Analox analyzer
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OP
GlennL
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I do, but I sense some personal remarks and when people start down that road rather than keeping a friendly debate then I bow out. I don't have nothing to prove to nobody on the internet. I'm not a keyboard Rambo so in regards to this thread in particular I have gotten useful info from a couple of positive contributors. After that, I'll let the people with more experience and knowledge than me get in a pissing match about the fine print.
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@tarponchik
The formula of a line is always y=mx+b. With single point calibration, b is always 0
the formula that we have to pay attention to for two point calibration y=m*l*x+b
y=readout on the screen, in this case ppO2
x=the output from the cell in mV
m=the multiple to get from mV to a determined ppO2. This is the initial calibration value. I.e. 12.6mv*1.66=20.9
l=the linearity of the cell. This is determined by a 2 point calibration with at least one of the datapoints from a value higher than the value you are reading. In most cases for nitrox, this is some value higher than a ppO2 of .32, preferably at least .5, but for accuracy, the most accurate gas will be done at 1.0 or 100% O2
If you calibrate with one point, you assume l=1
based on that formula, a 0% O2 calibration gas would give you an x value of 0, and anything multiplied by 0, is and always will be, 0. If you do a 2 point calibration with an x value of 0, it's not a valid calibration because you have no ability to determine what "b" really is.
Edit:
Example for single point calibration
We know the x value because that is what the cell is reading. In this case call it 12.6mV
We know the y value because that is our reference. In this case, call it 20.9%
The formula to get there is ppO2=multiple*linearity*mV
We assume that linearity=1 because there is no way to verify this.
"b" is always 0 for a single point calibration
Resultant formula
20.9%=1.66*12.6+0
When we do a dual point calibration, we have three formulas. x1 is always the lower of the two readings, x2 is always the higher of the two readings
y1=m1*x1
y2=m2*x2
l=m1/m2
In this case at the first reading we still determine that m1=1.66
for the second reading at 100%, we expect x2 to be 60.3mV, but it comes out at 54.3mV
y2=m2*x2
y2=100
x2=54.3
m2=1.84
To determine the actual line, we know that y=m*l*x. x=1.66 since that is what we determined with our first calibration gas, and l=m1/m2=.9 showing that the cells are only 90% linear. Resultant formula
y=1.49*x for all values between ppO2 of 20.9% and ppO2 of 100%, with bounds of (12.6, 20.9) and (54.3, 100).
If you want to draw a line from that, it would be
y=1.49*x+2.13 with a domain from 12.6 to 54.3
This is as accurate as we can calibrate without a pressure pot and a single gas. I understand your point about y=mx+b because we have to fix a reference point, however we have to assume linear function between data points, and anything outside of those data points is an unknown. In the situation above, we know that the slope of the line is 1.49 between ppO2's of 20.9% and 100%, but what we are unsure of is the slope below 20.9%, or above 100%. We have to make assumptions.
We know that any curve has to intersect (0,0), so we have a slope of 1.66*x for values up to x=12.6. We have a slope of 1.49*x for values between x=12.9 and x=54.3, but what we are unsure of is the behavior above that x value.
This is the dangerous part for rebreather divers and why they have to verify linearity up to a ppO2 of 1.6 so they can draw the curve between ppO2 of 1.0 and 1.6 which is what matters on a rebreather. Unfortunately most divers don't do this and are assuming linear behavior, but that does not verify any current limitations or altered linearity above a ppO2 of 1.0.
For O2 analyzers, we do not care about the linearity or current limitations above a ppO2 of 1.0 which is why cells from CCR's will get "Retired" to analyzer duty. They may not function properly above a ppO2 of 1.0, but they may function just fine or well enough between .2 and 1.0. You still have to determine the bounds of your calibration scale, and anything outside of those bounds is unable to be considered accurate.
Using a 2 point calibration of ambient and EAN32 is only able to prove linearity between those two values, it is unable to be considered accurate outside of those bounds
The formula of a line is always y=mx+b. With single point calibration, b is always 0
the formula that we have to pay attention to for two point calibration y=m*l*x+b
y=readout on the screen, in this case ppO2
x=the output from the cell in mV
m=the multiple to get from mV to a determined ppO2. This is the initial calibration value. I.e. 12.6mv*1.66=20.9
l=the linearity of the cell. This is determined by a 2 point calibration with at least one of the datapoints from a value higher than the value you are reading. In most cases for nitrox, this is some value higher than a ppO2 of .32, preferably at least .5, but for accuracy, the most accurate gas will be done at 1.0 or 100% O2
If you calibrate with one point, you assume l=1
based on that formula, a 0% O2 calibration gas would give you an x value of 0, and anything multiplied by 0, is and always will be, 0. If you do a 2 point calibration with an x value of 0, it's not a valid calibration because you have no ability to determine what "b" really is.
Edit:
Example for single point calibration
We know the x value because that is what the cell is reading. In this case call it 12.6mV
We know the y value because that is our reference. In this case, call it 20.9%
The formula to get there is ppO2=multiple*linearity*mV
We assume that linearity=1 because there is no way to verify this.
