Reciprocity in electrical networks

[Raindog123]

In other thread @EB1000 made a statement: “Lorentz reciprocity? You do realize we're talking about audio cables, not antennas? The Lorentz reciprocity is a concept that applies to distributed systems, not a lumped system like an audio cable, in which non-reciprocity is defined as the variation in the transfer function of the cable, calculated from both ends (v2/v1 and v1/v2). A simple RC network is non-reciprocal, so one can claim that it's directional.”

This is simple not true. I would invite anyone to dust off their textbooks. But we can start with the Wikipedia:

“In general, passive networks are reciprocal. Any network that consists entirely of ideal capacitances, inductances (including mutual inductances), and resistances, that is, elements that are linear and bilateral, will be reciprocal.[2] However, passive components that are non-reciprocal do exist. Any component containing ferromagneric material is likely to be non-reciprocal. Examples of passive components deliberately designed to be non-reciprocal include circulators and isolators.[3]”

 

[BDWoody]

Who wants to argue with the physics professor?

Step right up.

 

[Spkrdctr]

I will! I like to argue intellectual ideas. So, my reply to that reciprocity is this. My dad can beat up your dad. There. I'm done!

 

[EB1000]

In other thread @EB1000 made a statement: “Lorentz reciprocity? You do realize we're talking about audio cables, not antennas? The Lorentz reciprocity is a concept that applies to distributed systems, not a lumped system like an audio cable, in which non-reciprocity is defined as the variation in the transfer function of the cable, calculated from both ends (v2/v1 and v1/v2). A simple RC network is non-reciprocal, so one can claim that it's directional.”

This is simple not true. I would invite anyone to dust off their textbooks. But we can start with the Wikipedia:

“In general, passive networks are reciprocal. Any network that consists entirely of ideal capacitances, inductances (including mutual inductances), and resistances, that is, elements that are linear and bilateral, will be reciprocal.[2] However, passive components that are non-reciprocal do exist. Any component containing ferromagneric material is likely to be non-reciprocal. Examples of passive components deliberately designed to be non-reciprocal include circulators and isolators.[3]”

Yes, a passive network is defined as mutually reciprocal by injecting current at one end and measuring voltage at the other, but no audio source is a current source and no audio sink acts as an open circuit, so mutual reciprocity does not guaranty v2/v1 = v1/v2, unless the network is mutually symmetrical. I think this is the basis for the cable directionality claim.

 

[Spkrdctr]

Oh, no! Not another one!
Is someone cleaning out under all the bridges in Norway?

Glad I could give you a morning laugh. It gets so serious here on some issues. Amir should sell flame suits! $19.99 each. Could raise money for the site.

 

[BDWoody]

Glad I could give you a morning laugh. It gets so serious here on some issues. Amir should sell flame suits! $19.99 each. Could raise money for the site.

He has asbestos underwear sets he sends out to his moderators... I think that takes up all production capacity.

 

[Raindog123]

so mutual reciprocity does not guaranty v2/v1 = v1/v2, unless the network is mutually symmetrical.

@BDWoody Can the prof now grade this excerpt? Or is it too soon - should let others to speak up?

 

[BDWoody]

@BDWoody Can the prof now grade this excerpt? Or is it too soon - should let others to speak up?

You are in control of this classroom Dr. Dog.

 

[audio2design]

If people took a minute to actually think and respond, perhaps they would not make posts like this that show ignorance.

I made a grossly exaggerated example, where a cable is represented by a 10R resistance, 1uF capacitance, and 1R resistance. Real world? No, but cables do not have consistent resistance, capacitance and inductance across their length.

 

[audio2design]

Yes, a passive network is defined as mutually reciprocal by injecting current at one end and measuring voltage at the other, but no audio source is a current source and no audio sink acts as an open circuit, so mutual reciprocity does not guaranty v2/v1 = v1/v2, unless the network is mutually symmetrical. I think this is the basis for the cable directionality claim.

Again, nice to see someone can actually think, as opposed to rushing to their keyboards to look erudite.

 

[MakeMineVinyl]

This is the dumpster fire that keeps on giving.

 

[EB1000]

And so is @audio2design's here:



Both are:

View attachment 126237

I only got the terms reciprocal and symmetric networks mixed up, but, the claim holds. An RC LPF is a non-symmetrical network, so input and output impedances are different, which will lead to different results if the network's terminals are swapped. Symmetrical means also reciprocal, but not the other way around.

