I actually remembered I built some time ago a half decent LF directional bridge (certainly better than the examples provided above, directivity was around 30dB), in the context I was looking to measure an output stage input impedance, up to the ULGF. So I dusted this bridge, got a roll of 50m of RG316 50 ohm cable and here are the results:
- Calibrated the directional bridge port using a 50ohm calibration kit. After calibration, the reflection magnitude and phase are illustrated in the first attachment. -65dB and phase all over the place are pretty good numbers, but this does not mean that the directional bridge can discriminate -60dB of reflections; the directivity still limits the measurements, the chart only shows that systematic errors are practically eliminated (or buried in the noise).
- Now measuring 50m of 50 ohm cable, open ended, between 20KHz and 50KHz. The result is shown in the other attachment, with the Smith chart full and magnified by 20dB.
For those less familiar with the Smith diagram, here's a few facts. The Smith chart is a convenient way to represent the complex plane. A open circuit is a dot on the right side of the of the horizontal diameter, while a short is a dot on the left side of the horizontal diameter. The frequency is the parameter of any curve on the Smith chart.
As the frequency varies, there is a trajectory on the Smith chart that shows the complex impedance; a frequency independent 50 ohm impedance will show as a dot right in the center of the Smith chart. The horizontal diameter corresponds to the real axis, these are pure resistive values, from zero (short, left) to infinity (open, right). Anything else has a real part and an imaginary part. The upper half of the Smith chart are containing the inductive impedances, the lower half the capacitive impedances. Very important observation: the Smith chart shows normalized impedances, to the characteristic impedance. So the results are independent on the magnitude an phase of the characteristic impedance. It would not make any difference if we would consider the characteristic impedance whatever impedance a speaker exposes at it's terminals, and the system could be calibrated to the characteristic impedance by connecting the speakers straight to the directional bridge. Nothing would change!
Circles with the center in the chart center are constant Gamma (the reflection coefficient) and the radius is exactly the Gamma value (the Smith chart is a unity radius circle). So a full circle would mean total reflections on the load (Gamma=1). That's what we are after, to see how much of a reflected we have. Recall that the standing wave ratio SWR is the ratio between the incident and reflected wave amplitude and SWR=(1-Gamma)/(1+Gamma) so a full circle in the Smith chart is also a constant SWR circle (once again, the frequency is the parameter).
So how do we interpret the measurements herein? Up to 50KHz, the 50m cable impedance terminated open is, and remains, an open. Even on the 20dB expanded chart diagram, it is still and open, for all practical purposes. Now, to get to a second order effects, the 50m cable is in fact capacitive; it has about 4nF of capacitance, which at 35KHz has an impedance of -1.6Kohm (compare to 50 ohm) and the real and imaginary parts of the impedance (normalized to 50ohm) are Re=1.00057 and Im=0.0861 These values are showing that at 35KHz the Smith plot is on the unity circle, with very little capacitive impedance to speak off. Being on the unity circle the end result is that Gamma=1 and SWR is virtually 0. For the hell of it, I calculated Gamma=0.997 and hence the SWR=0.004 or -47dB. This value is much lower than the estimated bridge directivity, so this value has actually no meaning/validity/interpretation, being just a number. But what this experiment shows is that 50m of 50ohm cable at 35KHz has a standing wave ratio SWR under any reasonable measurement capability. If some is able to find a LF directional bridge with a 60dB directivity, I am willing to redo these measurements. I'm not holding my breath, though.
These results are showing what is actually expected theoretically: any TL has reflections at any frequency. However, these reflections are almost impossible to measure at audio frequencies and can hence be safely ignored. Wait, do I hear Dan saying he can hear these?
Oh, and **** CB's measurements, he screwed it badly this time.
P.S. The network analyzer is a HP4195A
P.P.S. Some may entertain the same data shown in a conventional magnitude + phase plot. I'm attaching this as well. Net result, 0.04dB losses on 50m and an almost linear phase shift drop due to the 4nF of the 50m open ended TL capacitance. Same ****, another view.
