Impedance at audio is mixed with the very old and very new. We’ve all heard of 600-ohm cables, yes? These are impossible to make at RF frequencies without excessive cable size. At audio, the value is only true for a very narrow frequency range where the velocity of the cable is very low, raising the impedance.
Lets look at what IMPEDANCE calculations are, and quick see what the measured values tell us about audio cable.
At audio, the “impedance” can’t use the two reactive variables like RF, SQRT of L over C. We need to use an equation that is valid in the audio frequency range that takes FREQUENCY into account. Here is why frequency needs to be considered;
These are a few examples of cable velocity and frequency relationships. ALL cables will do this through the audio band. Look at the values at the far left of the trace. Do we see 90% velocity at low frequencies? No, we see values as low as 10% at 1 KHz or even less at 20 Hz!
To get an idea of the impedance of a low frequency cable, we need to use the equation
101670 / (Cap X Vp) = Impedance
Capacitance is stable through the measurement range as the chart below illustrates. The traces are for 1 KHz and 10 KHz values. ALL cables will exhibit stable capacitance with frequency, this is just a single example of a speaker cable.
1 KHz 10 KHz
AVG (pF) 14.893 14.441
STD DEV 00.166 00.202
Capacitance is stable so the attribute that influences cable impedance is the Velocity of the signal in the cables. The actual measured CHART for ICONOCLAST RCA and XLR show two things, first, each cable is IDENTICAL to the other cable reactively, and second the IMPEDANCE follows expected deviation across the frequency range.
What does the impedance do at the very low end? Yes, it goes UP as the Vp drops to 10% or less at 100 Hz. We only see a FLATTENING of the trace in the RF region above 100KHz.
The concept of a 600-ohm cable was derived through much study on LONG length telephone audio signals, and to excellent effect. Notice that the 600-ohm value in the example above is at just above 1 KHz, dead nuts in the frequency human hearing is centered around.
The “impedance” is NOT consistent at all, so the reference to 600-ohms is where that “spectral density” of the signal is greatest, and needs to be managed the closest to ideal with the same resistive load at the end of the cable to minimize reflections. But this can only happen for a cable that is a “transmission line” and for audio cables, about the only cable that meets that is a analog telephone cable as it is LONG enough to actually contain several wavelength is a cable length. Generally you need at least 10 wavelength in a cable length to act like a transmission line. From a PURE physics standpoint, ONE would work with ultimate physical perfection.
We have a problem, though, as the WAVELENGTH is different at every frequency from our frequency and Vp graph. What to do? Well, use the worst case. Lets us the 1 KHz value as an example that has a 20% value of the speed of light in a vacuum.
Wavelength = Wave speed / Frequency = 0.2(983,571,056 feet/second)/ 1000 = 196,714 feet
What do we see? An answer that is at a BARE MIMUMUM under the best of circumstances 196,714 feet long! This, for ONE wavelength at 1,000 Hz.
We don’t use cables this long in our systems. Our interconnects are terminated into INFINITY as an ideal number (actually 47K-ohms or the where abouts). This looks like a VERY large RESISTOR across the ends of the RCA or XLR cable.
A high impedance interconnect (sees a high impedance load, not 600-ohms!) has a very small current draw, but there is current as the cable looks like a capacitor that is being charged at the send end, and the signal amplitude observed at the receive end.
Capacitors don’t charge instantly, even though the current jumps to “infinity” at the start of a charge cycle and drops to ZERO after the capacitor (our cable) is fully charged. Circuits have capacitive reactance that defines how fast the capacitr can charge. Every circuit is different and the value of capacitive reactance is frequency dependent.
Capacitive Reactance, Xc = 1 / (2 F C)
F = frequency
C = capacitance
The use of high input ”impedance” (really resistance as we don’t have true impedance at audio) alleviates the cable from transmission line properties and falls back on a more lump sum attribute of capacitance and inductance. Inductance counts, too, as this value determines the instantaneous peak current applied to the cable at the transmit end that charges the capacitor…it DOES take CURRENT to CHANGE the voltage signal.
XL = 2 * *f * L
Notice this is the reciprocal of capacitive reactance. It takes TIME to change the voltage across a capacitor (what the cable looks like) and applied current is what changes the voltage level. The inductive reactance determines the initial maximum value of that current.
SUMMARY – All audio interconnect cables are high impedance (really resistive) terminated leads, and their capacitive and inductive reactance, that is based on their DESIGN, determine the voltage waveform distortions at the receiving end. With an ideal infinitely high load, the cables “impedance” is mitigated since no matter how high the cable impedance is, it is still “zero” relative to the infinitely high load value.
The current loop value is THROUGH the capacitance of the cable, and that value goes to ZERO once the cable is charged. Technically the LOAD can’t be seen by the cable as it isn’t there at infinity (not fully true, of course).
Each frequency is a different time based reactive set of values and alters the signal from an ideal instantaneous voltage value. When the voltage is zero the current is infinity, and when the voltage is at the maximum current is at zero. It takes TIME to move the voltage and current top opposite values. Add to this the SPEED that a voltage signal can travel down the wire (design’s dielectric value) which is also time dependent, and we can see wires aren’t perfect.
Using high impedance leads is a very good way to mitigate cable non linearities over speaker cables that see a low impedance cable terminated into a low impedance reactive load. We should be fortunate we don’t have 600-ohm transmission-line audio interconnect cables.