This is only the first scenario, the following ones also uses it.
Take a closer look and you will see it. A Zobel is a series RC with an AC signal across it and that is what we have here, the red plot confirms that. It is not a filter perse' - otherwise it would continue its 6dB/Octave slope and yet above 100KHz it will be flatlining. That's what a Zobel does.
A series RCR with an AC signal across it, is still a Zobel as it is the same as RRC and the AC signal is developed across the two 3R3 resistors and cap. If the cap was placed after the resistors and the DAC was Vout (low Z), then the signal across the cap would decrease infinitely, and that would be a low-pass filter. Not the behaviour here.
I am not sure where you see inductance in the circuit? The sourze Z of DAC is theoretically infinite, hence the finite 750R means 100% feedback and no gain.
The 'opamp' used for the modeling was generic. That is all that was needed for our purposes.
Cheers, Joe
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Next one is Scenario 3 - should have been 2, but announced it in the wrong order.
3. "Current DAC into Step-Up Transformers
We are not going to dwell on the pros and cons of using Step-Up Transformer for I/V. Instead just simply explain the Zobel that is used here is in effect 'over-cooked' in a way that you would not normally do on an audio transformer.
Usually the I/V resistor is on the Secondary, I am not going into any endless discussion here what the I/V value should be (only that it will be lower on the Primary than if used on the Secondary and calculated by the turns ratio etc, the value 15:1 is only typical).
What we need to concentrate on is the R & C that forms a Zobel. Usually you would come to some kind of decision of the I/V resistance and then under normal circumstances, depending on the characteristics of the transformer, to get the response flat, particularly at 20KHz.
But we need to over-cook the Zobel so that it is not flat, but gives a final response similar to the Red plot is Scenario 1.
Let's say we use Secondary I/V resistor and use Sowter's calculation on their website, used here:
Quote:
HOW TO CALCULATE THE I/V RESISTOR: First calculate the secondary current (Is). This is given by the primary current ( Ip) multiplied by the inverse of the voltage ratio. If the output current pf the DAC is 4 mA p-p, Is = 4/12.8 = 0.27 mA p-p which is 0.27 / 2.83 = 0.094 mA rms. If we want to get 0 dBu (0.775V) at the grid (Vg) we need:
Rsec = Vg/Is = 775/0.094 = 8.2 kOhms (I would prefer lower than that).
End of quote.
Of course this also affects output at 0dBFS and in theory the lower the Z, the better, but also lower output. No free lunch I am afraid.
This use of step-up device is not my favoured option. But we do come down to calculate the Zobel, and I would first engineer a Zobel that maintain flat response at 20KHz. The whatever C was, increase by 50% or so, then adjust R to pull the response down by near -2dB at 20KHz. If that resistance ends up to low, then vary C until you manage to get the end target.
Now we come to a problem: How to restore flat response. Some who have done the above (I am not one of them), they basically have said "don't bother."
If the above is part of a USB DAC, then you do have a recourse to flat response, by using JRiver Media Center. Use the settings I suggested back in post #461 to restore flat response in the 64 bit Parametric EQ.
Repeat here:
Select: High-shelf
Frequency: 40000
Bandwidth (Q): 0.7
Gain: 4dB
Set Clipping: Off
In the above, IF you have set it to -1.3dB @ 20KHz, then enter:
Gain: 2.6dB (and so on)
As I said, I am not going to entertain any long discussion re the transformer topology, other than to say that the reflected Zobel back to the Primary, has the exact effect, and very audible indeed, with respect to the "Rasmussen Effect".
Cheers, Joe
PS: Note the ultra-sonic filtering is still done by the transformer, it is a bandpass device. The Zobel is only a modifier of the response, to a curve we have arrived at experimentally.
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3. "Current DAC into Step-Up Transformers
We are not going to dwell on the pros and cons of using Step-Up Transformer for I/V. Instead just simply explain the Zobel that is used here is in effect 'over-cooked' in a way that you would not normally do on an audio transformer.
Usually the I/V resistor is on the Secondary, I am not going into any endless discussion here what the I/V value should be (only that it will be lower on the Primary than if used on the Secondary and calculated by the turns ratio etc, the value 15:1 is only typical).
What we need to concentrate on is the R & C that forms a Zobel. Usually you would come to some kind of decision of the I/V resistance and then under normal circumstances, depending on the characteristics of the transformer, to get the response flat, particularly at 20KHz.
But we need to over-cook the Zobel so that it is not flat, but gives a final response similar to the Red plot is Scenario 1.
