROL 第38卷第4期2018年8月 文章编号：1006-1355(2018)04-0100-06 乘用车起步抖动仿真建模研究 朱鹏，曾玉红，黄海波，丁渭平，杨明亮，姜东明 (西南交通大学机械工程学院，成都610031) 摘要：针对手动挡乘用车起步抖动问题，采用Simulink 建立一套包含动力总成系统、悬架系统及车身的当量整车动力学模型。在模型中同时考虑了离合器的摩擦特性和多级扭转非线性特性。仿真得到汽车起步过程中的整车动力学响应，对车身纵向振动加速度进行时域及频域分析，并通过多辆不同实车试验验证所建立模型的合理性。同时，采用车身纵向振动加速度幅值及标准差作为判断依据，结果表明模型仿真与实车试验误差在8%以内。另外还剖析了模型仿真与实车试验的误差成因，为进一步研究起步抖动问题奠定基础。 关键词：振动与波；起步抖动；当量整车模型；Simulink ；仿真建模中图分类号：TB533+.2文献标志码：A DOI 编码：10.3969/j.issn.1006-1355.2018.04.020 Research on Simulation Modeling of Vehicle Starting Judder ZHU Peng ,ZENG Yuhong ,HUANG Haibo , DING Weiping ,YANG Mingliang ,JIANG Dongming (College of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,China ) Abstract :Aiming at the starting judder problem of manual vehicles,an equivalent vehicle dynamic model including powertrain,suspension system and body is established by using Simulink.In this model,the friction characteristics of the clutch and the nonlinear characteristics of the multi-stage torsion are both considered.The dynamic response of the vehicle in the starting process is simulated,and the longitudinal vibration acceleration of the vehicle body is analyzed in time domain and frequency domain.The rationality of the model is verified by different vehicle tests.Meanwhile,with the amplitude and the standard deviation of longitudinal vibration acceleration as the judgment bases,the results show that the error between the simulation results and the experimental results is within 8%.In addition,the error causes between the model simulation and the real car test are also analyzed.This study lays a foundation for further research on starting judder of vehicls Keywords :vibration and wave;judder;equivalent vehicle model;Simulink;simulation modeling 手动挡乘用车在起步过程中，车身有时会产生前后方向的抖动，称之为汽车起步抖动问题，这是一种低频抖动现象，频率大约为5Hz ～18Hz 。离合器摩擦盘间激烈地自激振动及其与动力传动系在扭矩传递突变时产生的扭振综合作用是起步抖动产生的主因[1-2]。