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Understanding Skew and the Application of Delay-Matched Coaxial Cables

Abstract

There is a plethora of information regarding skew matched data cables such as Ethernet for Signal Integrity (SI) applications. Data cables carrying differential signals over multiple internal wires necessarily have key parameters such as skew―any delay offset between the propagating signals could mean signal distortion and a perceptible loss of quality. There is in contrast, a noticeable lack of information regarding skew-matched coaxial cables and their respective application considerations. This article overviews skew and the applications for skew matched coaxial cables.

Discerning Skew in Coaxial Assemblies

Skew for data cables is typically defined as the difference in propagation delay (time delay) between the differential pair with the least delay and the differential pair with the most delay in a cable assembly. Similarly, there is skew inherent to individual pairs due to differences in conductor length or velocity of propagation around the individual conductors. Velocity of propagation (VOP) is defined as the speed at which a signal propagates through a path. The VOP is often expressed as a percentage of the free space value of the speed of light. While this definition sheds some light on skew-matched high frequency cable counterparts, it does not take into account phase instabilities that can cause minor shifts in skew for coaxial assemblies.

More often than not, time delay is equated to group delay, and while they are roughly related, they are not identical. Group delay is the derivative of phase delay. For some, group delay is much more intuitive to understand as it can be roughly equated to the time it takes for a pulse to arrive at the receiver, or a rough estimation of the transmit time of a signal through a path. Group delay flatness, a measure of the variation in the group delay, is therefore an important measurement in some systems as it makes clear the abrupt changes in delay at the output of the DUT.

Time delay, however, is not the same thing as group delay. Time delay can be more accurately measured with phase delay. This is more clearly illustrated in Figure 1. For a signal propagating as a sine wave with an amplitude envelope applied to it, the group delay would be analogous to the time delay of the amplitude envelope while the phase delay would be the amount of time each frequency component of the signal suffers. A coaxial pair that has a high delay accuracy would not only need the wave patterns to match at the output, but also a matching of each frequency component.

Figure 1 image of phase matching between two coaxial cables

Figure 1: Maintaining a low differential skew between two coaxial assemblies requires phase-matching.
Source: https://www.quora.com/Intuitively-speaking-what-is-a-group-delay-function

Group delay is a helpful measurement to look at for dispersive media such as a waveguide, where several modes can exist at once. It is not particularly helpful for non-dispersive media such as the TEM-mode coaxial cable as it remains pretty consistent across its bandwidth. Phase delay, however, can vary. This can theoretically be understood as it is the integral of group delay with respect to frequency. For a coaxial cable, group delay is not a function of frequency but constant.

While the phase is a linear function of frequency as shown in Equation 1.

Equation 1 image of phase as a linear function of frequency equation

The time delay of the coax cable is therefore directly proportional to a coax’s mechanical length and permittivity of the dielectric as shown in Equation 2.

Equation 2 image of time delay equation for a coax cable assembly

Where τ is the delay time of the cable, L_MECH is the mechanical length of the cable, ε is the relative permittivity of the dielectric material, and c is the velocity of light. From a designer’s perspective, phase stable coaxial cables depend on the evenly matched electrical lengths of their transmission line. Where electrical length can be defined by Equation 3.

Equation 3 image of electrical length equation

This equation takes into account the permittivity of the dielectric material and therefore the effective phase length the signal must travel through the dielectric material. Changes in the electrical length can occur through temperature variations, frequency, mechanical stress (e.g.: flexing, vibrations, etc.), and equality of physical length. Phase stable coaxial cables are typically generating through extensive temperature conditioning or through the use of specialized dielectric. These cables are particularly important in systems utilizing multiple coaxes to fed energy from a common source, or to collect energy from scattered sources. A good example would be in a phased array system where intentional phase shifts cause constructive or destructive signal interference.

Skew, instead, takes into account two or more signal paths, where it can be defined as the difference in time delay (a.k.a: propagation delay) between two or more signal paths. Skew matching a pair of coaxial cables involves phase matching them to control their time delay. It is therefore important for skew matched cables to also be phase stable in order to reliability maintain a low level of skew despite flexure and temperature variations. Typically, the skew between a coax pair is proportional to the Channel-to-Channel delay match and is often measured in picoseconds (ps). The VOP is also a value that is measured in cables and ideally it will be consistent between the two cables, regardless of whether or not the cables have a matching physical length or phase angle.

Skew Matched Coaxial Cable Construction

As stated earlier, delay-matched coaxial cables, by nature, must be phase-matched and are therefore often individually phase stable in order to consistently maintain a delay match on the order of picoseconds despite frequency, temperature, or flexure. Phase changes during flexure cannot entirely be helped due to the changes in the cross-sectional area―the bend radius of the outer regions is larger than that of the inner conductor. These minute inconsistencies inner geometries ultimately causes changes in electrical length which, as shown in the earlier equations, are directly proportional to mechanical length and the dielectric constant. As follows, a phase stable coax would necessarily have both mechanical stability as well as temperature stability. Extreme flexibility in both the shielding and dielectric are needed to maintain mechanical stability despite flexure. Seemingly benign solutions such as a cable restraint could prevent cable flexures from causing inconsistent changes in electrical lengths between each cable and thus, larger than expected delays (See Figure 2).