Let's say we use Secondary I/V resistor and use Sowter's calculation on their website, used here:
Quote:
HOW TO CALCULATE THE I/V RESISTOR: First calculate the secondary current (Is). This is given by the primary current ( Ip) multiplied by the inverse of the voltage ratio. If the output current pf the DAC is 4 mA p-p, Is = 4/12.8 = 0.27 mA p-p which is 0.27 / 2.83 = 0.094 mA rms. If we want to get 0 dBu (0.775V) at the grid (Vg) we need:
Rsec = Vg/Is = 775/0.094 = 8.2 kOhms (I would prefer lower than that).
End of quote.
Of course this also affects output at 0dBFS and in theory the lower the Z, the better, but also lower output. No free lunch I am afraid.
This use of step-up device is not my favoured option. But we do come down to calculate the Zobel, and I would first engineer a Zobel that maintain flat response at 20KHz. The whatever C was, increase by 50% or so, then adjust R to pull the response down by near -2dB at 20KHz. If that resistance ends up to low, then vary C until you manage to get the end target.
Now we come to a problem: How to restore flat response. Some who have done the above (I am not one of them), they basically have said "don't bother."
If the above is part of a USB DAC, then you do have a recourse to flat response, by using JRiver Media Center. Use the settings I suggested back in post #461 to restore flat response in the 64 bit Parametric EQ.
Repeat here:
Select: High-shelf
Frequency: 40000
Bandwidth (Q): 0.7
Gain: 4dB
Set Clipping: Off
In the above, IF you have set it to -1.3dB @ 20KHz, then enter:
Gain: 2.6dB (and so on)
As I said, I am not going to entertain any long discussion re the transformer topology, other than to say that the reflected Zobel back to the Primary, has the exact effect, and very audible indeed, with respect to the "Rasmussen Effect".
Cheers, Joe
PS: Note the ultra-sonic filtering is still done by the transformer, it is a bandpass device. The Zobel is only a modifier of the response, to a curve we have arrived at experimentally.
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Hey Joe, I've just recently found this thread, and once we get rid of the static, there is some great work here - well done.
To explain my interest - I have been helping a friend mod his OPPO 95. I have used a transformer output on my Cirrus Logic DAC (demo board) for many years and he wanted something simiar on his oppo. To minimise irreversible change to the OPPO we took the output from the IV converter and have put it this through a Lundahl 1527XL tx 1:1. (funny story - of course the preference was to take the signal before it went into the opamp, no-one wants an op amp in the signal path. But my pal could not find any output from the DAC. Very confused he was, there was an output from the the op amp so where was the output from the DAC? Of course he was trying to measure the voltage at the input of the op amp - the virtual earth). When we implemented the tranny he felt that there was a definite improvement, albeit there was still some grain in the music. So - we put a 1st order LPF across the secondary of the transformer and guess what - grain gone, only beautiful music.
Now, this thread has inspired me - its time to bite the bullet, and take the signal before the IV converter. And of course we will be implementing the Rasmussen capacitor, intuitively it is better to put this cap into the signal chain at the earliest opportunity and it is a more slegant solution compared to my LPF after the transformer. This will mean a bit more surgery - we can't just take the signal off the op amp input, we need to physically cut some tracks or desolder the op amp. But hey, it's Chris's Oppo, not mine. All care, no responsibility!!
So we now have a sabre DAC, and a 1:1 transformer. I assume that we have to set this up in voltage mode, as there is no step up as would be required for a current DAC. Do i follow Scenario 5?
Thanks for your great work here, I admire your patience to get to this point.
To explain my interest - I have been helping a friend mod his OPPO 95. I have used a transformer output on my Cirrus Logic DAC (demo board) for many years and he wanted something simiar on his oppo. To minimise irreversible change to the OPPO we took the output from the IV converter and have put it this through a Lundahl 1527XL tx 1:1. (funny story - of course the preference was to take the signal before it went into the opamp, no-one wants an op amp in the signal path. But my pal could not find any output from the DAC. Very confused he was, there was an output from the the op amp so where was the output from the DAC? Of course he was trying to measure the voltage at the input of the op amp - the virtual earth). When we implemented the tranny he felt that there was a definite improvement, albeit there was still some grain in the music. So - we put a 1st order LPF across the secondary of the transformer and guess what - grain gone, only beautiful music.
Now, this thread has inspired me - its time to bite the bullet, and take the signal before the IV converter. And of course we will be implementing the Rasmussen capacitor, intuitively it is better to put this cap into the signal chain at the earliest opportunity and it is a more slegant solution compared to my LPF after the transformer. This will mean a bit more surgery - we can't just take the signal off the op amp input, we need to physically cut some tracks or desolder the op amp. But hey, it's Chris's Oppo, not mine. All care, no responsibility!!
