Is Absolute Phase Matching Relative?

Posted by Ben Biron on Wed, Dec 18, 2013 @ 03:00 PM

The process of phase matching, and the parameters that affect and control it can be a bit tough to get a handle on and so I thought it may help folks to present a brief explanation of the concept and to highlight some of the key elements of the specsmanship involved.

There are several types of phase matching requirements and associated tolerances, with the following being the most common.

  • Relative Phase: Phase matched in sets - All of the cable assemblies are matched to each other.(Relative)
  • Absolute Phase: Phase matched to an electrical length - As with a mechanical standard, this electrical length in degrees or time is determined by the customer or provided after the fact by kSARIA.(Absolute)
  • Phase matched in pairs or sets: Selected from large groups of phase matched assemblies.
  • Phase matched to a standard: All of the cables are matched to a standard. This standard may have been established from a previous lot or provided by the customer.
  • Phased offset matching: One or more cables are provided with a defined phase offset compared to each of the other cable assemblies.

It seems intuitive that in all cases, the physical length of the coaxial cable is trimmed as needed to achieve the desired result. Cut them all the same length and they will all match in electrical length, right?  Not really….

Velocity of Propagation

The velocity of propagation (Vp) through a coaxial cable is defined as the speed at which the RF signal travels within the cable relative to the speed of the same signal traveling in a vacuum (i.e. speed of light). For many applications where the coaxial cable is being used to simply feed a signal from one point to another, Vp will not be terribly important.

For applications where the phase of the signal is important, the velocity factor is indeed critical. In some applications, coaxial cables are cut to a specific electrical length to act as an impedance transformer or a resonant circuit.  In this case, the effect of the cable’s Vp on the electrical length needs to be taken into consideration in order to determine the actual physical length of coax cable.

The Vp of a cable is quoted as a figure which is less than "1" and is defined essentially by the dielectric material between the two conductors. Cables using a solid dielectric will have a low Vp, typically in the order of around 0.66, and those using foam (e.g. low loss cable) will have Vp figures ranging from about 0.80 to 0.88.  The Vp for the foam dielectric cable is closer to 1 (air) because of the air content in the foam. 

The velocity factor (Vp) of the cable is defined as the reciprocal of the square root of the dielectric constant:

velocity factor

For phase matched cables, the Vp is a critical parameter as it, along with physical length, establishes the electrical phase at the output of the cable relative to the phase at the input of the cable. Lower Vp results in shorter wavelengths. Cables with identical physical length but varying Vp factors will have significantly different electrical phase length. It is critical therefore to carefully control the Vp when fabricating phase matched cable assemblies. This is normally achieved through lot control and/or by selecting cable stock from the same manufacturing run.

In general, higher Vp cable would be used for phase matched cables because the wavelength of the signal would be at its maximum length, resulting in the highest value of inches per degree. The advantage of using a low Vp cable is that the length of cable required for the resonant length is shorter than if it had a high Vp. This can save on cost and weight, and can also be significantly more convenient to use and house.

Dielectric Materials

There is a variety of materials that are being used as dielectrics in coax cables. Each has its own dielectric constant, and as a result, coax cables that use different dielectric materials will exhibit different velocity of propagation factors.

 dielectric constants and velocity factors coax cables

Effects of Variation in Velocity of Propagation

For long assemblies, adjustment of the physical length is required to achieve desired phase match. Variations in Velocity of Propagation (Vp) can result in a significant physical length variation to achieve a specific electrical length. Typical Customer Drawings specify the electrical phase match and the mechanical length with a tolerance of plus something and minus nothing. When specifying phase length, it is strongly recommended that the cable designer allow some additional physical length tolerance. This additional physical length will serve as the controlling variable to achieve the desired electrical length (phase match). For very long cables, that additional physical length should be at least 5% of the total length.

To demonstrate this effect, let’s consider as an example a set of 4 matched 371 inch long cable assemblies for use up to 18 GHz. The nominal Vp of the cable is 82%, but due to manufacturing or material variations, the Vp can range from 81.0% to 83.0%.

Table 3 below shows the change in physical length required, based on changes in the Vp of the cable, to get equally matched cables.

Variation in Velcoity of Propagation 

At kSARIA, we measure phase length using a Anritsu 4640A Vector Network Analyzer (VNA) in Time Domain mode to first verify the Vp of the cable and then to trim each cable to match a given electrical length. Bearing in mind that at 18GHz, 1 degree of phase is about 0.0015” long, in order to achieve the desired phase matching window, it is critical that the assembly process (cut and trim) can be controlled to that level of accuracy.

Coupled with the use of state of the art precision tools and equipment, kSARIA’s design and process engineering team along with skilled cable assembly technicians can produce phase matched cables to exacting specifications.

So, is absolute phase matching relative?  It sure is.  It’s important to first understand what type of phase matching is needed.  Will all cables be matched to each other, or relative to a standard, or do they need to be matched to a specific electrical length in terms of degrees or in terms of delay time. It’s worth noting that if matched as a “SET”, that is, each cable is matched to all other cables in the set, and one cable is damaged the entire set would need to be replaced. This can be quite costly and time consuming.

If a set can be matched to a specific electrical or delay length and one cable gets damaged, a single replacement cable can be made.  For long cables, say beyond 10 Meters, it is important to specify (allow) additional length to facilitate trim efforts due to variations in the cables Velocity of Propagation.  Beyond phase matching, another characteristic that can be challenging is phase tracking. We’ll discuss that next time…

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Tags: Absolute Phase Matching, Coaxial Cables, Velocity of Propagation, Phase Tracking