Elvee,
You are concentrating on the rf performance of the system. As a topic, it is also of interest, but is not what I concentrate upon.
I speak of the audible consequences of the short transmission line fed and terminated by impedances significantly smaller than that of the line..
So, for the direction you have come from, your points are entirely valid. But not from the view I am speaking of. Wonderful discussion, btw, thanks for your posts...
Totally agree. Using 200 sets of elements for a 5 meter speaker run is time consuming, beyond the capabilities of most due to software limits, and most importantly, does not provide any insight into how the system will react in the audio realm. My t line model does.
Model a 15 foot 150 ohm t-line with 3.4 milliohm per foot wire (#12awg), fed by .1 ohm, terminated by a resistive 2 ohm load.
Now, apply a 20 volt step function to the input of the cable.
How long does it take for the load to settle to within 95% of the final value? That is, 9.5 amps or 19 volts?
Now, model the line with the same resistance, but make it an 8 ohm t-line.
How long does it take to settle to 95%.
In both cases, it is not there after 1 transit delay.
The primary question is...how far into the audible realm does that delay go? (Note we are sensitive to ITD's in the 2 to 5 uSec range midband.)
Then, how does one control that delay span given a typical speaker loading variation vs frequency?
I recommend using cables with characteristic impedances (high freq) in the 15 to 20 ohm range. That way, 2 ohm to 50 or 60 ohm loads will have a more consistent delay across the band, and when the cable Z rises in the audio band by a factor of 3 or 4, the delay still isn't too bad.
When a 150 ohm cable rises into the 400 or so ohm range down in the audio bands, the match to a speaker which drops into the 2 to 4 ohm load is too severe to maintain a good soundstage.
Elvee, you are attempting to use a smith chart. Forget it. Think of it in terms of energy transport. Energy can only travel down a t-line at the prop velocity if the energy has the V/I relationship of the line. If the load requires a V/I relationship that is not consistent with the line impedance, it will take multiple transits back and forth in the line before the load has either the voltage or the current that the amplifier is pushing.
jn
You are concentrating on the rf performance of the system. As a topic, it is also of interest, but is not what I concentrate upon.
I speak of the audible consequences of the short transmission line fed and terminated by impedances significantly smaller than that of the line..
So, for the direction you have come from, your points are entirely valid. But not from the view I am speaking of. Wonderful discussion, btw, thanks for your posts...
For audio lengths and audio frequencies, it's more important to think of the problem as settling time.
Totally agree. Using 200 sets of elements for a 5 meter speaker run is time consuming, beyond the capabilities of most due to software limits, and most importantly, does not provide any insight into how the system will react in the audio realm. My t line model does.
Not correct. Of course, using the modeling you've chosen won't show it anyway.
Model a 15 foot 150 ohm t-line with 3.4 milliohm per foot wire (#12awg), fed by .1 ohm, terminated by a resistive 2 ohm load.
Now, apply a 20 volt step function to the input of the cable.
How long does it take for the load to settle to within 95% of the final value? That is, 9.5 amps or 19 volts?
Now, model the line with the same resistance, but make it an 8 ohm t-line.
How long does it take to settle to 95%.
In both cases, it is not there after 1 transit delay.
The primary question is...how far into the audible realm does that delay go? (Note we are sensitive to ITD's in the 2 to 5 uSec range midband.)
Then, how does one control that delay span given a typical speaker loading variation vs frequency?
I recommend using cables with characteristic impedances (high freq) in the 15 to 20 ohm range. That way, 2 ohm to 50 or 60 ohm loads will have a more consistent delay across the band, and when the cable Z rises in the audio band by a factor of 3 or 4, the delay still isn't too bad.
When a 150 ohm cable rises into the 400 or so ohm range down in the audio bands, the match to a speaker which drops into the 2 to 4 ohm load is too severe to maintain a good soundstage.
Elvee, you are attempting to use a smith chart. Forget it. Think of it in terms of energy transport. Energy can only travel down a t-line at the prop velocity if the energy has the V/I relationship of the line. If the load requires a V/I relationship that is not consistent with the line impedance, it will take multiple transits back and forth in the line before the load has either the voltage or the current that the amplifier is pushing.
