I recently revised the materials used to build our silver USB cables in order to achieve even closer to optimal 90 ohm characteristic impedance.
Working with our metallurgist / wire manufacturer to create a 99.999% pure Ag mono crystal wire with extruded ETFE (Ethylene Tetrafluoroethylene) jacket having dielectric constant (εᵣ) of 2.5.
wire dimension with D = 1.10mm and d = 0.8mm
The radius of the trace (r) is calculated (D - d) / 2 = (1.10mm - 0.8mm) / 2 = 0.15mm.
The width of the trace (w) being twice the radius (w = 2r = 0.3mm).
L = (μ₀μᵣ/2π)ln(4h/w)
C = (2πε₀εᵣ/ln(4h/w))
Assuming a trace height (h) of 0.1mm:
L = (4π x 10^-7 x 2.5/2π)ln(4 x 0.0001/0.0003) = 1.78 x 10^-7 H/m
C = (2π x 8.854 x 10^-12 x 2.5/ln(4 x 0.0001/0.0003)) = 7.07 x 10^-11 F/m
The characteristic impedance Z is calculated as:
Z = sqrt(L/C) = sqrt(1.78 x 10^-7/7.07 x 10^-11) = 94.9 ohms
The wire is machine twisted with very high accuracy of pitch length.
The end result is a perfect bulk reel of twisted pair for use in our USB cables Impedance measuring 94.9 ohms well within +/- 15% engineering tolarence for USB 2.0 standards.
We will then add several layers of shielding, drain wires and dampening materials that are both piezoelectricity and mechanically tuned to react to and eliminate specific harmful resonant frequencies, as well as ensuring high frequency EMI noise created within the cable and external to cable is both drained to ground and dissipated to harmless heat energy.
Both power, signal ground physically seperated and electrically coupled from signal wiring to prevent interference.
Subjective listening comments: Sonically I cannot hear the difference between a similar cable thats out of spec by < / > 20-25 ohms +/- 15% of 90 ohm tolarence, I'm assuming associated reflections (jitter) are asynchronously midigated by the DAC. We had an aliexpress USB with silver signal wiring, with 4.9 star rating over 50 people rating it, it measured 170 ohms impedance... , It was a little exciting and sparkly within the first 5 minutes but quickly became fatiguing, a critical listening session and a/b reviled significant performance issues in imaging, linearity, timing and tone with a fatiguing harshness and to certain frequencies m that become quite bothersome once identified.
We will be running some tests with an APx555B Series Audio Analyzer to see exactly what's happening in the following few weeks, stay tuned for updates !