# Complex valued impedance

How exactly does the complex part of characteristic impedance affect things, explained in common sense terms?
Audioquest has these “ZERO” characteristic impedance power cables, I haven’t read their explanation but of course in their ad, they have to state that zero impedance is impossible but apparently they have somehow achieved a zero complex value. What are techniques for minimizing, even to 0, the complex valued part of impedance and how does this affect things?
(Again, please explain in common sense terms, I know only up to some complex algebra)

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That is some deep do do for someone with limited mathematical higher education.

Here’s an article in easy-to-understand terms. https://www.ad5gg.com/2018/09/25/what-is-characteristic-impedance/

That said, I have no idea what AQ is talking about.

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" ZERO Tech (No Characteristic Impedance)

The integrity of any audio transient (instantaneous peak-to-peak voltage swing and current) delivered from a power amplifier to a loudspeaker has always been compromised. Whether the amplifier is valve or transistor, regardless of class of operation, the amplifier’s source impedance and loudspeaker’s load impedance are never critically matched. The speaker cable’s characteristic impedance is yet another culprit in a highly compromised non-linear electrical circuit. AudioQuest has always stated that all cables cause damage because the output is never as good as the input. However, by eliminating a speaker cable’s characteristic impedance, AQ’s ZERO Technology is an unprecedented step towards reducing that damage. The result is greater dynamic contrast, better audio transient response, and bass slam that are rendered seemingly without effort because the cable is not electrically restricting (strangling) the music."

I’m lots of dumb when it comes to this electrical stuff, but my audiophile mentor always told me to match speaker cable gauge to a speaker’s impedance, and not to go “garden hose” gauge just because it looks cool. I don’t know, really. I love this hobby, but it’s a hat toss sometimes.

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There is no such thing as “impedance” unless at least 10 wavelengths are in the cable’s length based on the VP. Even at 20 KHz we have thousands of feet (figure 20 KHz travels at about 50% the speed of light in a cable, that’s ONE wavelength).

For audio, we really are damping simple reflections of STORED energy by either capacitance (voltage) or inductance (current). If we know the load, we can pad the cable with a zobel like network to remove the reactive and reflective energy. In short hand, make the cable and load more resistive so ALL the energy goes into the load. Some speakers already have them built-in to approximate most cables that are far, far less a problem than the speaker is.

A typical speaker is awful where the spectral energy is the WORST, making reflections pretty bad. Look at any speaker impedance curve and you’ll see significant deviations of tens of ohms below 200 Hz or so. No two speakers or amps act the same.

For a power cable, the power supply gets a juce of energy from the wall as it is used by the load to charge the internal capacitor bank. This requires low inductance so current moves along, not so much low capacitance as we are using CURRENT over VOLTAGE in a power supply. The wall voltage should be held CONSTANT unless too much current is required, then the wall voltage can sag.

Matching the “impedance” of a power cord at 60 Hz is pretty silly as the wave length is WAY, WAY, WAY longer, far longer than 20 KHz audio signal wavelengths, than the cord length at this frequency. And, each power suppy load won’t be the same. The word impedance is being used improperly to really mean a more uniform and low resistance path for either voltage or current depending on your design target. Audio is pretty guilty of this definition, low resistance path, for “impedance”. Just be aware of this definition.

Most of what is here is RF derived, and little use at audio frequencies, where we have simple reflections and not a true impedance. Simply put, you can offset reactance with a value opposite the articles value to bring it to a more resistive total “reactance” - but this is into a variable load most of the time. Thus, we miss the target more often than not.

Proof to this is WHY a cable can change what we hear from our amplifier and speaker. Each cable acts differently getting power to the load based on the resistive component value and at EACH frequency in real time - ouch!

best,
Galen Gareis

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“The word impedance is being used improperly to really mean a more uniform and low resistance path for either voltage or current depending on your design target. Audio is pretty guilty of this definition, low resistance path, for “impedance”. Just be aware of this definition.”

So just to clarify:
If I want to supply both voltage and current in spades, don’t I want a low resistance path, just that, yes? As in, when powering speakers.
I’ve understood impedance to mean frequency-dependent resistance. So don’t we want this minimized when powering speakers? Isn’t minimizing this just what we want to do when speaking of driving a speaker system? Right?

Just be aware the the word"mpedance" is defined differently at RF verses low frequency. At RF, it is the load that allows the maximum transfer of the signal, and this is not always the lowest “impedance”, but MATCHED impedance at RF.

We laso have the concept that we are tansfering a “signal” or we are doing “WORK”, not the same thing.

a speaker cable does WORK (watts), an interconnect cable goes into a theoretical infinity load (47K-ohm or higher) and we can per into the cable and transfer the potential voltage to another place. It isn’t doing any work. If we use a too low input resistance it will load down the op-amp delivering the signal and we will DISTORT the signal. too little resistance is bad in this case. The op-amp can’t deliver current to do WORK into the LOAD. It is designed more for VOLTAGE or potential.

For speakers, we have REFLECTIONS back and fouth between the amp and speaker as the speakers load value fluctuates all over with fequency, and this changes the amplifiers LINEARITY as it has to deal with non linear load. Amplifiers are tested into static 8-ohm loads, not a speaker. This iswhy amplifiers sound different when the specs are “the same”. Well, into 8-ohms they might be.

Cables also vary their impedance properties with frequency as the Vp changes. The resistance becomes a factor. Capacitance and Inductance stay pretty much the same swept to frequency but the Vp at low frequencies does not and this alters the cables “impedance”. A waves speed is proportional to frequency. At higher frequency it reaches the dielectric’s maximum of 1/ (SQRT(e)). “e” is the dielectric constant value.

At RF, which is at 1 MHz but better yet above 10 MHz or higher, we test the resistive component at 1 KHz believe it or not. Capacitance is the same at RF at 1 KHz and is more stable to test at a lower frequency.

If you know the DIELECTRIC at RF, Vp = 1/(sqrt(e)), and you know the capacitance at 1 KHz, you can calculate the cable impedance; Zo=101670/(C * Vp).

Some will point out the RF impedance is a RATIO of the wire center to the innershield or distance between two wires in a twinaxial. yes, but don’t forge that the CAPACITANCE is derived by the dielectric’s properties and distance. So it is all interrelated. Change the wire spacing and the RATIO and the CAPACITANCE both change. Or, hold the RATIO the same and change the DIELECTRIC material to change the capacitance.

So a the “ratio” impedance method works with a set dielectric material such that the capacitance is known. The ratio method allows a designer to estimate the SIZE of a cable as we CHANGE the center wire, as an example, to lower attenuation. An RG59, RG6 and RG11 all have the same RATIO with a fixed dielectric material between the center wires dimension and the dielectric dimension under the shield.

So low frequencies are CHANGING their spots so to speak. We can never design across ALL of them at once.

Some circuits like a speaker cable deliver POWER, and the load to optimize that CHANGES with frequency. Other circuits (interconnect) deliver a POTENTIAL value and to do that, we must REMOVE the CURRENT so we don’t do work. Work (watts)= (amps * potential).

It isn’t easy to model low frequency as it isn’t fixed in the time domain like RF. Amps, wires and spaeakers all are changing as we look at different frequencies, each effecting the other.

Best,
Galen Gareis

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