Agreed. Hope everybody on this continent had a good one. It was kinda hot in the NE.
I too enjoy the level of expertise all are bringing into this discussion. Also, my thanks.
jn
Elvee,
For modeling, assume the effective dielectric constant of the cable to be 4. That is a reasonable number for zip cables where the insulation thickness is not too crazy, and sets the velocity of propagation of the cable at half lightspeed.
L in nH times C in pF equals 1034 times EDC, so for modeling, use the product of LC as being 4136. An L of 100 nH per foot gives a C of 41.36 pf per foot.
jn
For modeling, assume the effective dielectric constant of the cable to be 4. That is a reasonable number for zip cables where the insulation thickness is not too crazy, and sets the velocity of propagation of the cable at half lightspeed.
L in nH times C in pF equals 1034 times EDC, so for modeling, use the product of LC as being 4136. An L of 100 nH per foot gives a C of 41.36 pf per foot.
jn
Not particularly. I see the problem in its entirety, and it can be broken down into two domains: the HF one, that can be tackled with text book transmisson line principles based on the usual simplifications, and the LF one that requires the full, unabridged theory to be properly treated.
We can safely say that above 1MHz, all problems can be treated using the HF approximations, whilst below 10KHz, all problems belong to the LF category.
Where a particular cable sits in this range depends very much of its construction
To be honest, I don't think that normal audio cables of this type have a direct audible effect (there may be other effects linked to the amplifier, as Bob pointed out), but if we want to analyze the effect of this cable anyway, we have to do it properly, ie using the proper theory/model
Why not, but I am not sure it simplifies the problem in a useful way
When I say that the usual transmission line concepts like matching, etc, are essentially useless at audio frequencies, I mean the simplified theory, based on a fixed and resistive characteristic impedance, flat group delay, etc
The modelling I have chosen takes all the LF effects into account
There is no simple and unique answer to that, it depends on all the parameters of the line
Same answer
Agreed
I have no set opinion on this aspect
This again is based on the simplified TRL model. At audio frequencies, all practical cables have a significant dispersion, and this means that energy at different frequencies will travel at different speeds. Also, a strong reflection will almost always occur because of the nature of the characteristic impedance.
Matching could achieved at a spot frequency, purely by chance, because the speaker's impedance is complex and variable too, but normally that won't be the case
For the reasons I explained earlier, I am not going to create new models in the near future, but I can make simple calculations based on these figures, assuming 12AWG: the characteristic impedance will be around 50Ω, and the LF cut off will be at 5.4KHz. Since the transition region extends well beyond this frequency, this means that practically all of the audio spectrum falls into the LF region and must be analyzed as such
There were power of 10 errors at some places
That depends on whether or not you are sensitive to or look for, frequency based timing delays for the power delivered to the load. The closer the line and load match, the closer the delay gets to one transit time.
As we've both stated, at lf the resistance of the line is fixed, but the impedance goes nuts, typically a factor of 3 to 5 higher. This of course renders an analytical solution to the frequency dependence on power delivery to the load a rather daunting task.
That doesn't stop one from using my model, but it does set constraints.
By choosing a line impedance based on L and C, (skip R/G for a moment).
1. One is using the HF model. This is only accurate up in and above the amplifier open loop unity gain frequency, so amp stability would be visible via that set of numbers.
2. All calculations of system settling time and power delivery delay will be the minimal numbers of the system. In other words, it is a lowball number. If one finds it takes 10 uSec for the model to achieve 90 or 95% of final value, reality will be considerably longer. Based of course, on the actual impedance of the line at the frequency of interest.
3. Note the 10 uSec. That number exceeds the human capability of ITD discernment within the 500 hz to 2 or 3 KHz band (undithered). Any alteration to the delivery of power to the speaker that exceeds 2 uSec in magnitude CANNOT be discounted.
4. Zip cables also suffer proximity effect within the audio band based on the specific geometry, which of course alters both R and L. Another factor which may be small, but will indeed alter cable Z a tad. Again, impossible to analytically derive effect level for normal humans. (I have a co-worker who is not restricted in this fashion.)
