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Cross Coax Cables Design vs Zip Cord

by August 29, 2004

There seems to be a trend lately for DIY self proclaimed audio gurus to design alternative speaker cable designs using Coax cables (namely Belden 89259). While their efforts should be applauded, they should also be cautioned to consider any deleterious effects that may result, while also objectively analyzing their designs against conventional and proven twin feeder ones (ie. 12AWG Zip Cord) to determine if the design characteristics (namely DC Resistance, Inductance, and Capacitance) are at least equal to justify their design efforts. With that in mind, I have analyzed one of the Cross Coax cable designs popularized by Jon Risch (http://www.geocities.com/jonrisch/index2.htm) and compared it to ordinary 12AWG Zip Cord.

Zip Cord Analytical Analysis

Equation for External Inductance

L = 0.281*Log(B/A) (uH/ft) Eq(1)

where B is the space between two conductors and A is the Radius of each conductor.

This equation is valid for the total loop inductance (both conductors) of a parallel wire transmission line. It represents the EXTERNAL inductance of the conductors. However at audio frequencies, where skin effect is not a major factor, the total inductance becomes (external + internal) where external is listed in the above equation Eq(1) and internal inductance of a straight wire of circular cross section carrying a uniform low frequency current is 1.27*10^-3 uH/in, independent of wire size. (Source, Noise Reduction Techniques in Electrical Systems, 2nd Edition, Henry W. Ott)

Thus skin effect at high frequencies is actually responsible for eliminating internal inductance of the wire and thus we should see inductance drop as Rac becomes the dominant factor of total cable resistance where (Rtot = Rdc + Rac).

Thus to calculate total Inductance at audio frequencies, (Ls) the complete equation is:

Ls = 0.281*Log(B/A) + 2*(12)*1.27*10^-3 uH/ft Eq(2)

Thus for 12AWG Zip Cord it is assumed to be insulated with a dielectric whose relative permittivity value is 1.5. Most practical dielectrics tend to have a higher value, but the effect is diluted since part of the surrounding E-field is in the air. Thus A = .040 and the conductor spacing is about 0.15 inches (center to center). Thus L = .191uH/ft . Monstercable 12AWG Zip is specified at about 0.16uH/ft, which demonstrates they probably did not account for internal inductance in their calculations.

Measurements

Using a Hewlett Packard HP 4275A High Frequency LCR Analyzer, RLC parameters of 12AWG Original Monster Zip Cord were measured.

Note: The 4275A was first properly calibrated within its respected bandwidth (10KHz to 10MHz). The DUT leads were kept as short as possible and kept as close together as possible without electrically shorting. The measurements and calibration process was repeated twice for consistency.

Measured Results:

  • Rdc = 1.5mohms/ft or 3.0mohms/ft (round trip)
  • Ls = .192uH @20kHz (Note: this measurement was done on the HP 4275A)
  • Cp = 18pF ± .02 from 20Hz to 20kHz, decreasing to 14pF up to 200kHz

Measured on: HP LCR 4275A

Frequency

Ls

Rs

10 kHz

0.192 uH/ft

Beyond measurability

20 kHz

0.190uH/ft


40 kHz

0.190 uH/ft


100 kHz

0.187uH/ft


400 kHz

0.185 uH/ft

20.5 mohms/ft

1 MHz

0.180 uH/ft

54.8 mohms/ft

4 MHz

0.162uH /ft

145 mohms/ft

10 MHz

0.120 uH/ft

Infinity




Note: In the future when a low frequency LCR meter becomes available, these measurements will be retaken for more precision within the entire audio band from 20Hz to 20kHz.

As you can see, as skin effect causes Rs to increase, inductance drops. As we approach 4 MHz, Rs becomes significantly large resulting in extreme reduction of internal inductance and thus Ls approaches the value of the external inductance Eq(1).

*Note Rs at DC = Rdc = 3.4 mohms/ft thus as 20kHz, Rs should = 1.34*3.4 = 4.56 mohms/ft.

Any readings on the LCR meter significantly lower than this for frequencies 20kHz or greater are rejected since the LCR meter cannot accurately measure Rs for those frequencies. As we approach 10MHz, Rs becomes so large that it cannot be accurately measured on this LCR meter.

Independent Source for Cable Metrics of 12AWG Monstercable Zip Cord

Here is a link to another cable vendor that compares their "exotic" cables with various other vendors, including Monstercable, and also confirms the metrics that I calculated.