So we now have a sabre DAC, and a 1:1 transformer. I assume that we have to set this up in voltage mode, as there is no step up as would be required for a current DAC. Do i follow Scenario 5?
Thanks for your great work here, I admire your patience to get to this point.
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As I said, the inductance appears at the virtual ground. It is caused by the finite bandwidth of the opamp. For your simulation to have any meaning at all the opamp must have finite bandwidth, although it may be ideal in all other respects. If you don't know what this bandwidth is then you can draw no conclusions at all from your simulations. I assumed 50MHz, but it could be lower than this - which would make the inductance larger.Joe rasmussen said:
Of course, an inductance after the 3.3 resistor will cause a rise at HF which may counteract the fall caused by the 1uF cap. All I am saying is that before you postulate some unknown effect in the DAC output you first have to consider all the known effects in the rest of the circuit.
If it turns out that circuit theory is not welcome here then I will take your advice.scott wurcer said:
Sorry, but I can't see the point you are making, or more to the point, how it relates to the discussion.
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Next one, this is my preferred approach with "Current" type DACs.
2. "Current" DAC into Low Impedance Passive I/V
Passive I/V into twin 3R3 resistors and using 1uF. Same values as before. The OTA is a "Operational Transconductance Amplifier" with no feedback. There are a number of those, OPA660 and OPA860/861 come to mind. As slew rate free as you can get.
With tube circuits I have seen 33R resistors, this will generate +20dB and be suitable for tube input with gain. The cap would then need to be scaled to 0.1uF - again the Zobel shape will be the same.
Now the question arises, can we correct this to flat response at 20KHz? Again, some may say "don't bother" and if this is a USB DAC, use JRiver again to EQ the response flat.
Another possible way: I did some modeling of the OTA and this worked - I have not physically built this, but all indication is that carefully tweaked/adjusted, this can return a flat repose:
I was able to see that I could source 120mH encapsulated choke rated at 8mA and DCR of 70 Ohm, these are available. Modeling show those values above do work, but may be needed to scaled it to get the desired gain or output level relative to 0dBFS.
Once again, we see evidence that this is also a Zobel rather than a filter. This should be expected since we have the twin 3R3 terminated into virtual earth in Scenario 1. (theoretical zero Z) and here again similarly, they are physically grounded, so the response, being about -2dB at 20KHz and about half a dB down at 10KHz, with the same values as before. Here is the plot:
There is that shaped curve/plot. Definitely a Zobel. Of course, in real life there is likely to be added filtering at a point further down the chain, so the final filter cumulatively is a proper low-pass, but the 'effect' directly on the DAC pins/output is not really low-pass, but a Zobel.
Again, we shall see this is the case when we get to Scenario 5. "Voltage" DAC into 1:1 Transformer, where again it is the transformer that does the filtering and the response is an actual Zobel on the Secondary.
Cheers, Joe
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2. "Current" DAC into Low Impedance Passive I/V
Passive I/V into twin 3R3 resistors and using 1uF. Same values as before. The OTA is a "Operational Transconductance Amplifier" with no feedback. There are a number of those, OPA660 and OPA860/861 come to mind. As slew rate free as you can get.
With tube circuits I have seen 33R resistors, this will generate +20dB and be suitable for tube input with gain. The cap would then need to be scaled to 0.1uF - again the Zobel shape will be the same.
Now the question arises, can we correct this to flat response at 20KHz? Again, some may say "don't bother" and if this is a USB DAC, use JRiver again to EQ the response flat.
Another possible way: I did some modeling of the OTA and this worked - I have not physically built this, but all indication is that carefully tweaked/adjusted, this can return a flat repose:
I was able to see that I could source 120mH encapsulated choke rated at 8mA and DCR of 70 Ohm, these are available. Modeling show those values above do work, but may be needed to scaled it to get the desired gain or output level relative to 0dBFS.
Once again, we see evidence that this is also a Zobel rather than a filter. This should be expected since we have the twin 3R3 terminated into virtual earth in Scenario 1. (theoretical zero Z) and here again similarly, they are physically grounded, so the response, being about -2dB at 20KHz and about half a dB down at 10KHz, with the same values as before. Here is the plot:
There is that shaped curve/plot. Definitely a Zobel. Of course, in real life there is likely to be added filtering at a point further down the chain, so the final filter cumulatively is a proper low-pass, but the 'effect' directly on the DAC pins/output is not really low-pass, but a Zobel.
