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PostPosted: Wed Mar 16, 2005 4:57 am 
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I?ve been reading through some old DAC-related threads, and found some folks making a rather surprising claim that op-amps are unsuitable for audio DAC I/V conversion. The thread where this is mentioned is called ?Best opamp for I/V conversion? (DAC)?, over at ?the other place?. The justification given for the statement about op-amps was that an article by Barrie Gilbert, which was unavailable on the web at the time, proves the point. This article, ironically titled ?Op-amp Myths?, had been removed from the web a while back. In a recent web search, I found the article again, along with another Gilbert article called ?Are Op-amps Really Linear?? which has already been the subject of another very long thread about PIM distortion. These articles can be found here http://archive.chipcenter.com/analog/c014.htm and here http://archive.chipcenter.com/analog/c007.htm.

The quote that apparently led to the conclusion that op-amps are unsuitable for audio DAC I/V conversion is as follows:

(Begin Gilbert's words) ??consider an OPA used to convert the output current from a DAC to a voltage, that is, the classical transresistance function. Let the feedback resistor that scales this function be RF. Now model the op amp as an integrator -- which you really must -- and consider the voltage swing at that "virtual ground" in response to a current step. To begin with, the output from the op amp doesn't move at all; its initial response is ramp-like, as the amplifier performs the operation VOUT = -VIN/sT1. But what is VIN in this case? Well, it is simply the DAC output current step, call it IDAC, times the feedback resistor RF. For a typical case of IDAC = 2 mA, RF = 5 kohms (for a final output of 10 V) the input step is also 10 V!? (End Gilbert's words)

And yet Elso, in this post http://www.diyaudio.com/forums/showthread.php?postid=397071#post397071 measured the voltage at the inverting input of the op-amp at his DAC output and found it to be 10 mVp-p. So there?s three orders of magnitude difference between Elso?s measurement and Gilbert?s calculation of the same quantity. This begs a couple of questions:

1.) What?s different (if anything) about the conditions of Gilbert?s calculation and Elso?s measurement?
2.) Do these differences in conditions account for the vast difference between Gilbert?s predicted results and Elso?s actual results?

Fortunately, the answer to (2) is ?yes?, assuming Elso?s circuit is similar to that recommended by Burr-Brown/TI in their DAC data sheets. To see this, I?d like to determine two things:

1.) What?s the worst-case current step of the DAC given that the digital signal was produced using an A/D whose analog input was band-limited to 20 kHz?
2.) Given that DAC current step and the real-world component values and op-amps of the manufacturer?s recommended application circuit, what?s the worst-case differential input voltage to the DAC op-amp (between pins 2 and 3)?

For this analysis, let?s assume a Burr-Brown PCM-1794 DAC with an output stage as recommended in the data sheet in Figure 24.

Gilbert?s analysis assumes a full-scale jump in the DAC bit count. Is this reasonable given the band-limited nature of the analog circuitry prior to the A/D? Jocko asked that same question here http://www.diyaudio.com/forums/showthread.php?postid=401769#post401769. Boholm answered in the following post that a 22.05 kHz full-scale sine wave, sampled at the peaks, will make that happen. It turns out that a sine wave at exactly one-half the sampling frequency doesn?t meet the Nyquist criterion. To see this, assume the samples are shifted by a quarter of a period from the peaks. The first and all subsequent samples will be at the zero crossing, so it can?t be reconstructed. But suppose we take a 20 kHz sine wave that?s full-scale, and assume the zero crossing of the sine wave is exactly half way between the sampling instants, and the sine wave is rising during that time. In this case, the peak-to-peak digital value will be:

Sample step = sin(pi * 20 / 44.1) * full scale, or
Sample step = 0.9894 * full scale.

This might as well be full scale. This is beginning to look bad. But what?s the effect of an oversampling digital filter? The first sample above for the rising sine wave is very near the negative peak, and the second near the positive peak. For an oversampling digital filter, this single step will be split into N steps, and since we?re assuming a PCM1794, N will be 8. What will the intermediate samples look like? Well, if the digital filter is doing its job, those samples should look like a reconstruction of the original sine wave, since the shape of a sine wave is invariant to filtering. Since the sine wave looks approximately like a line in this interval, it becomes clear from a graphical argument that the step size of the DAC will be reduced by a factor of approximately N, the oversampling ratio. So for 8x oversampling, we?re looking at a worst-case DAC step of 1/8 of full scale for a digitized full-scale 20 kHz sine wave. A non-oversampling DAC is at a disadvantage here.

