# Understanding intrapair skew in automotive cables

As the transmission of high-definition video data continues to increase in modern automobiles, so too do the performance requirements for automotive cables such as high-bandwidth differential shielded twisted-pair (STP) cables. These requirements are especially critical for cables connecting modules such as automotive head units to display modules typically located in the rear seat of a car or as part of the automotive instrument cluster.

This article will focus on a key parameter called intrapair skew, which affects data jitter across 100-Ω STP cables. It will demonstrate how engineers can optimize the performance of high-speed, high-bandwidth differential signaling by understanding and mitigating the effects of intrapair skew.

Most engineers pay close attention to the frequency-domain parameters of differential cables such as attenuation characteristics and return-loss specifications, but not enough attention to time-domain parameters like intrapair skew.

Intrapair skew is an aberration in differential cables, caused by unequal propagation delays on each of the wires that make up the differential pairs. The negative effects of intrapair skew are too often overlooked during the design of a high-speed communication link that uses differential cables. One way to understand the time-domain effect of intrapair skew is to observe how the eye width reduces due to an increase in inter-symbol interference (ISI), a type of data jitter caused by an increase in intrapair skew, as shown in Figure 1.

Figure 1 Eye diagrams measure ISI across differential cables. Sources: Texas Instruments

The effects of skew on mode conversion and electromagnetic compliance (EMC), on the other hand, are not as intuitive and can be surprisingly abstract. To better understand these effects, the author has developed a simple mathematic model using basic trigonometric equations to understand intrapair skew.

As shown in Figure 2, a differential transmitter drives two wires that make up an STP cable on one end; the other end of the cable is connected to a differential receiver.

Figure 2 The diagram shows differential data transmission over an STP cable. Sources: Texas Instruments

In an ideal STP cable, theoretically with zero skew, the time delay for a signal to travel on the positive side will be exactly the same as the time it takes for that signal to travel on the negative side. However, in an actual STP cable, the positive side will never match the negative side perfectly due to variations in manufacturing tolerances of the cable. The length of the positive side of the conductor would be different from the negative side, resulting in intrapair skew.

In Figure 1, the increase in intrapair skew progressively reduces the width of the eye diagram. In the limiting case, if the intrapair skew equals the time period of the differential data, then the received differential signal that the receiver sees would be zero.

A mathematical model helps reveal the effect of intrapair skew on both signal quality and electromagnetic compatibility for systems using differential signaling. The following analysis assumes transmission of a single-tone sine wave. First, it derives the equations for an ideal case without any intrapair skew, followed by a case with a finite amount of skew.

How to determine intrapair skew (ideal):

• Data_plus = Asin (ωt)
• Data_minus = –Asin (ωt ) = Asin (ωt + π), where π is radians (180 degrees out of phase)
• Data_minus is the differential version of Data_plus and is basically same as Data_plus, but 180 degrees out of phase

Equation 1 expresses the differential voltage for ideal case (skew = 0):

VCM_ideal = (Data_plus + Data_minus)/2 = ((Asin (ωt) + Asin (ωt + π ))/2 = 0;

VDiff_ideal = (Data_plus – Data_minus) = Asin (ωt ) – Asin (ωt + π )

= 2Asin (ωt )                     (1)     [Equation 1]

Where there is no skew, the common mode voltage VCM_ideal = 0

How to determine intrapair skew (non-ideal):

• When there is an intrapair skew of φ radians, φ = x/T (where T is time period [seconds] and x is skew in seconds)

Equation 4 expresses the non-ideal case:

Data_plus_sk = Asin (ωt );

Data_minus_sk = Asin (ωt + π +φ) (or –Asin (ωt + φ));

Equation 2 expresses the common voltage VCM_skew for the non-ideal case of finite skew.

VCM_skew = (Data_plus_sk + Data_minus_sk)/2;

= [Asin (ωt ) – Asin (ωt + φ)]/2                  (2)     [Equation 2]

Equation 3 calculates differential skew for the non-ideal case, while Equation 4 expresses the differential voltage with skew as a function of common mode voltage and ideal differential voltage.

VDiff_skew = (Data_plus_sk – Data_minus_sk);

= Asin (ωt ) + Asin (ωt + φ)                         (3)    [Equation 3]

Adding and subtracting Asin (ωt) to Equation 3 results in Equation 4.

= 2Asin (ωt) – (Asin (ωt) – Asin (ωt + φ)) (from Equations 1 and 2)

= VDiff_ideal – 2 x CM_skew                      (4)    [Equation 4]

Differential voltage in the presence of intrapair skew is the difference between the differential voltage with no skew and the common-mode voltage in the presence of skew.

Also, looking at Equation 3, if φ = π (or 180 degrees), then the differential voltage = 0.

This means, for a signal of period T, if the total skew between the positive side and negative side is T, the differential voltage will be 0.

Equation 4 shows that a differential signal, in the presence of intrapair skew, will break down into a sum of the perfect no-skew differential signal and the common-mode signal. Any skew in an STP cable will directly translate into common-mode noise (based on Equation 4). Any common-mode signal, depending on the shielding effectiveness of the enclosure of the cable harness, will radiate into the air as electromagnetic emissions and will adversely affect EMC.

From the receiver’s perspective, it is indeed possible to de-skew the signal, and Equation 4 shows how to do that. So, if intrapair skew can create common-mode signals, then it is also possible to de-skew a signal by removing the common-mode signals. This would need a physical component that effectively attenuates common-mode signals while passing differential signals.

Figure 3 shows such a component that attenuates common-mode signals, and hence reduces intrapair skew while passing differential signals. This component is called common-mode choke because it attenuates or ‘chokes’ the common-mode component of the signal. Since these common-mode chokes need to work at very high frequencies, usually these tend to be passive electrical filters that block common-mode signals while passing differential signals unimpeded, as shown in Figure 3. Common-mode chokes are available in very small physical sizes—as small as an 0805 or even an 0603-resistor designed for PCB mounting.

Figure 3 A common-mode choke in a high-speed serial link that uses a twisted-pair differential cable. Sources: Texas Instruments

Figure 4 shows the effectiveness of common-mode chokes in mitigating intrapair skew.

Figure 4 The diagram shows skew improvement achieved by using a common-mode choke. Sources: Texas Instruments

To summarize, it’s possible to successfully transmit and receive high-resolution digital video using an STP cable in a vehicle, provided that the wires in the cable are well balanced with minimal intrapair skew. Intrapair skew can have two major effects on high-speed data communication, manifesting as:

• Jitter (as shown in Figure 2, on the effect of skew on the eye diagram seen at the receiver input)
• Common-mode noise, adversely affecting EMC (as shown by Equation 4)

Engineers can use the concepts and mathematical models in this article to understand and analyze the intricacies of the successful use of STP cables to transfer high-resolution video data in vehicles, especially as video resolutions in vehicles incorporate resolutions of up to 8K.

This is Signal Chain Basics blog # 165 written for Planet Analog.

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## 1 comment on “Understanding intrapair skew in automotive cables”

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October 3, 2021

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