All said and done, I see absolutely NO analytical methodology which will be able to mathematically derive even the simple answer to this cable, this frequency, for any speaker load (or even just pure resistance). It is too complex for most, and that assumes the bog standard speaker model using linear elements. As I stated previously, I am also interested in measurement of the non linear resistive increase due to proximity and eddy current dissipation of a vc in the gap, the inductive change caused by lenz constriction, and the velocity dependence on Rs and Ls. I've not seen any speaker model which entertains these factors, perhaps you have?
I certainly understand you backing away from modeling the problem, it is indeed daunting, and I understand your reasoning.
That is why I've developed the test. As you can see, it's very simple but accounts for all the foibles people get trapped with when trying to measure high slew rate low impedance circuits.
For the casual reader, this is exactly what I am speaking of with the 3 to 5 range of cable Z, albeit using a more technical term.
Which is precisely what I've been pointing out with regard to the line to load match, and the settling time thing..
Which is why I previously stated that the best one can hope for is to get the cable Z into the range of the load being driven. For a perfect match, there will be NO delay, but if the line goes to 150 and the load goes to 2, the delay will be significant. Bringing the line to say, 10 at hf means at audio it will go to roughly 30, which brings the match closer and the delay variation across the audio band would be lowered.
Of significant note here is your use of the word "matching". That is impossible for speaker loads across the audio band. That is not the goal here. The goal is, how does the cable to load mismatch affect the time it takes for the signal to arrive at the load.
It is easy enough to create any cable hf Z by geometry. 50 is not a limit. I made a meter of 4 ohm cable with a dielectric coefficient of 3 using kapton for use in liquid helium, 15 feet of 4 ohm using multiple cat5e cables to get from the amp to the dewar, and a simple non inductive 4 ohm bifilar resistor I dunked in the LHe. The performance was great, I pushed 10 uSec risetime 40 volt square pulses 50 uSec long, there was no overshoot, no ringing.
What drives me crazy is the fact that no participants pointed out those gross errors..
jn
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I think we generally agree (I have no opinion about the audibilty of this type of distortion in this context though):
That said, the electroacoustic effects in themselves are perhaps even more interesting than the amplitude/phase distortions, as they have the potential to create non-linearities
There may be more accessible alternatives though: what we want is a low impedance, staying consistent at frequencies as low as possible.
This mandates the use of lots of copper to reduce the lineic resistance, but also a large spacing, to create enough lineic inductance. Unfortunately, this requirement contradicts the need for a low impedance. This could be solved by using a very high k dielectric, but there may be an alternative:
If the insulating material is made of a ferrite/polymer composite, the L will be increased without needing a large spacing, and the ferrite in the polymer will also have other desirable effects: it will increase the permittivity, and also the losses. This will introduce a non-negligible G term in the equation which will help keeping the LF impedance under control
No I haven't. The problem is already frightfully complex without these, I think including them would make things very difficult, even in sim. My computer already struggles when I use purely linear models in a moderately complex configuration.
That said, the electroacoustic effects in themselves are perhaps even more interesting than the amplitude/phase distortions, as they have the potential to create non-linearities
Quite impressive, but not within the reach of the average audiophile (nor mine).
There may be more accessible alternatives though: what we want is a low impedance, staying consistent at frequencies as low as possible.
This mandates the use of lots of copper to reduce the lineic resistance, but also a large spacing, to create enough lineic inductance. Unfortunately, this requirement contradicts the need for a low impedance. This could be solved by using a very high k dielectric, but there may be an alternative:
If the insulating material is made of a ferrite/polymer composite, the L will be increased without needing a large spacing, and the ferrite in the polymer will also have other desirable effects: it will increase the permittivity, and also the losses. This will introduce a non-negligible G term in the equation which will help keeping the LF impedance under control
I made one and pointed it out
We do indeed. I do admit that how I've approached the problem is not generally used, so it can initially be confusing. Probably a result of my poor way of describing and explaining...sorry.