This is an improvement, but not nearly enough to account for the discrepancy between Elso?s measurements and Gilbert?s calculations. So what else is different? Looking at the application circuit of the PCM1794 in Figure 24 of its data sheet, you can see that there?s a capacitor of 2200 pF in parallel with the 750 Ohm feedback resistor. Does this capacitor make a difference? To see, look back at Gilbert?s assumptions. He?s assuming the feedback network is just a resistor. A large current step causes a large differential voltage to appear at the op-amp input, because the voltage across the feedback resistor changes almost instantaneously due to the current step. But in the case of the application circuit, the capacitor prevents this instantaneous voltage change. In the ideal case, the I/V converter acts as a low-pass filter with a time constant of 750 Ohms and 2200 pF. A typical technique for determining whether the circuit will go into slew rate limiting is to compute the output response assuming linear operation, calculate the maximum time rate of change of the output, and if that rate of change is much less than the slew rate, the assumption of linear operation was a good one. Let?s proceed in that way and look at the deviation of the output from its DC value under an ideal op-amp assumption. That becomes:

v_out(t) = I_DAC * R * (1 ? exp(-t / (R*C))

Taking the derivative at t = 0 to get the maximum value, we get:

dv_out / dt max = I_DAC / C.

The current I_DAC is 7.8 mA. For the non-oversampling case, this results in a slew rate of 3.55 V/us, and for the 8x oversampling case, the slew rate is 0.44 V/us. The non-oversampling case is enough to produce significant distortion in a mediocre op-amp, but the oversampling case is out of trouble for a good op-amp.

Now let?s look at how to compute the differential input voltage. The open-loop transfer function A(s) of the op-amp is:

A(s) = A0 * w0 / (s + w0)

Approximating this as an integrator, we get:

V0(s) = Vi(s) * A0 * w0 / s

Solving for the input, we get:

Vi(s) = s * V0(s) / (A0 * w0)

In the time domain, this is:

vi(t) = (1 / (A0 * w0)) * d/dt { v0(t) }

That is, the input voltage is the derivative of the output voltage, divided by the gain-bandwidth product in radians/sec. The output voltage rate of change must be in Volts/sec. This voltage is the peak voltage for an output step in only one direction. The peak-to-peak voltage will of course be twice that above.

Let?s compute the peak-to-peak input voltage for the application circuit of Figure 24 in the TI data sheet. Since I don?t know what the gain-bandwidth product of the 5534 is when an external compensation cap of 22 pF is used, I?m going to ?arbitrarily? assume the gain-bandwidth product is 14 MHz. Plugging this number into the formula above and multiplying by two to get p-p values, and assuming the 8x oversampling case we get:

Vp-p = 2 * 0.44E6 / (2 * pi * 14E6) = 10 mV p-p

Now you know why I picked 14 MHz :-). With 8x oversampling, a feedback capacitor of 2200 pF and a gain-bandwidth product of 14 MHz in the I/V op-amp, the differential input voltage will be about 10 mV p-p for a full-scale 20 kHz sine wave. This is what Elso measured, and there?s nothing unreasonable about this number at all.

I?d have to conclude from this that the claims of op-amps being unacceptable for audio DAC I/V conversion are greatly exaggerated, if not outright false. This assumes the I/V converter has a sufficiently large feedback capacitor. Note that I?m not saying that improvements can?t be made with discrete circuits, but rather that they are not strictly speaking necessary.

This brings up another point, associated with Jocko?s experiences with current feedback op-amps as DAC I/V converters. Current feedback op-amps will oscillate with a feedback capacitor, and therefore can?t see the benefit of this configuration and the reduced output time rate of change that it brings to voltage feedback designs. The current feedback op-amp output will be forced to change very rapidly, which is completely unnecessary considering that the final output must be low-pass filtered anyway. This results in transients of current at the inverting op-amp input, giving unnecessary stress on the op-amp. In fact, the worst situation I can imagine is a non-oversampling DAC feeding a current feedback op-amp.


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PostPosted: Wed Mar 16, 2005 5:44 am 
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Maybe we can have one of those "more technical discussions" that we hoped would take place here, without getting pooped on by the usual crowd from diya.

Ok........let us assume that a discrete circuit.......without feedback will work better........just for now. I claim that it does. Charlie Hansen will back me up. OK, big deal.

Sure an op-amp will obviously work, but how good? I agree with your points about the digital filter. But about
current-feedback, I disagree.

For those who may have forgotten..............I do not like "current-feedback". (The first guy who kvetches that it really isn't current-feedback is going to get booted off.) It did not matter if it was for an I/V stage, or a power amp. Likewise, it did not matter if it was an op-amp, or discrete. So, let's not go into what it sounds like and why.