Questions welcomed, BS will be politely ignored.
- Calibrated the directional bridge port using a 50ohm calibration kit. After calibration, the reflection magnitude and phase are illustrated in the first attachment. -65dB and phase all over the place are pretty good numbers, but this does not mean that the directional bridge can discriminate -60dB of reflections; the directivity still limits the measurements, the chart only shows that systematic errors are practically eliminated (or buried in the noise).
- Now measuring 50m of 50 ohm cable, open ended, between 20KHz and 50KHz. The result is shown in the other attachment, with the Smith chart full and magnified by 20dB.
For those less familiar with the Smith diagram, here's a few facts. The Smith chart is a convenient way to represent the complex plane. A open circuit is a dot on the right side of the of the horizontal diameter, while a short is a dot on the left side of the horizontal diameter. The frequency is the parameter of any curve on the Smith chart.
As the frequency varies, there is a trajectory on the Smith chart that shows the complex impedance; a frequency independent 50 ohm impedance will show as a dot right in the center of the Smith chart. The horizontal diameter corresponds to the real axis, these are pure resistive values, from zero (short, left) to infinity (open, right). Anything else has a real part and an imaginary part. The upper half of the Smith chart are containing the inductive impedances, the lower half the capacitive impedances. Very important observation: the Smith chart shows normalized impedances, to the characteristic impedance. So the results are independent on the magnitude an phase of the characteristic impedance. It would not make any difference if we would consider the characteristic impedance whatever impedance a speaker exposes at it's terminals, and the system could be calibrated to the characteristic impedance by connecting the speakers straight to the directional bridge. Nothing would change!
Circles with the center in the chart center are constant Gamma (the reflection coefficient) and the radius is exactly the Gamma value (the Smith chart is a unity radius circle). So a full circle would mean total reflections on the load (Gamma=1). That's what we are after, to see how much of a reflected we have. Recall that the standing wave ratio SWR is the ratio between the incident and reflected wave amplitude and SWR=(1-Gamma)/(1+Gamma) so a full circle in the Smith chart is also a constant SWR circle (once again, the frequency is the parameter).
So how do we interpret the measurements herein? Up to 50KHz, the 50m cable impedance terminated open is, and remains, an open. Even on the 20dB expanded chart diagram, it is still and open, for all practical purposes. Now, to get to a second order effects, the 50m cable is in fact capacitive; it has about 4nF of capacitance, which at 35KHz has an impedance of -1.6Kohm (compare to 50 ohm) and the real and imaginary parts of the impedance (normalized to 50ohm) are Re=1.00057 and Im=0.0861 These values are showing that at 35KHz the Smith plot is on the unity circle, with very little capacitive impedance to speak off. Being on the unity circle the end result is that Gamma=1 and SWR is virtually 0. For the hell of it, I calculated Gamma=0.997 and hence the SWR=0.004 or -47dB. This value is much lower than the estimated bridge directivity, so this value has actually no meaning/validity/interpretation, being just a number. But what this experiment shows is that 50m of 50ohm cable at 35KHz has a standing wave ratio SWR under any reasonable measurement capability. If some is able to find a LF directional bridge with a 60dB directivity, I am willing to redo these measurements. I'm not holding my breath, though.
These results are showing what is actually expected theoretically: any TL has reflections at any frequency. However, these reflections are almost impossible to measure at audio frequencies and can hence be safely ignored. Wait, do I hear Dan saying he can hear these?
Oh, and **** CB's measurements, he screwed it badly this time.
P.S. The network analyzer is a HP4195A
P.P.S. Some may entertain the same data shown in a conventional magnitude + phase plot. I'm attaching this as well. Net result, 0.04dB losses on 50m and an almost linear phase shift drop due to the 4nF of the 50m open ended TL capacitance. Same ****, another view.
