Abstract

This article demonstrates that intra-pair skew cannot be properly defined on a screened single pair (shielded pair of wires), as the signal launched in a single wire does not propagate as such along the pair due to inter-wire coupling.

This coupling and propagation behavior is illustrated using an analogy with the coupled pendulum system. The measurement results can be described using a combination of the common and differential propagation modes. This is confirmed by TDR results of signal propagation.

Introduction

"In-pair skew" is defined as the difference of the propagation time between the signal traveling in one wire and the other wire of a pair (see IEC 62783-1-1:2022). This time difference is expected to affect the differential signal and hence perturb the integrity of the communication.

However, literature is not clear about this topic and different publications highlight the difficulty in interpreting the measurement results.³

Ports Definition for Single Pair

Measurements performed for this study are done using a four-port network analyzer. The cable is connected according to the scheme of Figure 1. As usually defined, “a” and “b” are the incoming and reflected waves, respectively

Figure 1. Connection scheme with port numbering.

• S_mn represents the response at port “m” of a signal send on port “n”

Hence:

• S₂₁ represents the response at the far end of the first wire of a signal sent from its near end
• S₄₃ represents the response at the far end of the second wire of a signal sent from its near end

As per IEC 62783-1-1:2022, Intra-pair skew is defined as propagation time (phase) difference between S₂₁ and S₄₃.

Single Wire Measurements on Pair

As S₂₁ represents the signal propagation in one wire of the pair, it is expected to be a smoothly decreasing curve. However, measurement does not show the expected behavior (see Figure 2). Measured S₂₁ is a “bumped” curve with dips falling to zero (or close to) at regular frequency intervals.

Figure 2. Measured S₂₁ on a single pair (red curve) and its expected behavior (blue dotted line).

Owing to the noise disturbance, phase computation at frequencies where the amplitude is close to zero is difficult. Moreover, closely looking at the dips where the signal amplitude falls close to zero (see Figure 3), the phase curve shows jumps of π. 

Figure 3. Phase of S₂₁ around a point where the module of S₂₁ is close to zero. One can see a phase distortion and a jump of π in the absolute value of the phase.

These jumps lead to a non-linear curve when unwrapping the phase (see Figure 4). This observation is not compatible with the common understanding of single wire signal propagation.

Figure 4. The phase distortion of Figure 2 shown in the unwrapped phase representation. A phase jump of π is clearly visible. 

Figure 5. Measured S₄₁ on a single pair. 

Note that S₄₃ and S₂₃ are similar to S₂₁ and S₄₁ respectively.

Data Interpretation: The Coupled Pendulum

In order to get a tangible picture of coupled modes propagation in a screen pair, a direct analogy with the behavior of a coupled pendulum is used. The model shown in Figure 6 consists of two equivalent pendulums coupled with a spring.

Figure 6. The coupled pendulum model.

In this mechanical example, a stable oscillation corresponds to the situations where both pendulum are excited (oscillate) in phase or 180° out of phase. These modes are called “eigenstates” (see Figure 7).

Figure 7. In phase and 180° out of phase modes.In our screened pair system, this can be related to the common and differential modes of propagation, which represent the eigenstate of the pair excitation. The displacement amplitudes of the pendulum correspond to the voltage amplitude on the wires (see Figure 8).

Figure 8. The common and differential propagation modes in a screened pair and associated electrical field distributions.

When exciting only one pendulum, it is well known and understood that the energy of the system is periodically transferred over time from one pendulum to the other (see Figure 9). Moreover, the system presents a phase shift of π between two successive swings of the same pendulum.

Figure 9. The coupled pendulum when one single pendulum is excited at time T₀. After a while (T₁) all the energy is transferred to the other pendulum.

The periodic movement of the pendulums over time is shown in Figure 10.

Figure 10. Oscillations of both pendulums over time.

(Continued on next page.)