Here is something that we can kick around, and Andy can do some number crunching to test this idea.

The guys that used to be Enlightened Audio......in Fairfield, IA.......wrote some advertising stuff about why current feedback did not work. It had to do with settling time, and thermal tails in the silicon. If you look at the settling time, it is not good for 16-bit operation, more like 10-12 bit operation. It has been over 12 years, the details evade me. But they made a convincing argument that conventional voltage feedback (integrator style I/V) was the way to go. Only natural, they used '553x OPAs.

So.....your first assignment is to investigate that, so we can put the current-feedback part to rest.

Elso used a 1 KHz tone, which I conclude means a sine wave. Charlie is obviously refering to a square wave. So, maybe there lies the difference.

The input Z of one of my thingies is not zero, but whatever number it is, it is constant. The virtual ground of the integrator will rise with frequency. So there is one possible cause. There is also the possibility that the input Z amy move around with large step inputs, as the loop tries to compensate, due to time lag. I dunno..........feedback is too hard for hillbillies like me to understand. Open loop is easier, and it sounds different. Therefore, according to the First Rule of Audio, it has to be better. The Three Rules of Audio

Jocko


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PostPosted: Wed Mar 16, 2005 6:16 am 
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Okay, I propose "The sixth rule of audio". That should be "There are not three rules of audio, there are five."

More later, but not until after work tomorrow...


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PostPosted: Wed Mar 16, 2005 7:19 am 
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Hi Andy, I did this measurement as Charles Hanson said there was a large voltage to measure. I can repeat it with a large square wave. But I am not a measurement guy. For me it sounds just fine with an OPA627BP which is kind of funny as this is a very expensive opamp combined with a very cheap DAC(TDA1543).
The opamp used is not the whole story. Also crucial to good sound is bypassing, powersupply scheme for opamp & DAC, quality of IV resistor and feedback cap and output buffer. Even the transformer for the DAC matters and I am now using a 100Watt type that just fits the case.
I also tried Pedja's idea with the AD844 and a huge pile of other opamps including current feedback types.
I am now sure that the pleasing results I have will not satisfy Jocko as we have very different systems and music we like. For me no Frank Zappa but Scarlatti. I like my Khorns, Jocko hates them. [No Fred, Nina Hagen was a youth sin]
Audio is a funny universe reigned by Jocko's laws. Chris Owen has a Ikea foot stove with a DAC tucked away in it. He is also using an opamp as IV but the AD opamp (AD8610) I do not like and the DAC (TDA1545) I do not like either. Yet his DAC toy is adored in some circles and selling well.

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PostPosted: Wed Mar 16, 2005 8:10 am 
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Why do you think that I don't listen to Scarlatti? Last time that I checked, he isn't French.

(Guess I need to ban myself for the rest of the day now.............)

BTW..........the universe is even more strange if you can find the "File 13" link. Uh, huh-huh.

Jocko


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 Post subject: Scarlatti and File 13
PostPosted: Wed Mar 16, 2005 8:32 am 
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Jocko Homo wrote:
Why do you think that I don't listen to Scarlatti? Last time that I checked, he isn't French.

(Guess I need to ban myself for the rest of the day now.............)

BTW..........the universe is even more strange if you can find the "File 13" link. Uh, huh-huh.

Jocko

Jocko, Just a wild guess actually......
He is Italian just like you!
Love to see the File 13 link.

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PostPosted: Wed Mar 16, 2005 3:08 pm 
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Hmmmmmmm............you might be right.

You will have to find it yourself. You are starting to sound like a newb over at diya......."oh, please, jocko, i your good diy buddy........i need for you to do this for me........"

Here we are........12 hours later, and already we are filling this thread with our usual array of inside jokes while Andy slaves away at his job. Maybe I really should ban myself for the rest of the day.

Jocko


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PostPosted: Thu Mar 17, 2005 3:17 am 
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Okay, I went back through my previous post and realized it was pretty verbose. You guys probably fell asleep reading it. So I thought I'd summarize it and also add a couple of pictures.

1.) Gilbert's analysis of the I/V says that for an instantaneous step of current into the I/V, the op-amp differential voltage will reach a peak value of Istep * RF, where RF is the feedback resistor. For a full-scale cuttent step, this will usually result in hard slew rate limiting as there will be a large voltage across the differential input.

2) Data book circuits have a capacitor in parallel with RF to combine filtering with I/V. This greatly reduces the peak differential input voltage for an input that's a step of current. My previous post calculated a peak input voltage of 5 mV (10 mVp-p) assuming the following:

a) An op-amp with 14 MHz gain-bandwidth product, a feedback resistor of 750 Ohms, and a feedback capacitor of 2200 pF.

b) DAC is a 1794, providing a current step of 7.8 mA / 8, or 0.975 mA. The factor of 8 is the reduction of the maximum possible current step due to the 8x oversampling.

