What is Skew?

If someone responded quickly, they might say that skew is the difference in delay (arrival time at a destination) between two signals. However, let’s consider this more closely. Imagine there are two traces with the same propagation delay and length, but one of the traces encounters a discontinuity that slightly alters its rise time. In this scenario, the two signals might transition at slightly different times, not just because of the discontinuity itself, but also because the timing difference now depends on the selected threshold, as illustrated in Figure 1. In this context, this requires a deeper consideration of skew: what it is, how it is measured, its significance depending on the context, and ultimately, which definition to adopt.

Figure 1. Traditional time domain skew definition.

Taking a step back, it is important to note that skew plays a crucial role in the loss/timing budget for the following reasons:

• In serial channels, skew can degrade the signal and manifest in the frequency domain as increased insertion loss and even dips in insertion loss for large skew values.
• In synchronous channels, it can distort the differential crossing and affect setup-hold times.

As frequencies increase, these distortions may become more pronounced. For instance, a 112G PAM4 signal has a fundamental frequency of 28 GHz and a bit time of around 18 ps. A seemingly minor 1.8 ps of skew would represent 10% of the unit interval, considering 224G PAM4 raises concerns that could lead to significant issues.

Before delving into the specifics of different skew measurements, it is helpful to illustrate the importance of skew by creating a channel.

Equivalent Channel

Let’s try this exercise. In Figure 2, if the question is posed of whether the channels are similar, what would the response be? These two channels look very similar.

Figure 2. Equivalent mystery channels.

However, as illustrated in Figure 3, one channel is a differential pair (without coupling) featuring a small stub and no skew, while the other is a differential pair with skew. 

Figure 3. Mystery channels revealed.

Skew can manifest in ways that are easily confused with various other distortions in a skew-less channel. Here is a perspective on it:

• In a single-ended signal, various “bad” elements create distortions such as losses, reflections and dispersion.
• When multiple lines are introduced, as in a differential pair, all the additional distortions that can occur between the signals are added to that list. Skew is simply one of those factors.
• This added “bad stuff” can behave similarly to many other common distortions, as illustrated in the equivalent channel.

The concept of skew is broad, but when discussing very small skew values, it typically refers to the skew between the two legs of a differential pair, known as intra-pair skew. Let’s examine how skew has traditionally been measured, along with its advantages and challenges.

Frequency Domain Definition

When skew is being discussed in general, it is important to note that for coupled transmission lines, such as those in differential pairs, in-pair skew is calculated not only by the “difference in delay” of each individual line, but also by considering the cross-coupling from the adjacent signal. Essentially, the skew definition for single-ended traces without coupling is based solely on the difference in phase delay for each leg in isolation. However, in a differential pair, there is likely some degree of coupling, which complicates the skew definition.

In coupled structures, skew is defined as the difference in odd mode delay for each line, as illustrated by the equation in Figure 4.

Figure 4. Odd skew calculation.

The key takeaway is that once the signal is processed appropriately, the methods for measuring skew are generic; they simply need to be applied to the correct post-processed waveform.

Since it has been established that the methods for measuring skew are generally applicable, it can be assumed that these structures do not experience crosstalk unless stated otherwise. Therefore, when referring to a differential pair (or p-n, or skew-p and skew-n), it denotes two uncoupled traces used in a differential pair.

With that clarification, it can be stated that one traditional and well-defined approach to measuring skew is in the frequency domain (see Figure 5).

Figure 5. Frequency domain single-ended phase delay.

To calculate skew, the phase delay is taken and the difference between them (skew) is computed, as illustrated in Figure 6.

Figure 6. Frequency domain skew definition.

In Figure 6, two different skew responses are shown. In Figure 6a, the skew is created using a single, flat delay across all frequencies; the delay remains constant at every frequency point. In Figure 6b, the same delay is generated by adding extra length to one leg of the differential pair. In this case, the difference in length results in a frequency-dependent delay due to the dielectric constant varying with frequency; therefore, the delay also becomes frequency-dependent. This latter case results in higher skew-threshold sensitivities compared to the former flat-frequency response.