Again, we shall see this is the case when we get to Scenario 5. "Voltage" DAC into 1:1 Transformer, where again it is the transformer that does the filtering and the response is an actual Zobel on the Secondary.
Cheers, Joe
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If you are trying to model a circuit which includes C R and L then you may draw incorrect conclusions if you ignore the L. You show HF behaviour which may be consistent with the presence of L, yet you seem to deny that there is any L present.Joe Rasmussen said:
Have a think about how a virtual ground is formed by an opamp with feedback. Then think about what that virtual ground would look like if the opamp (like all real opamps) has finite bandwidth from a dominant pole. You will find that a virtual ground is never a short, rarely a low value resistor (except at DC), but usually a low value inductance. This fact can be ignored in most audio circuits, but not in the case of I/V arrangements for a current output DAC.
I hope that there is a realisation of the hours that it has taken to present this information.
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I don't think I am drawing any incorrect conclusions and it baffles me why you would think I was.
BTW, I don't even use virtual grounds, so it's all a bit mute. Ask those that do, but for now that is not central to the discussion at hand, as this is not about modeling an opamp, but rather what is central is a passive network added before the I/V and the I/V virtual earth is but one scenario to cover. So, this topic is not about modeling opamps, it is also about using transformers and so on, to achieve a desired and somewhat unusual 'effect' right on the DAC's outputs and how/what triggers it. It seems to be a Zobel network rather than a low-pass filter and indeed its primary effect is entirely below 100KHz, that is KiloHerz and not MegaHertz - so inductance may be an exotic conversation to be had under other circumstance, but not in this instance.
By the time I am finished, there will be FIVE scenarios presented, opamp I/V is but one of them. I ask please, that they be viewed in an overall context, and then you will see why I am not drawn into your opamp discussion for now. Later perhaps, no problem.
Cheers, Joe
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About banning yourself?
Maybe it would help if I should set the record straight: Scott's reaction seems to be based on a misunderstanding of my mentioning the name of Keith Eichmann, the inventor of the famous RCA Bullet Plug - it seems he thinks I have slighted Eichmann or Scott thinks that Eichmann is some kind of charlatan. He is yet to reveal to me which is his position and he has left me confused about that, but I can say that Keith Eichmann is a friend and I drove up to Queensland weekend before last and spent quite a bit of time with him. This is not yet widely known, that a company he and Rob Woodlands started up in 1998, called ETI (owned by Rob), has fallen into the hands (third) of owners who have ceased to pay Keith royalties. That is a statement of fact. I now have to be careful as I cannot make any comment that sounds like an accusation, or they (and they very likely know me and because I use my real name), I could get sued. So for now I can only say there is a dispute where both sides claim to own the IP and one side has refused to offer proof and saying "sue us' and 'we are not paying you any more.'
We can only ask questions, but I can say (and I have samples here) that Keith's new Bullet Plugs are a big improvement over those from ETI. You can't be sued for having an opinion, only from making accusations - and I ask only questions. And I don't have any financial stake in this, only a sense of right and wrong - which is Scott's byline/signature line, if you look. "...while the question of what is right and what is wrong has seemed all-important."
True!
This story needs to be known about more widely, we live in a world where we still have 'free press' where we can ask 'questions'.
So don't ban yourself, OK?
Cheers, Joe
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Correct me if I have misunderstood you, but you appear to be saying "Look, I add a capacitor but the effect is as though I added a CR instead." I am just pointing out that in the case of the current output DAC fed into a virtual ground the actual circuit is not as simple as you appear to think, yet this is perhaps the simplest one of your examples and so perhaps the best one to fully explore what you are saying.Joe Rasmussen said:
The incorrect conclusion you may be drawing is that the 'C acts like CR' is due to some effect in the DAC output. If so, of course, you can discover what it is merely by examining the model used for the DAC in your simulation. The cause of the effect must be in the model. If the DAC model is merely a perfect current source then we can be absolutely certain that it does not produce the observed effect. Hence we need to look elsewhere, and the obvious place is the opamp model.
This topic is unavoidably about modelling opamps (and everything else in the circuit). You introduced the virtual ground circuit and said that the Effect can be seen there. If the Effect in that circuit can be explained by simple circuit theory then maybe it can elsewhere too. When tackling a potentially difficult problem it is always best to tackle it in the simplest possible situation. Adding in transformers etc. just muddies the waters as we know that they are difficult to properly model.
Are there any advanced TINA, SPICE, etc opamp models that capture these complex and dynamic input parameters?
No need for an advanced model. A simple opamp modelled as an integrator or a high gain low pass filter will exhibit this inductive virtual ground when used in the inverting configuration. For some reason this fact does not seem to be well known, as most people just assume that the virtual ground is equivalent to a vanishingly small resistor.