I show a schematic below, with a plot of the differential input voltage vs time for a current step of 0.975 mA. The op-amp is modelled as an integrator using a SPICE controlled voltage source and Laplace expression. The (s+1) in the denominator is from SPICE not liking the infinite DC gain of an integrator. So this is really an open loop BW of 1 rad/sec. The number 87.965e6 is just 2pi times 14 MHz. This plot is without the capacitor, and shows a differential input voltage (the voltage at the "Diff" node) of 700 mV peak. That's enough to rail a BJT input stage with no degeneration.


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PostPosted: Thu Mar 17, 2005 3:22 am 
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Now here's the plot with the capacitor. The peak input voltage is close to the previous calculation of 5 mV. That's a 140x reduction in the differential input voltage from the no-capacitor case. That, along with the 8x reduction from oversampling gives the 3 orders of magnitude difference between Gilbert's gloom and doom, and Elso's measurements. For a negative-going current step, the peak differential input voltage will be -5 mV, resulting in a 10 mVp-p voltage. Same as the previous calculations.


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PostPosted: Thu Mar 17, 2005 5:48 am 
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Ah, but.........

You are using a modern DAC. The old ones only did +/- 1 mA or so.........+/- 1.6 mA I think for the dreaded TDA1541. The values of RF where much higher. And it was 4X at best for that part. (And even worse........Philips put a zero in the transfer function of the o/s filter to cancel out one of the poles in the analog stage. Great........much RF junk into the front end of the integrator!)

Anyway............good reason to use higher order o/s, and modern DACs.

Keep up the good work, and we will try to keep the THD level down while you are at work.

Jocko


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PostPosted: Thu Mar 17, 2005 6:54 am 
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Andy,

Thanks for finding those links. Barrie Gilbert is a pretty smart cookie, and I had been kicking myself for not saving the web pages.

I liked your thorough analysis, and even made it *almost* all the way through the first post without falling asleep! :zzz: :zzz: :zzz: :mrgreen:

It seems that on paper adding a feedback capacitor in parallel with the feedback resistor of an op-amp based I-V converter can sidestep some of the worst problems involved in using an op-amp in this location.

Of course, in practice, things may be a bit different.

For starters, try putting some inductance in series with the feedback capacitor of your simulated circuit. For a good SMT part you are probably looking at something around 10 - 20 nH or so. For a small leaded part (such as a 5 PCM Wima), something on the order of 30 - 50 nH would be more realistic. You should also add in some inductance for the associated traces. Somewhere between 10 - 20 nH per inch is about right depending on the thickness of the PCB and the presence (or lack thereof) of a ground plane. You will also want to add a resistor for the ESR, maybe around 0.5 ohm for starters. I have no idea how much difference these parasitic elements will make, but it should be interesting to see.

Next, your simulation has the far end of the feedback cap tied to the output of an ideal integrator. You are much more experienced with simulations than I am, but I would expect that the inductive output impedance of a real op amp would mean that node won't be "nailed down". It might be interesting to use a more accurate model for the op-amp and see what happens.

Then there is the problem of the capacitor itself. It's pretty tough to find one that doesn't screw up the sound. When I built my first Leach amp in the late '70s, I was always underwhelmed with its sound quality. Finally after a couple of years I pulled out the capacitor in the passive LP input filter (intended to keep out-of-band signals from generating TIM, kind of like the situation we are currently discussing). The difference it made was shocking. All of a sudden this amp sounded like the great amp I had heard other people build. At the time I attributed it to the ability of the human ear to be influenced by the presence of ultrasonic signals (I think the filter had a 35 kHz pole). But later I realized that the problem was actually because the capacitor I had chosen was a ceramic unit (the capacitor articles in Audio magazine came out a couple of years later).

It just seems silly to me to use an op-amp that will *for sure* be overloaded if any high-frequency signals reach it, and then put it in a place where the fastest signals in the entire audio chain are present, and then hope you can keep things happy with a capacitor.

Besides, designing audio with op-amps is like baking deserts with Betty Crocker mixes.

Edit -- Andy, I thought you lived in San Diego, but your icon now says Colorado. Why don't you come up to the Ayre factory some time and do some listening?


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PostPosted: Thu Mar 17, 2005 4:05 pm 
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35kHz ... wouldn't that start affecting the phase-shift at 3.5kHz? Perhaps it smeared the harmonic integrity of the signal a bit.


