Cables: Speaker Cable Design, Part 1

In this series, we’ve discussed the basics of audio cable design (Part 1 Part 2 Part 3), RCA and XLR interconnect design, and now we look at speaker cables. These are a very different animal than high input-impedance interconnecting cables. A speaker cable connects to an extremely inconsistent 2 to 32 ohm (or even lower and higher!) reactive load created by the speaker. RCA and XLR interconnect cables see a much more consistent and resistive load, making their electrical measurements far easier to predict. While speaker cable also suffers from the non-linearity of the velocity of propagation in the audio band, it has an additional challenge. It has to be lower in impedance to better match the speaker load, but when the velocity of propagation is going down, this naturally increases the cable’s impedance. How is all this managed? This paper is a walkthrough on how ICONOCLAST speaker cable addresses some of these issues.

Design Brief

1) Conductors

The first decision is how much CMA (circular wire area) you need based on the application. This isn’t always an exact science, as the cable length and speaker type will change the calculated answer. The speaker cable becomes a part of the crossover network in the speaker. The amplifier sees both components as one load, and it’s easy to see why this is a reactive relationship.

Speakers vary by design so their “back EMF” load into amplifiers varies. Amplifiers of differing design react to the back-EMF differently, and the overall performance can be hard to predict. The goal is to “remove” the cable as best we can between the amplifier and speaker. Cables should not be tone controls, but then that’s the goal of every component!

The analysis below looks at the calculations made to settle on the total CMA for benign reactions to the frequency response of a typical set of loudspeaker loads. And yes, these are not real-time resistive loads but as always, an approximation. To avoid speaker frequency-response interactions, the general rule of thumb is that you want the total speaker-cable resistance to be less than 5% of the speaker impedance plus the cable resistance value.

For most practical applications of 0 to 35 feet, 9,600 CMA per polarity should work well to be resistively invisible to the speaker or amplifier. We want the load to be the speaker, not the cable. How we get to the approximate 9,600 CMA per polarity is the hard question. For those that want the
easy way out we have one: 1313A, a basic Belden speaker cable. If we want to design a better measuring cable, let’s see what can be done with Belden technology.

In order to figure out what best to do, I looked at things that indicate what not to do. We all know by now that multiple smaller wires are better than one fat 9,600 CMA solid or stranded wire–to a point! At this stage I’m listening for time-based issues with the audio. You want the signal to be most uniform through the wire for improved current coherence (more identical frequency-arrival times). To make that happen, we decrease the wire size so that the skin-depth penetration goes deeper into the wire, evening out the differences in current magnitude with respect to frequency. This technique better aligns the signal speeds through the wire. I said “better” as there is no perfect way to do this, but we can certainly be better.

The depth is calculated based on frequency and material. The wire size does not change the penetration, it does change the minimum current found in the center of the wire. The smaller the wire, the closer the center current magnitude matches the surface current as signal frequencies go up. Studies were made on various geometries that would hint at what type of conductor to use, and how many. Once we limit ourselves to the ~9,600 CMA resistive box, what are the various design limitations inside this parameter?

Probably the easiest starting point is a cable with multi-sized wires is a flat design. Yep, just keep lining up smaller wires and stop when you reach the proper AWG size. But when tested, there are issues with parallel-wire that lead (pun there?) me away from this simple design.

Above is a Teflon® ribbon cable I used to test polarity symmetry, and capacitive symmetry within each polarity. This data is available if you are interested. It says that the consistency of flat cable is not perfect. The closer each wire gets to the opposite polarity, the higher the capacitance, and more robust the ground reference. For all intents and purposes, each and every wire in this cable acts like a separate wire. Any cable with more than one wire per polarity will have this issue to contend with. How can we do better on capacitance control in each polarity?

For the answer to that we need to turn to inductance. When you separate the two polarities in a flat design, inductance is seemingly well controlled. Each parallel wire has current going in the same direction in each polarity half, so the magnetic fields cancel one another. The closer to the center of the ribbon cable you go, the more the opposite polarity’s different current direction upsets the symmetry of the inductive cancellation. There is non-linearity through the “flat” polarity, too, but it is worse near the edges of each polarity where the “design” changes.

Two wires with the same current direction next to each other cancel some of the fields gauss density between them, and two wires next to each other with opposite polarities reinforce the magnetic field lines. Below are two close proximity wires, with negative going into the page, and positive coming out of the page. Notice that the current direction “adds” between the wires with the magnetic field flux lines in the same direction. If we flip the current direction of one of the wires, the currents cancel but now we have two of the same polarity to get the cancellation effect.

This is the problem with zip-cord. We can get low capacitance, but it is not practical to get the lowest inductance.