Figure 2 image of a phase matched coaxial cable assembly

Figure 2: To minimize skew, matched coax cable assemblies should be constructed of the same materials and have the same mechanical orientation in use.

Changes in electrical length will inevitably occur due to the inner and outer conductors’ coefficients of thermal expansion (CTE); a parameter that indicates the growth/shrinkage of a material in various temperatures. The metallic materials used for the inner conductor and shielding will grow and contract with temperature, causing a change in electrical length. This is often offset with dielectric cores such as expanded (microporous) Polytetrafluoroethylene (ePTFE) where the dielectric constant decreases with an increase in temperature. This in effect limits the changes in phase that occur with changing temperatures. It is for these reasons that simply purchasing two off-the-shelf coaxial cables of the same physical length and materials does not necessarily offer high delay match accuracies below 5 ps. Firstly, the materials may or may not be phase stable, secondly, it is paramount that the physical length be close to identical―a 1mm difference between cable lengths with an identical velocity of propagation (VOP) at 74% equates to almost 5 ps difference in propagation delay between the two lines (Refer to Equation 4). Because of this, the electrical delay of coaxial cables is not only a function of the cut of the transmission line, but also related to the precision with which the connectors are attached.

Equation 4 image of equation for propagation delay between the two lines

Why picosecond accuracies over wide bandwidths?

Parallel bus architectures in the past have been sufficient for transferring data at medium throughputs. These topologies, however, become far less economical when attempting to transfer greater gigabit per second data rates. This implies that designers would have to correspondingly increase the clock frequency or add signal lines. Increasing the width of the parallel bus, or adding lines inevitably increases the size of the system with an increase in I/O cells, pins, and their respective interconnections. Increasing the clock frequency quickly does not become feasible as all transmitted data needs to arrive at the receiver simultaneously. This can be accomplished over short distances, otherwise issues such as crosstalk, inductive and capacitive noise coupling, and parallel data skew can become unmanageable. Because of this, high-speed serial buses such as Serializer/Deserializers (SerDes) are often implemented for VLSI/LSI applications. In other words, it is much simpler to synchronize one clock to the transmitted data over synchronizing multiple lines of data.

It has therefore become critically important to synchronize the serial data stream with the clock, this is also known as clock and data recovery (CDR). In other words, the pulse waveform at the output of the differential receiver needs to maintain the high timing resolution of the original pulse signal in alignment with the rising and falling edges of the waveform. As with any real system, there is always some inherent jitter contributed from the transmitter, but it has become increasingly important to discern the jitter that is being contributed from the PCB or link (cable).

Embedded clocks have a clock frequency that is inversely proportional to the unit interval (UI). The UI can be defined as the time duration of a pulse and is measured in picoseconds. Eye diagrams are a useful tool in understanding the jitter of a differential signal as it lays out waveforms from multiple UIs with either the embedded clock or a reconstructed one. As digital logic advances to support increasing switching rates, the UI’s become smaller. For instance, a 12.5 Gbps clock frequency corresponds to a 80 ps UI (or bit length) whereas a 50 Gbps clock frequency corresponds to a 20ps UI. Relevant performance metrics such as jitter could be difficult to discern in a test system with a relatively high differential skew. This is especially true in high data rate applications where the misalignment of rise and fall times generates a much less open eye. Moreover, electromagnetic analysis over wider bandwidths becomes important as necessary equipment such as oscilloscopes need to capture usually up to the 5th harmonic to more accurately reconstruct signals in the time domain. For a data link running at 28 Gbps, analysis is required from DC up to 40-50 GHz. And, as CMOS technology evolves to support faster switching rates, it becomes increasingly important to be able to minimize skew to enable testing over wider bandwidths without additional data-dependent jitter.

In the realm of ethernet, current iterations 40G and beyond ethernet are often without a SerDes function and will likely use parallel, multi-lane architectures. The alignment of the parallel channels is accomplished through the use of a striping function. The receiver physical coding sublayer (PCS) performs skew compensation with alignment markers to reassemble a 40G and beyond aggregate data stream. In theory, any lane can then be used for clock recovery. As shown in Table 1, optical transceivers for 40G, 100G, and 400G technologies contain 4 to 16 lanes with each lane offering 10 to 50 Gbps speeds. A minor offset in synchronicity between each lane can ultimately reduce waveform quality. It is therefore increasingly necessary to measure key parameters such as bit error rate (BER) and jitter with multichannel test equipment and to subsequently obtain transmission media that adds minimal skew.

Table 1 image of optical transceivers form factors, data rates and line rates

Table 1: 40G, 100G, 200G, and 400G optical transceivers

Conclusion

The increased use of differential signal communication has called for reliably delay-matched transmission lines for test with <1 ps skews. When coaxial assemblies are used as the medium, it is important that the cables are very close to the same physical length and constructed of the same materials to ensure a tight skew accuracy. Skew in a test system can limit the reception of the differential signal and add deterministic jitter such as data-dependent jitter― ultimately causing errors in received data.

This article was originally published in Microwave Journal.

Understanding Skew and the Application of Delay-Matched Coaxial Cables

Abstract

Discerning Skew in Coaxial Assemblies

Skew Matched Coaxial Cable Construction

Why picosecond accuracies over wide bandwidths?

Conclusion

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