 

[Spkrdctr]

I got sucked into this thread again with the search term "dumpster fire". I'm a sucker for this intellectual stuff.......

 

[RayDunzl]

I made a grossly exaggerated example

How about an actual example?

 

[preload]

How about an actual example?

I’d settle just for an explanation for why any of this matters and why anyone should care.

 

[MarkS]

It doesn't matter (in audio) and no one (in audio) should care.

But as a matter of principle, cables are directional if they are not symmetric (that is, physically equivalent) when the ends are switched. For example, take a coax cable that is one meter long, and crimp it 1/4 meter from one end (not enough to short it, just enough to change the capacitance at the crimp). Connect an AC voltage source to one end and a passive load to the other end. The power delivered to the passive load wlll be different depending on which end was connected to the source and which end was connected to the load. Lorentz reciprocity does not apply, because these two connection set-ups are physically different. (To apply Lorentz reciprocity, you have to consider a situation where one end of the cable is left open and the other end has the passive load; now you can connect the voltage source to either end, but you are not allowed to move the passive load from one end to the other.)

On the other hand, as a matter of practice in audio, the difference in the power delivered in the two cases is far too small to matter. The electrical wavelength of a 20kHz signal is several miles (exactly how many depends on the material surrounding the conductors in the cable). Nonuniformity of a cable only matters if your cable length is a significant fraction of that, and then only if the physical nonuniformity is large.

 

[audio2design]

Why does it matter? Because with this alternate truth reality we seem to live in, and the lack of respect given to science within this hobby/pursuit, the people who identify as technical / experts need to hold themselves to a higher standard. If we don't, then why should we expect lay people to trust us?


Grossly exaggerated examples work just fine. Where this all came out was whether cables are not directional because signals are AC. An argument was made and has been made repeatedly that because signals are AC, direction does not matter. The opposite is true. It may not matter because of the magnitude of parameter variation at the frequencies of interest, but not just because they are AC.


This was never about audibility, it was about accuracy of communicated information.

 

[mansr]

Grossly exaggerated examples work just fine. Where this all came out was whether cables are not directional because signals are AC. An argument was made and has been made repeatedly that because signals are AC, direction does not matter.

That is true at audio frequencies and typical domestic cable lengths, provided the cables are not pathological. "Articulation consoles" are pathological.

 

[audio2design]

It doesn't matter (in audio) and no one (in audio) should care.

But as a matter of principle, cables are directional if they are not symmetric (that is, physically equivalent) when the ends are switched. For example, take a coax cable that is one meter long, and crimp it 1/4 meter from one end (not enough to short it, just enough to change the capacitance at the crimp). Connect an AC voltage source to one end and a passive load to the other end. The power delivered to the passive load wlll be different depending on which end was connected to the source and which end was connected to the load. Lorentz reciprocity does not apply, because these two connection set-ups are physically different. (To apply Lorentz reciprocity, you have to consider a situation where one end of the cable is left open and the other end has the passive load; now you can connect the voltage source to either end, but you are not allowed to move the passive load from one end to the other.)

On the other hand, as a matter of practice in audio, the difference in the power delivered in the two cases is far too small to matter. The electrical wavelength of a 20kHz signal is several miles (exactly how many depends on the material surrounding the conductors in the cable). Nonuniformity of a cable only matters if your cable length is a significant fraction of that, and then only if the physical nonuniformity is large.

I started this mess, because I tried to clarify, with an oft quoted expert, who stated that because audio signals are AC, directionality of the cable does not matter. That statement, is false. It is AC that makes cables have the potential to be directional. I don't think anyone with a modicum of technical know how believes that any practical cable in the audio range has audible differences based on direction. I could probably make something that would show an easily measured difference, but it would not be practical, though I could probably throw a pretty sheathing on it, mention graphite and quantum in the advertising, and charge $5,000 for it because it is directional

 

[audio2design]

On the other hand, as a matter of practice in audio, the difference in the power delivered in the two cases is far too small to matter. The electrical wavelength of a 20kHz signal is several miles (exactly how many depends on the material surrounding the conductors in the cable). Nonuniformity of a cable only matters if your cable length is a significant fraction of that, and then only if the physical nonuniformity is large.

Are you saying that now would be a bad time to start talking about at what length transmission line effects really come into play if we target settling to -120db and 40KHz bandwidth? Ya, probably too early.