Cables: Time is of the Essence, Part 2

[In the last issue of Copper, we began a series of articles by Belden engineer Galen Gareis on the science involved in the design of audio cables. We continue here with Galen’s explanation of the varieties of time-based distortions found in audio cables, and will conclude with Part 3 in Copper #50.—Ed.]

4)  Capacitance and inductance with respect to frequency

Capacitance, the ability of the cable to store a charge, is set by the dielectric (the insulation). Some dielectric materials like PVC are not linear, meaning they respond differently at different signal frequencies. More stable dielectric like Teflon offer frequency-linear capacitance. So: the quality of insulator material makes a difference.

Teflon has the lowest dielectric constant of any solid plastic, offers a low capacitance with the thinnest walls of any material, and is durable. It is also expensive to buy and process, but is used in good cables because of its performance, in spite of the cost.

Cheaper dielectrics need a greater wall thickness to achieve the same target capacitance, but a thicker dielectric means a greater space between the two conductors of a cable (the loop area), which increases inductance. This moves us further from the ideal goal of a cable with zero reactance.

5)  Rise-time and decay-time distortions

All cables store and release energy (current or voltage) reactively to the frequency being electromagnetically moved through the wire, adding time-based distortion.

A cable is very reactive to voltage changes at low frequencies. This is because any capacitance absorbs low-frequency AC voltage changes, and starts to look like its carrying a DC signal. As you go up in frequency, the effect drops away, and the cable becomes more “resistive”, with less reactance to voltage change. The cable’s capacitance is very stable in a given design, but the capacitive reactance is frequency-specific. As the frequency goes higher, the reactance decreases.

Another way that cable capacitance causes a problem in RCA and XLR interconnects is with current inrush. Interconnects terminate into a very high impedance, which limits current flow. When you apply a voltage across an interconnect, there’s a momentary inrush of current to “fill” the capacitance of the cable. Cables with lower capacitance mitigate the inrush current issue, but even so, this causes current to “lead” voltage, causing a time shift in the signal.

RCA and XLR interconnect are terminated in the “infinitely” high impedance (47k-ohm or higher). This looks like a pure capacitor to the Input/ Output stage. A capacitor looks like more like short circuit initially, and becomes an “open” as time progresses and the capacitor is charged to a steady state condition. I/O devices have to behave with the initial in-rush current and not current-limit the signal.

In speaker cables, it is changes in current that carry the signal. A speaker cable sees a pretty low resistance load (2-32 ohms) so there is a large current magnitude in low impedance speaker cables. These changes are affected by the inductance of the speaker, which varies depending on frequency. Inductance opposes current flow, so we see that the speaker signal is affected non-linearly by the speaker load. The resistance, or reactance, to current flow increases as frequency increases.

Since voltage leads current in an inductive circuit, we again see a time shift caused by speaker cable—but this time by inductance, instead of capacitance as with an interconnect. Another consideration for speaker cables is that the speaker’s impedance is very non-linear where the spectral current density is highest—namely, at low frequencies. Ideally, we want a speaker cable that is purely resistive, but that’s impossible since a cable is a vector of capacitance and inductance.

6) Skin effect and Rs (proximity effect)

Skin effect is a tendency for AC to flow mainly along the outer surface of a conductor. Skin depth is the point inside a wire where the current decreases to 37% the surface current magnitude. While this depth varies based on material and frequency, it does not vary by wire size. So as we reduce wire size, the current magnitude is larger through a greater proportion of the wire. Keep making the wire smaller, and the current magnitude in the wire’s center gets gradually closer to the surface current, especially at higher frequencies. DC diffusion couples through the entire wire’s cross section.

So why do higher frequencies travel more along the surface? A wire’s impedance (AC resistance) is driven by its self-inductance, or the tendency of changes in current to be impeded by the wire itself. Since these changes occur more frequently with higher frequencies, wires have higher resistance as AC frequency goes up. And so, as frequency increases, the current finds the path of least resistance, which is closer and closer to the surface, where the self-wire inductance is nearest to zero.

The Rs of a cable, also called Proximity Effect, changes WHERE current flows in closely spaced wires. The electromagnetic field “pulls” the current to the inside surface of two parallel wires, and removes the current from the outer reaches away from the two most closely spaced wires. More current amplifies the proximity effect. Larger wires see a very pronounced rise in Rs as frequency goes up. Much of the conductor is “empty” of current. Smaller wires are most “filled” with current as the same aggregate AWG size takes several more smaller wires and this decreases the current in each wire and mitigates proximity effect. Current is divided between each wire, and less current in each wire mitigates the proximity effect. Smaller wires also improve the current linearity through the wire’s cross section as frequency increases, further mitigating proximity effect.

The skin effect and the proximity effect both superimpose themselves, and are best managed with more, smaller wires to make each conductor more efficient.

Once we flatten the velocity change as best as we can with a good dielectric design, we also need to time-align the effects of the dielectric at all frequencies using small wires. Bigger wires will cause even more signal speed change relative to frequency, because the inner electrons are so far from the dielectric material. But even at the same frequencies, a bigger wire can cause time variations—because the high frequency currents nearer the “skin” travel faster than that same current near the center of the wire, causing an effect known as group delay. Low frequencies will ALWAYS travel slower then high frequencies in passive cables, so the issue will always be with us through the audio electromagnetic spectrum.

[We’ll conclude Time is of the Essence next issue—Ed.]