Frequency-dependent skew can arise from differences in transmission line lengths, such as bends or when the two members of a differential pair run over different dielectrics, which often occurs with reinforced fiber weave fabrics. When the delta length in the transmission line has a frequency-dependent dielectric constant (resulting in frequency-varying delay), the skew also becomes frequency-dependent, as shown in Figure 6b.

Regarding the advantages and disadvantages of this process, they can be summarized as follows:

• Unambiguous Definition: Each frequency arriving at the endpoint can be observed with a different delay.

• Usage Concerns: How can this information be effectively applied?
• Complexity for Practical Use: For example, is the skew at 100 MHz more significant than at 20 GHz?
• Communication Challenges: A single number would be easier to convey for marketing purposes.

Some of the perceived challenges of this methodology can be addressed by performing measurements in the time domain.

Time Domain Definition

Skew is most commonly defined in the time domain by selecting a threshold and measuring the delay difference at that threshold, as illustrated in Figure 1. As previously mentioned, the primary drawback of this method is that the skew can vary based on the chosen threshold. This issue becomes more pronounced when the signals are not identical. For example, one line may experience slight discontinuities, the driver might be somewhat asymmetric, or the two lines in the differential pair may not be driven with the same rise time. Additionally, significant coupling between the lines can affect their shapes, as seen in Figure 1, where one line tends to influence the other.

To examine how skew variability is affected by the threshold, Figure 7 shows a substantial difference in skew as the threshold changes. This variability raises the question: What is the true skew in this topology?

Figure 7. Time domain skew variation due to threshold.

Should the skew be defined using the 50% point of these waveforms?

Alternatively, should the 10% point be selected to focus on capturing the true delay while minimizing the impact of variations in edge shape?

It is important to note that, as shown in Figure 7, the two signals appear quite similar in shape. In this case, the skew arises from two different-length single-ended transmission lines. With coupling, the signals influence each other, leading to differences in the shape of the positive and negative sides, which further complicates the threshold skew discrepancy.

If one were to categorize the advantages and disadvantages of this approach, they might say:

• Simple, yielding a single number.

• Ambiguous; the skew is dependent on the threshold, meaning any desired skew value can be provided based on the chosen threshold.

Both the time and frequency domain definitions of skew have their advantages and disadvantages, leading to a desire for a more clearly defined and easily measurable way to define skew. This prompts consideration of what is important for the receiver. To maximize what the receiver sees, an alternative approach known as the pulse correlation method will be introduced.

Pulse Correlation Skew Method

To illustrate this method, consider a simple example shown in Figure 8.

Figure 8. Skew seen at the receiver.

Imagine there are two drivers that exhibit slightly different rise times (3 and 5). Additionally, there is a noticeable delay difference in the traces, which are assumed to be single-ended for simplicity (without coupling between them); one has a delay of 11, while the other has a delay of 13 (resulting in a -2 difference).

It is important to note that delays are unitless; it does not matter whether they are measured in seconds, femtoseconds, or any other unit. For this example, the absolute values are not crucial, but it is essential that all delays are expressed in the same unit—whatever that may be—and that the relative differences between them are understood. 

When observing the signal at the receiver, it becomes apparent that the differential signal appears distorted based on the phase delay delta of the transmission line and the differences in signal shape (represented here by the varying rise times, but it could relate to other factors as well). The unusual shape observed at the receiver can be readily explained by examining the two waveforms at the input of the differential receiver.

The question now being asked is: How much should one pulse signal be delayed relative to the another to maximize signal energy at the receiver?

One effective method for determining the optimal alignment between two pulses is to perform signal correlation and select the delay value at which the correlation is maximized. This correlation indicates the delay necessary to align one waveform with the other to achieve the highest energy at the receiver.