起步抖动问题严重地降低了车辆的舒适性，同时加速了传动系统部件的疲劳失效。 现已见诸报端的针对汽车起步抖动问题的文献 收稿日期：2017-12-16基金项目：国家自然科学基金资助项目（51775451）； 中央高校基本科研业务费理工类科技创新资助项目（2682016CX032） 作者简介：朱鹏（1993-），男，成都市人，硕士研究生，主要研 究方向为汽车噪声与振动。 通信作者：丁渭平，男，陕西省咸阳市人，工学博士，教授。 E-mail:dwp@https://www.doczj.com/doc/d713277423.html, 大多集中在离合器接合过程中的动力学研究，以及基于实车试验的起步抖动主观感受研究。上官文斌等人[3]建立了离合器接合过程中的传动系动力学特性分析模型，说明离合器从动盘扭转刚度对于起步抖动的影响。陈权瑞[4-5]同时考虑离合器摩擦特性及多级扭转非线性特性建立了离合器接合过程的传动系统动力学模型，研究了离合器设计参数对汽车起步抖动的影响。袁智军等人[6]认为离合器摩擦片的摩擦因数突变会导致所传递的摩擦力矩不稳定，从而引发起步抖动。文献[7]从离合器摩擦片材料、压盘结构等全面分析了离合器部件本身对于起步抖动的相互映射关系。陈玉华、孙涛[8-9]等人通过大量实车试验结合主观评价总结出了一套起步抖动评价方法，但他们的研究仅仅局限于离合器部件本身，对于整车起步抖动的评价效果欠佳。另外，实车试验结合主观评价所涉及的试验车辆较多，试验较为费时 万方数据
L1与C1组成的低通滤波器将200-54的分频点选在1.5kHz，这里将它的分频点恰当进步，主要是单元特性好，更重要是音频的功率八成都会集在中低频，恰当进步低频单元的截止频率，能够充分发扬单元专长，给出的声响将愈加丰满有力度。若是分频点过低，不光丧失了单元优势，反而还会加剧中频单元的担负，导致振幅过载、失真增大等弊端。 尽管中频单元的有用频响宽达800Hz～10kHz，L2、L3与C2、C 3组成的带通滤波器仅取其 1.5～6kHz的一段频带，这也是它的黄金频段。L4、C4构成的高通滤波器将YDQG5-14的分频点定为6kHz，本单元的下限截止频率也获得较高，将愈加轻松自如地在高频段发扬它的专长。因为合理的挑选分频点，3个单元各自都作业在声功率最高的频带，故体系的归纳灵敏度也要比各单元的均匀特性灵敏度高出1～2dB。 分频器元件少，电路也很简单，关于分频电容器最起码的要求是高频特性好，耗费及容量差错小。当前的聚丙烯CBB无极性电容器的耗费角正切值仅为0.08％～0.1％，高频功能优良，体积小、无感、价廉，完全能担任Hi-Fi体系分频电路的需求。本音箱选用耐压为63V的CBB21、CBB22电容器，9.4 uF的用2只4.7 uF的并联即可。高耐压电容在分频器上无大含义，价钱却成倍上升。不要盲目崇拜那些进口货洋电容，这类电容并不一定能显着改进音质，价钱却高得惊人，有时1只10 uF的电容往往超越一只中低频扬声器单元的价格。 分频线圈L的内阻R0巨细直接关系到传输功率与音质，在胆机中分频器与输出变压器二次侧线圈、扬声器音圈及传输馈线呈串联回
(一)、分频器作用和特点 1、基本分频任务：由于现在音箱的种类很多，系统中要采用什么功病能的、几分频的电子分频器还是要灵活配置的，现在通常用的电子频器有2分频、3分频、4分频等区分，超过4分频就显得太复杂和无实际意义了。当然现在的电声技术日新月异，目前还有一些分频器在分频的同时还可以对音频信号进行一些其它方面的处理，但不管什么类型电子分频器的主要功能和任务当然还是分频 2、保护音箱设备：我们知道不同扬声器的工作频率是不一样的，一般来说口径越大的扬声器其低频特性也越好，频率下潜也越低。就好像在相同情况下，18寸扬声器的低音效果一般会比15寸扬声器的低音效果好些；相反中音部分就要采用较小口径的扬声器了，因为通常情况下现在的纸盆振动式扬声器口径越小发出的声音频率也就越高；以此类推高音部分的振动膜片也应该很小才能发出很高频率的声音来。既然扬声器这么复杂，种类又如此繁多，那么如何保障它们能够安全有效的工作就显得很重要了。电子分频器可以提供不同扬声器各自需要的最佳工作频率,让各种扬声器更合理、更安全的工作。