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PostPosted: Fri Mar 18, 2005 3:11 am 
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Jocko Homo wrote:
You are using a modern DAC. The old ones only did +/- 1 mA or so.........+/- 1.6 mA I think for the dreaded TDA1541. The values of RF where much higher. And it was 4X at best for that part. (And even worse........Philips put a zero in the transfer function of the o/s filter to cancel out one of the poles in the analog stage. Great........much RF junk into the front end of the integrator!)


I was pretty surprised at how much current the PCM1794 puts out. Not only is it 7.8 mA p-p, but the peak current is more than 10 mA! I've shown the graph below. That's getting into BUF634 territory if an op-amp is used. BTW, the current I showed in my sim is 1/8 of the p-p current - it wasn't intended to show a full-scale step. But with no feedback capacitor, the idealized theory predicts the peak differential input voltage with a DAC step of Idac is Idac * Rfb. So I think it's just a matter of what output voltage is chosen, and the same voltage spike could happen with low Idac, high Rfb or high Idac, low Rfb.

Charles Hansen wrote:
It seems that on paper adding a feedback capacitor in parallel with the feedback resistor of an op-amp based I-V converter can sidestep some of the worst problems involved in using an op-amp in this location.

Of course, in practice, things may be a bit different.


Actually, I approached the problem from the opposite direction of what you're saying. After seeing the post with Elso's measurement results that indicated no problem whatsoever in practice, and contrasting those results with Gilbert's "on paper" prediction of gloom and doom, I felt like I had to find some explanation for this. The explanation is of course that the circuit Gilbert analyzed is different from the actual circuits in use in a fundamentally important way. It appears that Gilbert was thinking in terms of a more general high-speed data acquisition system, rather than audio in particular.

I agree with your concerns about the capacitor modeling, and I'm quite sure that modeling its inductance would result in a larger predicted differential input voltage. My purpose for making the sim so simple was first to make the assumptions about the op-amp the same as Gilbert's (by just assuming the op-amp OL response is a simple integrator). Secondly, I'm a strong believer in Hamming's motto, "The purpose of computing is insight, not numbers". Simple models help give insight, while more complex models are more accurate, but often at the expense of insight. When one attempts to answer the question "Can I account for three orders of magnitude difference between a theory and a measurement?", then utmost accuracy takes a back seat to understanding of the fundamental ideas.

I also agree with your concerns about capacitor quality in filter circuits. The DAC output has to be filtered in some way anyway, so this is a concern for any topology of analog DAC output circuitry. I don't think leaving the output unfiltered is a viable solution, but I don't think that's what you're advocating either.

Charles Hansen wrote:
It just seems silly to me to use an op-amp that will *for sure* be overloaded if any high-frequency signals reach it...


That statement needs qualification before the "for sure" label can be put on. Namely, what's the frequency and what's the signal level? I could give examples, but I'm sure you know what I mean.

Charles Hansen wrote:
...and then put it in a place where the fastest signals in the entire audio chain are present, and then hope you can keep things happy with a capacitor.


I guess there's just a difference of opinion here. My conclusion is "no problem given a proper design". It appears to me that you're characterizing the standard technique of using a simple active low-pass filter here as a hack. I'd say that, given an op-amp is to be used in this application, not using an active low-pass filter here is a hack, for reasons already described.

Charles Hansen wrote:
Andy, I thought you lived in San Diego, but your icon now says Colorado. Why don't you come up to the Ayre factory some time and do some listening?


I used to live in Orange County, CA and commuted 35 miles each way to an area of LA that's right near the LA airport. This past summer, I moved to CO. I live in Louisville, very close to Boulder. It is just beautiful out here! I would love to come out and visit. Thanks very much for the offer!


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PostPosted: Fri Mar 18, 2005 3:54 am 
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Charles Hansen wrote:
It just seems silly to me to use an op-amp that will *for sure* be overloaded if any high-frequency signals reach it...


Ack, ignore my previous response to this! It's too late to edit it now. What you're saying I think is that the op-amp will overload with a large enough current step without the capacitor. That's a good point. But in a similar way, many MOSFETs will oscillate without a gate stopper. So is it silly to use MOSFETs at all then, because they will oscillate without a gate stopper? Is the gate stopper just a hack? Or can the gate stopper just be considered proper and standard engineering practice, and what happens to a design engineer not using proper engineering practice is his/her own fault? It's a fine line.

My original post was not to claim that an op-amp was the optimum solution, but to state that claims to the effect that they are completely unsuitable for DAC I/V converters are greatly overstated.


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PostPosted: Fri Mar 18, 2005 9:37 pm 
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OPA627/37 datasheet, page 11:


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