For instance, in Figure 8, with a bottom trace delay of 13, if skew is defined as the delay difference, one might conclude that a delay of -2 on the bottom trace (adjusting it to 11, equal to the top trace) would yield the best outcome. However, as demonstrated in Figure 9, this assumption is flawed because the analysis did not account for the rise time difference; the asymmetry in the differential signal (DIFF) illustrates this point.

Figure 9. Correlation: non-maximum energy.

To achieve optimal energy alignment, the skew actually requires an additional -1. This means that for this receiver, the ideal scenario would involve a delay of 12 for the bottom trace, rather than the 11 shown in Figure 10. Consequently, in this case, the correlation skew in the right figure is 0, and the differential signal perceived by the receiver exhibits significantly better symmetry.

Figure 10. Correlation: maximum energy.

By comparing the DIFF traces in Figures 9 and 10, it becomes evident that the symmetry of the skew-correlated waveform in Figure 10 is improved compared to that in Figure 9. This enhanced symmetry contributes to a more optimal eye opening at the receiver. Therefore, it is logical to measure skew in relation to this ideal symmetry.

This method also offers features that the traditional time domain edge skew method lacks. Notably, it is not dependent on a threshold (since no threshold is defined), but it is important to recognize that it has its drawbacks. Here is a summary of the pros and the cons of this method:

• Threshold-independent; produces a single value
• Provides a straightforward and valuable metric due to its singular nature
• Represents the optimal intra-pair skew needed for the receiver to maximize energy
• Accounts for differences in trace shape.

• Pulse width dependent; though it exhibits less variation compared to the edge threshold method, some dependency still exists
• The computation algorithm is somewhat more complex, and there are concerns about integrating deterministic distortion (such as reflections and ringing) on the pulse, particularly in reflective topologies.

Time Measurement Example

It would be valuable to evaluate the performance of both algorithms (the edge method and the correlation method) through real measurements using a time domain instrument. Conducting multiple measurements on a device under test could yield insights into the potential advantages and disadvantages of each approach.

Figure 11 illustrates the skew measurement for a coupled uniform differential pair using both the edge method and the correlation method.

Figure 11. Time domain skew measurements. (Source: Samtec Corporation.)

The measurement process is outlined as follows:

• Edge Method: A step signal is sent as a time domain reflectometry (TDR) signal. A threshold is set at the 50% point of the reflected waveform on each leg of the pair. The measured delay is divided by two (given that TDR readings represent double the actual physical delay), and skew is calculated by subtracting the delay between the two lines of the pair.
• Correlation Method: A step signal is also sent as a TDR. The incident and reflected impulse responses are generated by differentiating the step. A pulse response is then created by convolving these impulses with a 500 ps pulse. The two reflected pulses from each leg of the differential trace are correlated, and the resulting delay from the correlation is divided by two to obtain the skew.

By repeating these measurements 800 times, clear differences in sensitivity between the two methods can be observed, both in the track and in the histogram. Notably, the correlation method yields a more stable track and standard deviation for the skew measurement. Furthermore, the variation of skew due to pulse width appears to be significantly smaller with the correlation method compared to the edge threshold method; this aspect is outside the scope of this article.

Conclusion

In summary, as demonstrated in the equivalent channel example, intra-pair skew is a crucial metric when working with multiple lines. Its behavior, measurements, and interpretations are closely linked to other forms of signal degradation, making the definition of a single skew value a nuanced issue that requires careful consideration.

This work has introduced three distinct methods for measuring skew:

• Phase Delay vs. Frequency
• Time Domain Edge Threshold
• Time Domain Pulse Correlation     

Each method presents its own advantages and disadvantages. It is important to recognize that when measuring very small skew values, noise and other factors can easily affect the results. Generally, edge methods are convenient and applicable in many situations, but they may provide lower resolution and sensitivity compared to correlation methods. If understanding delay differences at specific frequency ranges is a priority, the frequency method may be more suitable. Ultimately, the choice of measurement technique should be guided by the context and the specific goals of the skew measurement.