Not exactly - if you go back and see previous posts, this has to do with the DAC itself, this has to do with some kind of load sensitivity of delta-sigma DACs, where shaping its sub-100KHz response means we can find a sweet-spot that means a non-flat response (one penalty trade-off that can be recovered for the most part) and what options we then have to recover that flat response if so desired, as some are just happy to leave it.
We have also established that it is the Delta-Sigma Modulator (or SDM) that is at the heart of this - this was established by using a discrete (non-IC) straight 5.6MHz DSD Modulator without any low-bit elements (no algorithms here) and yet putting a Zobel network on this Modulator output that shaped the response being flat @ 1KHz, -0.5dB @ 10KHz and -2dB @ 20KHertz, that is very clearly audible. And so they are with every D-S DAC we have tried so far, both "current" and "voltage" types. So the SDM operating point takes front and centre in this discussion and the effect can only be triggered using passive circuitry.
It has not been kept any secret that the 'effect' is not fully explained, but rather that the proof that the 'effect' actually exists. We don't always know why something caused a cancer, but we find ways to treat it and the patient, while research goes on as to the original cause(s).
So while I understand you may want to have a discussion of opamp I/V, it is not really on topic here - but you should take a look at the Hawksford paper (click for download PDF) on this subject, where opamp misbehavior leads to jitter-like misbehavior in "current" I/V - no mention of inductance though and I am the last person to pick an argument with Hawksford. 😀
So please keep in mind the topic is called re "Rasmussen Effect" and is about the SDM before any opamps or even totally passive post-DAC, transformers etc. The FIVE Scenarios cover most bases I can see.
Cheers, Joe
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But I think many of us are interested in finding out an actual explanation - which is why we ask questions that might occasionally seem irrelevant from your point of view, but helps us understand more clearly what effects have been accounted for and what haven't.
Theoretically being the key word here. For the PCM1794, the impedance of the current outputs is known to be quite low (under 1K apparently) and varying wrt frequency. It's discussed in this thread, with posts 148-149 being the more relevant.
Ok, as far as I understand, the output of this DAC is PDM..ie Pulse Density Modulation.
The output pins swing (balanced operation) between B+ and B- in opposing phase/polarity.
According to the output resistance of the DAC output pins stages, adding a value as high as 1uF between the output pins will cause slew rate reduction of each of the individual outputs.
As a primary effect, this should not cause change in the differential value of the output.
There are secondary effects however.
The output impedance of the individual outputs stages cannot be guaranteed to be perfectly matched, so this is a cause of differential error according to the loading caused by the 1uF cap which translates to HF rolloff in the differentially recovered/filtered AC audio output.
Further, this 1uF cap is (variable repetition rate) effectively commutated between the +/- supplies, and is of high enough value to cause supply modulation and excitation of supply ringing/resonance.
This reinforces Joe's assertion that Supercaps (40 ohms internal R) across the individual supplies are required.
These supercaps provide substantial supply damping down to extra low frequencies.
Joe's observation that the 1uf value is not absolute and is subject to 'sweet spot' value selection further reinforces the above statements.
Reduction in the slew rate of the individual outputs will reduce longitudinal feed through of HF harmonics across the differential recovery/filtering stages.
This reduction in slew rate will also allow reduction in amplitude errors in the filter stage opamps, and consequent IM products.
The overall -1.5 dB droop at 20kHz, which translates to -1dB at 10 kHz can also cause a subjective 'softening' of the output, which can be agreeable.
Lessening of longitudinal feedthrough induced noise will also cause lessening of slew induced IMD products in downstream amplification.
I have no doubt that the 'Rasmussen effect' can bring subjective improvements, but perhaps not for the reasons that Joe thinks.
Dan.
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I think opamps are a not good solution in post-DAC circuits, and I am not alone. But I cover opamps in my FIVE scenarios for completeness, right?
Eventually, when posting the next Scenario, then all FIVE will speak for themselves - and since all bases are covered, there will be no excuse for at least trying one of them, whether opamp or not - as opamps is not really the issue, but a passive network on the output of a delta-sigma modulator (SDM) has a significant impact on the sound of the DAC, whether or not an opamp is used, it is very obvious.
Cheers, Joe
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Ah Dan, but you don't know what I think.
Look, my attitude is straight forward, let the rain fall where it falls, let the solution be what it is. It matter nothing what I think, but as you speculate, so do I, and your speculation in no way contradict anything I have said here or with many others privately.
Enjoyed our discussion on the phone the other day.
Cheers, Joe
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