[Manufacturer (Nordost) removed referenced page]

Thus we now have two sources (Analysis, Measurements) that confirm inductance of 12AWG Zip Cord is no greater than 0.191uH/ft @20kHz. In any event, I am not sure where the .25uH/ft estimate that Jon Risch specified came from, but it seems like a bit of a stretch, actually quite a bit, 1.3 times reality! Perhaps this value was measured with non parallel adjacent conductor spacing throught the cable under test, or the accuracy of the measurement was corrupted by improper instrumentation calibration and/or set-up. In any event, test equipment, set-up, cable tolerance, etc can all lead to different measurements. It would not be unreasonable to measure about .20uH/ft for this cable within the audio range as that is within a +-5% tolerance. However the .25uH so called measurement that Jon Risch boasts about is over 30% off. For more RLC data on various Zip Cords, I suggest reviewing our latest Cable Face Off article where we objectively compared several common and "exotic" cables.

For this exercise, we will analyze 12AWG Zip Cord with the calculated value of Ls = .191uH/ft and the extreme .25uH/ft case that Jon Risch claimed (just to be fair to Jon)

Jon specified Cp = 21pF which seems about right. Rdc is about 3.4mohms/ft (round trip) as he suggested as well (1.7mohms X 2), though I have measured DC resistance of 12AWG zip to be slightly lower (1.5mohms x 2), but lets not split hairs here.

Basics of Twin Feeder Cables (Zip Cord)

As spacing (center to center) between parallel wires increases, inductance also increases, but capacitance decreases.

As spacing (center to center) between parallel wires decreases, inductance also decreases, but capacitance increases.

As you go to thicker gauge wire (say 10AWG), the radius increases, thus inductance decreases which is exactly opposite of what Jon Risch implied. At the same time, the thicker gauge wire results in an increased spacing between the conductors, slightly increasing inductance, and thus should somewhat nullify the lower inductance advantage of the heavier gauge wire (assuming the same quality dielectrics are used and spacing is kept proportionally minimal for both cases). Due to this relationship, inductance should not vary appreciably from using lower or thicker gauge wire within a couple of gauges of 12AWG, in fact it should decrease somewhat provided that conductor spacing is minimized. Thus two advantages of lower gauge wire would be to further reduce DCR resistance and minimize insertion loss, and reduce inductance to minimize high frequency roll off, again assuming conductor spacing is kept to a proportionally minimized and comparable dielectrics are used.

Visit our Calculating Cable Inductance article for a more indepth study on cable inductance and the impact skin effect has on it.

Again being conservative, we use the calculated metrics for quality 12AWG Zip Cord for our analysis:

  • Rdc = 1.7mohms/ft or 3.4mohms/ft (round trip)
  • Ls = .191uH/ft
  • Cp = 21pF/ft

Coax Speaker Cable

(Jon Risch Cable Recipe using 89259 Belden Cables)

(see http://www.geocities.com/jonrisch/spkrcbl1.htm)

Belden 89259 Cable Specifications

http://www.bluejeanscable.com/pages/technicaldocs/89259tech.htm

As you can see, Ls = .092uH/ft, Cp = 17.3pF/ft, Rs(shield) = 2.6 ohms/1000ft, Rs(conductor) = 15 ohms/1000ft

Thus Jon Rischs configuration, essentially cross connects shield and center conductors of adjacent coax cables, thus Rs = 2.22 mohms/ft (2.6*15/(2.6+15)) which is 1.3 times greater than ordinary zip cord as Jon claimed. Cp now becomes 17.3pf + 17.3pf = 34.6pf/ft + twisting effects should yield at least 49pF/ft depending on how many twists/ft achieved and uniformity of twists, which is 2.2 times greater than zip cord, however Ls should be about .092uH/ft assuming no twisting or mutual inductance. However as Jon correctly pointed out since the two cables are cross-connected, the amount of mutual inductance coupling is increased over the single coax, primarily where the two braids run next to each other through the thickness of two very thin teflon jackets. It is this which further reduces the total inductance, and not the twisting. Since Jon Risch's cables illustrate twisting, Ls may decrease further somewhat depending on amounts of twists and assuming the twists are tightly packed. Jon Risch claims the inductance of his cable is .067uH/ft, which is not unreasonable. However, be cautioned that failure to provide consistant and uniform twisting and tightly pressing of adjacent cables together may increase inductance due to larger loop area.

Ls for this Cross Coax Cable design is about 2.85 (.16/.067) times lower than Zip Cord, NOT 3.7 times lower as Jon Risch again mistakenly claimed.

Thus the metrics for Jon Rischs Coax Cable construction are:

  • Rdc = 2.22mohm/ft or 4.44mohms/ft (round trip)
  • Ls = .067uH/ft
  • Cp = 49pF/ft

 

About the author:
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Gene manages this organization, establishes relations with manufacturers and keeps Audioholics a well oiled machine. His goal is to educate about home theater and develop more standards in the industry to eliminate consumer confusion clouded by industry snake oil.

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