That's why I'm essentially "punting", and instead pursuing a hardware testing approach. It will serve me well at work as well, we have 180 coils to drive with a 10Khz BW, about 35 meters from the amps, and delay here limits the accuracy of the final machine..
Well, the liquid helium I agree. But making a half inch wide copper stripline with about 1.5 mils of kapton or even double stick tape in between is trivially done by even the most casual of observers. And the cat5e matched line, that was just 6 cables paralleled, all solids together, all stripes together. Again, casually easy for all. The drive was a SWTPC tigersaurus 250, modified a tad for speed and output capability..
The cat5e design is easy to do, Z will be 100 divided by the number of pairs. Within a jacket, the 4 pair are magnetically orthogonal by design, non coupling twist pitches. Outside the jacket, distance serves. Problem is guage, cat5e is kinda small.
I personally recommend using 4 zip cords per channel, each twisted to decouple them. 4 pair drops the system to roughly 30 ohms rf, 100 audio. Given speakers in the 2 to 50 ohm overall range, it limits differences in delay to a smaller number. This solution is easily expanded, but 120 as the base impedance simply because the insulation is geometrically thicker than cat5e. It's also simple enough to guage the zip to give a reasonable delivery guage, like 4 to 8 runs of #18 for example.
I've made a coaxial 6 ohm 12 guage using braid, and stripline 4 ohm using braid as well. Both tested reasonably well and consistent from 20 hz out to roughly 50 KHz IIRC.
jn
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I am just finished with a casual test. Put a parallel pair of 5.6 ohm mills 12 watt resistors in series with my speaker wire. Subjectively, the 8ohm speakers sound far better in every way at the end of a 300B single ended amp. My question in regards to properly matching cables between amps and speakers; how does one arrive at a reference as to what the system ought to sound like? Mine now sounds more "real" and layered than "just wire", but of course I would be more pleased not to have resistors in a system I'm trying to make as uncomplicated as possible.
It changes the effective Qts of the drivers, yes.
Not necessarily. The cabinet may have been tuned for a very high output impedance amp. Tho is this case, that's pretty high! You can only know with good measurements.
Maybe. But maybe not enough distortion to be audible. Again, you'd have to measure to be sure.
I don't believe the bass resonance to be a factor. Using a line level 2nd order highpass filter at 500hz. Bass duties carried by a different amp. I accept the distortion hypothesis, but am using 105 db / watt mid and treble horns, so I doubt the amp is strained in any way. Still wondering how to ascertain what the right sound is.
Not really. The resistors are on the amp's 8 ohm terminals, biwired cable feeds direct to mid driver, and to a cap on the tweeter driver. Maybe the resistors are just "topping up" the drivers impedance dip for a better match with the output transformers. If that's the case, maybe I could get a similar result from a small gauge (higher resistance) speaker cable , and skip the added resistors?
As to "what you should hear"? Go to a live blue grass or jazz festival, outdoors and listen with your eyes closed, about 30 feet away. Then go hear similar live music in a confined space, at least 15 feet away. Then go listen to similar music in your space. Any thing you can do that drags your system closer to the two live venues is what you should pursue, while trying not to screw up what you didn't need to change. If resistors get you there, so what?
Bud
Bud
That makes sense. Think I will leave them in, rather than trying to find wire with similar overall series resistance. Tired of playing for now. Just finished fixing faulty new stepped attenuator, hardwiring all wiring to it, including biwired outputs, only to find Yaqin "direct in" still goes through its volume pot. Kind of lowers fun in hobby to do everything right and still catch one in the 'nads. Who'd think to check if a direct in really was a direct in first?
Thanks for that reference, Scott, some very good information. I note particularly the chart of current-generating phenomena, showing how triboelectric effects in standard cables reaches into the danger zone - and the difference a low noise cable can make ...
The Keithley site is full of good material - here's a nice snippet:
So, maybe cables do matter ...
In audio line level waveform transfer the maximum current amplitude is mA's or less: say, 2V peak driving 10's of K's at the load. "tens of nanoamps of current" is hitting the -80 to -100dB area of the real, audio signal we're interested in - where everyone starts arguing about whether the 'noise' can be heard ...
So, maybe cables do matter ...
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