设想一下：假如系统中中高音音箱没有经过电子分频器分频，而是直接使用了全频段的音频信号，那么这些中高音音箱在低频信号的冲击下就会很容易损坏，因此，电子分频器除了分频任务外，正常的使用它更重要的功能还有：保护音箱设备。 3、增加声音的层次感：假如一个音响系统中有很多只不同种类的音箱，的确没有使用电子分频器，不同种类的音箱都使用未经分频的全频信号，那不同音箱之间就会有很多频率叠加、重复的部分，声干涉也会变得很严重，声音就会变得模糊不清，声场也会很差而且话筒还会容易产生声反馈。如果使用了电子分频器进行了合理的分频，让不同音箱处在最佳工作状态下，这样不同音箱之间发出的声音频率范围几乎不会重复了，这样就减少了声波互相干涉的现象，声音就会变得格外清晰，音色也会更好、更具有层次感了！ (二)、缺点和不足 1、太多分频选择会导致思想混乱：俗话说有利就有弊，和其它专业音响的周边设备一样，电子分频器也不是十全十美的，有些时候系统中需要分频的音箱多了就会显得很复杂，因为不同的音箱就需要有不同的分频点、不同的工作频率段，对于水平一般的音响师来说，在这样的情况下使用电子分频器分频时会让他们觉得无从下手。因此细心仔细的调整是很重要的，同时我们还可以尽量少用4分频，采用2分频或3分频的方法，这样可以简单些，也会让我们的调整思路变得更加清晰些。 2、使用电子分频器后会导致声效下降：虽然使用电子分频器的优点很多，但由于它硬性的规定了不同音箱的工作频率范围，因此也使得这些音箱的效能受到了限制，没有完全发挥出来，浪费了很大一部分资源。例如：一只双15寸的全频音箱不经过电子分频器时可以发出很正常、较大的声音来，但如果经过了电子分频器分频后在200Hz以上频率工作的话，那这只音箱的丰满度和震撼力就会全没有了，因为此时音箱的低音给电子分频器切掉了。同样情况下我们利用电子分频器也切掉了大部分低音音箱的高音部分，虽然这样音色可能会好听了，但不可否认的是低音音箱也浪费掉了大量的能量。这对于音箱数量较多又注重音色的音响系统来说还无所谓，但如果一套音响系统中音箱数量不多又不注重音色只是要大声些，那此时还是不使用电子分频器现实一些。
摘要： 相位噪声指标对于当前的射频微波系统、移动通信系统、雷达系统等电子系统影响非常明显，将直接影响系统指标的优劣。该项指标对于系统的研发、设计均具有指导意义。相位噪声指标的测试手段很多，如何能够精准的测量该指标是射频微波领域的一项重要任务。随着当前接收机相位噪声指标越来越高，相应的测试技术和测试手段也有了很大的进步。同时，与相位噪声测试相关的其他测试需求也越来越多，如何准确的进行这些指标的测试也愈发重要。 1、引言 随着电子技术的发展，器件的噪声系数越来越低，放大器的动态范围也越来越大，增益也大有提高，使得电路系统的灵敏度和选择性以及线性度等主要技术指标都得到较好的解决。同时，随着技术的不断提高，对电路系统又提出了更高的要求，这就要求电路系统必须具有较低的相位噪声，在现代技术中，相位噪声已成为限制电路系统的主要因素。低相位噪声对于提高电路系统性能起到重要作用。 相位噪声好坏对通讯系统有很大影响，尤其现代通讯系统中状态很多，频道又很密集，并且不断的变换，所以对相位噪声的要求也愈来愈高。如果本振信号的相位噪声较差，会增加通信中的误码率，影响载频跟踪精度。相位噪声不好，不仅增加误码率、影响载频跟踪精度，还影响通信接收机信道内、外性能测量，相位噪声对邻近频道选择性有影响。如果要求接收机选择性越高，则相位噪声就必须更好，要求接收机灵敏度越高，相位噪声也必须更好。 总之，对于现代通信的各种接收机，相位噪声指标尤为重要，对于该指标的精准测试要求也越来越高，相应的技术手段要求也越来越高。 2、相位噪声基础 2.1、什么是相位噪声 相位噪声是振荡器在短时间内频率稳定度的度量参数。它来源于振荡器输出信号由噪声引起的相位、频率的变化。频率稳定度分为两个方面：长期稳定度和短期稳定度，其中，短期稳定度在时域内用艾伦方差来表示，在频域内用相位噪声来表示。 2.2、相位噪声的定义 以载波的幅度为参考，在偏移一定的频率下的单边带相对噪声功率。这个数值是指在1Hz的带宽下的相对噪声电平，其单位为dBc/Hz。该定义最早是基于频谱仪法测试相位噪声，不区分调幅噪声和调相噪声。 单边带相位噪声L(f)定义为随机相位波动单边带功率谱密度Sφ(f)的一半，其单位为dBc/Hz。其中Sφ(f)为随机相位波动φ(t)的单边带功率谱密度，其物理量纲是rad2/Hz。