Questions welcomed, BS will be politely ignored.
Attachments
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Yeah, good luck with "two identical transformers" at low frequencies, for a 60dB directivity required here. JN, you should know better...
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I have posted exactly what is needed to duplicate CB's work.
And it is not difficult to make two very close to identical transformers. Since primary was one turn, all that is needed is a 31 turn secondary on each core.
While it might be difficult to mass produce identical toroidal inductors, it is trivial to match a pair hand wound.
Air core inductors using 1 cm square copper conductors in mass production will have a 2% range (from our experience with industry on four continents), but in a lab (well ok, a basement) tweaking one small hand wind is pretty trivial. All one needs is a way to measure the inductance accurately and adjust slightly. I'll use my HP gas chromatograph.
CB seemed to have no problem gettin 53dB at 1khz, you call that messed up?
And still, the crux of the discussion, being impact on load current rise vs load impedance, goes untouched.
Surprise surprise.
Wait a minute, are all your measurements unloaded?
Jn
And it is not difficult to make two very close to identical transformers. Since primary was one turn, all that is needed is a 31 turn secondary on each core.
While it might be difficult to mass produce identical toroidal inductors, it is trivial to match a pair hand wound.
Air core inductors using 1 cm square copper conductors in mass production will have a 2% range (from our experience with industry on four continents), but in a lab (well ok, a basement) tweaking one small hand wind is pretty trivial. All one needs is a way to measure the inductance accurately and adjust slightly. I'll use my HP gas chromatograph.
CB seemed to have no problem gettin 53dB at 1khz, you call that messed up?
And still, the crux of the discussion, being impact on load current rise vs load impedance, goes untouched.
Surprise surprise.
Wait a minute, are all your measurements unloaded?
Jn
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I'm surprised nobody has mentioned that this has already been discussed on another site recently (without all the huffing & puffing)
Radio Frequency (RF) Analysis of Speaker Cables/Reflections | Audio Science Review (ASR) Forum
Radio Frequency (RF) Analysis of Speaker Cables/Reflections | Audio Science Review (ASR) Forum
There's not much for adults. I've used my Apple TV maybe a couple of hours,
and it's 3 years old. Just finished the Next Generation series on antenna TV,
now it's movies or nothing. There is Brian Greene on Einstein tonight on PBS, though.
I met him here some years ago, he's a good science popularizer.
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Fun. There is no huffing and puffing because the members of that forum are in agreement with the conclusions, despite the inaccuracy. I believe this forum has significantly more intelligent members (technical/engineering wise of course).
He made a simple mistake in his conclusions. He said that the delay was in the low microsecond range, 1.2 for his example, but then said the rise time of a 20 kHz signal was 17.5 microseconds, much slower so negated the impact. Given his erroneous argument, a 1 KHz rise time of 350 uSec would mean we cannot distinguish ITD in that regime, which is demonstrably incorrect by close to two orders of magnitude.
He doesn't understand human localization. Even with the recently linked 1Khz and 6.9 uSec shown as demonstrably audible (using weird test signals),his argument flies in the face of that.
I am confident he was referring to me as the fellow engineer, primarily because he mentions biwiring as well.
His analysis of the delay caused by the cable to load mismatch was quite correct however.
Oh, he also used 93 ohms, zip is typically 150 due to the insulation thickness.
Had he come to correct conclusions concerning ITD, he might have continued down the path I cleared and tried the 150 ohm impedance with a speaker load value that ranges from say 6 ohms to 60. Then, the difference in delays must be compared to ITD thresholds.
Then, calculation of what impedance range would be needed to span, such that a non linear time variant load shift sufficiently to read those thresholds.
Since he did not understand ITD, the post died..