To prove the point, a single bonded pair used in ICONOCLAST measured by itself is 12.5 pF/foot and 0.196 uH/foot inductance, about what 1313A reference zip cord is. This isn’t the best reactive variable balance of L and C for a premium current delivery cable. Also, in the tested flat design there are inconsistent ground plane issues that have to be resolved, and there are inconsistent electromagnetic field cancellation properties. The problems are locked-in by the geometry of this cable specimen, same as the issues with zip-cord.

Can we use what is good about a flat cable, and mitigate the bad aspects? The answer to that question lies in a bonded pair used at radio frequencies, and to get to the answer for speaker cable, we need to re-invent what a bonded pair does at audio.

First, what is a bonded pair? It’s simply two co-joined wires—a geometrically consistent zip-cord design with superior adjacent-wire bond technology. The precision C-C of each wire controls impedance at RF to an incredibly small variation. A plain zip cord doesn’t have the symmetry complexity, giving it poor magnetic field cancellation properties. Adding wires to the zip cord to make it a flat cable just adds to the capacitive and inductive “cable in a cable” issue, as every wire follows its own drummer. Coherence is improved with more small wires that add to the same CMA, but we don’t really have a single like-polarity for each signal anymore.

Tests show the inconsistent capacitance in a flat arrangement. Tests can also show the inductance issues with zip cords. A single bonded pair is 0.196 uH/foot inductance. This value is far too high for the state-of-the-art R, L, and C cable that is the intent of the project. How is using another bonded pair zip-cord component going to fix this mess? The answer lies with XLR interconnect cable. We need to build star-quad arrangements of bonded pairs. Visualize the currents using the right hand rule:

Like the XLR design we discussed, two bonded pairs in a quad arrangement show ideal field cancellation. This property of star quads tells us fundamentally we need two polarities using many wires in a star-quad arrangement. The eventual solution was a compromise, as is usually the case in audio cables. The design devised a way to create star quads throughout, a process that varied between near perfect, and slightly imperfect. It was done with 100% consistency within each polarity so every wire measured the same inductance and capacitance to the opposite polarity, and made significantly lowered inductance with only a moderate rise in capacitance. The capacitance was increased on purpose, I might add! More on why I did that later.

The image shows the variation in the star quads between like bonded pairs in a polarity. The question is, Does it work? Capacitance measured 45 pF/foot between polarity wires, and inductance measured 0.08 uH/foot. Capacitance variation, and the electromagnetically tied inductance variation, is superb. The difference in reactive stability between each wire in a single polarity, and between each polarity measures significantly better in ICONOCLAST. Tolerance is +/- 0.5 pF @ 1 KHz or more than five times tighter variation than the 8R28064 flat cable.

To arrive at the 9,600 CMA DCR requirement, the wires were braided on a GHz capable braider. The braider needed a symmetrical arrangement, so an even number of bobbins was chosen (12), giving 24 wires per polarity. 9,600 CMA / 24 = 400CMA per wire, or a 0.020” 24 AWG wire.

Many braid design iterations were trialed before I froze the design around the proper braid relationship to arrive at a suitably balanced reactive cable measurement.

People will “guess” that ICONOCLAST is a bonded pair Ethernet cable, and it is not. The reasons and design are not the same at all. All that is the same is the coincidence of a 24 AWG solid copper wire, common to Ethernet.

Each polarity is braided and flattened–yes, our flat shape! We essentially “fold” the flat cable over on itself into one polarity. Then, opposite polarities are tightly bound to keep loop area to a minimum, critical to inductance as the formula is geometry controlled, and not determined by the material used for the dielectric.

Textile braid bonding of the two polarities

The finished assembly of the bonded polarities

An awful lot of testing was done to identify the weaknesses of various designs. We wanted to avoid:

  • Inconsistent capacitance in each wire
  • Inconsistent inductance in each wire
  • Inconsistent ground plane interaction between wires and polarities
  • Inconsistent wire DCR among all wires
  • Poor polarity DCR values (too high or too low total CMA)
  • Inconsistent dielectric performance between each wire
  • Poor frequency coherence in each wire

After all the testing, a 20-mil wire diameter in a 24-wire (12 bonded pairs) woven polarity was created to match the design to the electromagnetic requirements. The final design that drove the final wire size is 100% symmetrical in every measure on every wire.

Woven single polarities achieve class-leading performance in polarity-to-polarity and wire-to-wire consistency, while also providing exceptionally low reactive variables. The superposition of the magnetic fields drive inductance down from 0.196 uH/foot to 0.08 uH/foot, a 59% reduction in inductance, while holding capacitance to just 45 pF/foot. L and C can be changed based on the woven design, and was optimized for speaker cable applications.

Look for the second part in the next issue!