Jn
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With all due respect JN, read again and perhaps get a crash course in Smith diagram. Otherwise you may look like you have no idea what you are talking about. Hint, since the Smith diagram is normalized, the load is irrelevant, it will always show reflections between the extreme limits (open and short, that is SWR between +1 and +1 😀). Somebody else mentioned this already, it is not the cable reflecting, it's the load, end of story. FYI, the cable can be considered as an impedance transformer, but this has nothing to do with reflections at such low frequencies. And at such low frequencies the cable will simply transform Zload in... (drums rolling) ...Zload.
Come up with your own measurements and please stop parroting CB's results. Until independently verified, they are pure BS. Since CB is no longer around, the burden of proof is on you, I did my share of work here.
FYI, RF directional bridges up to the GHz range have at best 40dB directivity (Agilent instrumentation devices), and those are much easier to balance, since they use precision baluns and/or microstrip lines. 53dB directivity @10KHz, I want to see this, until it's as much as BS. Here's the best I've ever heard about, less than 40dB, 1.3 VSWR (crap) and under 30dB isolation (crap) https://www.minicircuits.com/pdfs/PDC-10-6.pdf
And please stop attempting to be the judge, jury and executioner. You don't always own the truth.
P.S. Forgot to mention, I measured 50 meters of cable @35KHz and got zilch in terms of reflection. 5 meters at 10KHz, that's well over an order of magnitude of directivity required to get anything relevant. Even 53dB is very low, 60dB directivity is a minimum you could cross your fingers at, and then attempt measurements.
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Yea, his second last paragraph beginning "The other argument that has been made is how the reflections impact our perception of location" shows that he knows little to nothing about psychoacoustics & localisation & makes general & incorrect assumptions about masking, binaural hearing but he does leave the door open with "Of course, different frequencies will see different impedances in real speakers, thus the reflections will be different for different frequencies. This could cause the image to shift (vary) with frequency. Clearly it can get complicated... What is also clear is that transmission line effects can matter in speaker cables, though whether these effects are audible I can’t say."
Not a lot different actually. This was already discussed here several times.
it's sort of me telling Mark I honestly can't hear his reverb tails and it doe not matter to me or telling him they don't exist.
The way I read the huffing & puffing going on here is that there are a number of people telling JN that he is totally wrong both theoretically & experimentally which is far different to saying that the effect is insignificant & therefore inaudible.
Oh, was that what that circle looking thing was?? I thought it was that funny pattern on Spock's console..😀
For completeness, I would have shown not only test results for an open , but also short, and mismatch.
But that's just me.
But, then again, I would not try to measure an LCR exponential using a network analyzer, nor tried to use a smith chart as proof of something an analyzer was incapable of finding. How exactly do you plot an LCR exponential on a smith chart btw?
I would focus on the crux of the discussion, but again, that's just me.
Blast from the past, last time I used a smith chart was for stub tuning, nice to see one again..
AH, almost forgot...this statement of yours should be engraved in granite:
syn08 ""any TL has reflections at any frequency""
YOU ARE CORRECT!!!! Where is PMA when ya need him?
Now, let's stick to the regime of interest, the first 10 uSec or so of the step response.
And please, stop trying to create a straw man argument implying I said the cable is reflecting, I've always stated "mismatch between cable and load". Nice try however..
Jn
For completeness, I would have shown not only test results for an open , but also short, and mismatch.
But that's just me.
But, then again, I would not try to measure an LCR exponential using a network analyzer, nor tried to use a smith chart as proof of something an analyzer was incapable of finding. How exactly do you plot an LCR exponential on a smith chart btw?
I would focus on the crux of the discussion, but again, that's just me.
Blast from the past, last time I used a smith chart was for stub tuning, nice to see one again..
AH, almost forgot...this statement of yours should be engraved in granite:
syn08 ""any TL has reflections at any frequency""
YOU ARE CORRECT!!!! Where is PMA when ya need him?
Now, let's stick to the regime of interest, the first 10 uSec or so of the step response.
And please, stop trying to create a straw man argument implying I said the cable is reflecting, I've always stated "mismatch between cable and load". Nice try however..
Jn
Agreed. I suspect the underlying issue is that, if I am correct, all the cable fanatics would come out of the woodwork saying told ya so. Anarchy would reign. Our rule over the forum as the cable gods would come to an end...
So, do everything to challenge, discount, argue, such that the end results are never tested.
Or, could just be disagreement of a technical matter.. Sometimes the actual technical arguments are not easy to wrap your head around.
Cheers,
Jn
I'm about to give up; I can't decide if JN is deliberately playing ignorance, or if JN is attempting to shift the discussion focus.
How in hell do you want to plot a RLC exponential (time domain) on a Smith chart (frequency domain)?
And I thought we are not talking about step responses in a TL, that's a completely different kettle of fish. I just had earlier today the exchange below:
So please state clearly what are we talking about here.
Ah, almost forgot... yes, and for all purpose it is negligible in audio applications. simon7000 using 3000ft. of cable on a stadium is allowed to moan about, and Dan is allowed to claim he can hear these reflections, and then use his goop to alleviate them.
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Guys, what level of matching would be a good target for matching two toroids for the dual transformer coupler?
Jn
Jn
Welcome to the party, pal.
That is why I asked about the smith chart and plotting an RCL exponential, you can't.
So sit down take a breath, and read..
A step response test is used to see how fast a system can respond.
A cable with LC connected to a load R, given a step input, will have an exponential rise to final value determined by all three parameters. For the same LC, varying the load R will cause a variation in the exponential rise time.
Using a TL model with a step is viable as long as you do not wait too long, as then you have to include R and G (I hate mr G 😉 ). And, for the first 10, 20 uSec (roughly the ITD range of interest), the distributed LCR cable model produces the exact same response as a TL.
A speaker is never a single impedance throughout the audio range. As a consequence, the exponential rise time at any frequency will be dependent on the varying load. Unfortunately, we cannot separate the delay response by frequency using the step, all we can do is bracket the delay range based on what the cable would do into the various resistances the load presents.
My magnetic experience also tells me that the speaker impedance presented to the amp (through the cable) will be modulated by the speaker's acceleration, velocity, and position. That variation of impedance must exceed some value such that the ITD thresholds at specific frequencies are violated, otherwise the effect is inaudible.
I currently do not know how to measure the drive power induced impedance modulation caused by magnetic nonlinearity effects. I do however, contend with such at work, just not for speakers. Think of measuring the 2khz impedance of a driver while it is being pushed by a lower frequency, say 30 Hz. In addition to the magnetic forces being position and acceleration dependent, the coil inductance can change a factor of two(no shorting ring), the 2khz mag field is being dragged past the two conductive surfaces of the gap (and if present, a shorting ring inward but not outward) at velocity, and the compliance of the cone is being modified by the air pressure on it's surface. A rather complex set of variables and conditions.
So this is not a TL discussion per se, it is a discussion of magnetic nonlinearities impacting soundstage and how to test for that, derailed by some who are fixated on "a short TL cannot support reflections at any audio frequency". Thankfully, you stated otherwise, and yes, there has to be a mismatch...
Ps. Is .1% a numerically derived number, a rough estimate, or a guess? 22mH is 22 uH match, I will have to check the HP tomorrow. CB clearly wound his carefully, the winds are evenly distributed and tight. I can't test permeability, so could only use the HP.
Jn
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Poor Dan...he is the only constant on this forum.
Everybody gangs up on him...constantly.😀
Jn
Everybody gangs up on him...constantly.😀
Jn
Hey, I can polish turd stereo systems, I can make digital sound like vinyl, I can turn vinegar into wine, that's just routine. I laugh my a*** off every time you guys think you know all there is to know about electrics and magnetics and energies, I do know that I don't. I look forward to the day that I present to you guys the real results of my investigations, for you guys there will be joyful enlightenment and realisations, my reward is making the world a better place. Always remember "He who laughs last laughs best".
Dan.
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