"b" is always 0 for a single point calibration
Resultant formula
20.9%=1.66*12.6+0
When we do a dual point calibration, we have three formulas. x1 is always the lower of the two readings, x2 is always the higher of the two readings
y1=m1*x1
y2=m2*x2
l=m1/m2
In this case at the first reading we still determine that m1=1.66
for the second reading at 100%, we expect x2 to be 60.3mV, but it comes out at 54.3mV
y2=m2*x2
y2=100
x2=54.3
m2=1.84
To determine the actual line, we know that y=m*l*x. x=1.66 since that is what we determined with our first calibration gas, and l=m1/m2=.9 showing that the cells are only 90% linear. Resultant formula
y=1.49*x for all values between ppO2 of 20.9% and ppO2 of 100%, with bounds of (12.6, 20.9) and (54.3, 100).
If you want to draw a line from that, it would be
y=1.49*x+2.13 with a domain from 12.6 to 54.3
This is as accurate as we can calibrate without a pressure pot and a single gas. I understand your point about y=mx+b because we have to fix a reference point, however we have to assume linear function between data points, and anything outside of those data points is an unknown. In the situation above, we know that the slope of the line is 1.49 between ppO2's of 20.9% and 100%, but what we are unsure of is the slope below 20.9%, or above 100%. We have to make assumptions.
We know that any curve has to intersect (0,0), so we have a slope of 1.66*x for values up to x=12.6. We have a slope of 1.49*x for values between x=12.9 and x=54.3, but what we are unsure of is the behavior above that x value.
This is the dangerous part for rebreather divers and why they have to verify linearity up to a ppO2 of 1.6 so they can draw the curve between ppO2 of 1.0 and 1.6 which is what matters on a rebreather. Unfortunately most divers don't do this and are assuming linear behavior, but that does not verify any current limitations or altered linearity above a ppO2 of 1.0.
For O2 analyzers, we do not care about the linearity or current limitations above a ppO2 of 1.0 which is why cells from CCR's will get "Retired" to analyzer duty. They may not function properly above a ppO2 of 1.0, but they may function just fine or well enough between .2 and 1.0. You still have to determine the bounds of your calibration scale, and anything outside of those bounds is unable to be considered accurate.
Using a 2 point calibration of ambient and EAN32 is only able to prove linearity between those two values, it is unable to be considered accurate outside of those bounds
Last edited:
victorzamora
Contributor
I've been giving this a lot of thought, and I think that at the end of the day it comes down to one thing: Over-analysis.
OP has an answer they seem comfortable with, which is really what matters. For the rest of the (frankly useful) conversation, I think it's fairly safe to say that calibrating at a single, known point is more than good enough for reacreational mixes.
EAN21 is a plentiful and fairly-well-known gas and is close enough to the recreational mixes that you're normally fine....and close enough for current deco theory. A halfway decent sensor will be good enough to function. I caught my really bad sensor by just being cautious. I requested EAN32, the adjustment knob was far too far out of whack for my liking, and then it read low....much lower than is acceptable for gas supposedly EAN32. I tested with another analyzer (might've been yours) and it read right-at EAN32. Even on O2 it didn't get up to EAN32 on the readout. The cell was D-E-D.
As for the nitty gritty being discussed, I'm not sure I agree that the equation is y=m*b*x, either.
The formula for a basic linear equation is y=mx+b. In this case, it’s:
PO2=Multiplier*mV output by the cell + 0.
The 0 is the known-zero y-intercept. With an ideal cell, you only need those two points. The y-intercept clearly stays the same, but what changes is the linearity. The PO2=Multi*mV equation only functions on actually linear cells. Cells aren’t perfectly linear, especially around higher PO2 values….so the “fudge” commonly performed by CCR divers is the factor you called “linearity.” That essentially reduces the slop of the line to better approximate the near-or-over 1.0 pO2 values CCR divers run their units at.
That “linearity” fudge is a very safe way of correcting the line near the high-pO2 readings CCR divers want, much like ignoring it is safe for recreational EANx divers using pO2 of 0.21 as calibration gas for our mixes. It’s close, so it’s mostly fine.
The reason I’m disagreeing with y=m*x*b equation you provided is that it’s not what real cells follow….it’s a modified slope to make high-pO2 readings more accurate, and make extrapolations beyond pO2=1 more accurate. However, real cells aren’t linear, regardless of the slope you attribute to them. The best-fit line I could come up with was a second-order polynomial in the form of y=ax^2+bx. The “c” (times x^0) would be zero due to the known-zero y-intercept.
This really goes back to the beginning, though: Does any of this matter? Not to me. A single-point calibration using air is more than enough for me, especially with a periodic check at pure O2 to validate no severe limiting. Oxygen is easy enough to come by (most shops that fill N2 and any shop catering to CCR or Tech divers will have it, and we always keep it laying around). However, that cell going bad the way it did opened my eyes to needing to apply my brain and use logic to check for issues.
For CCR, I’ll do the linearity checks and math in the y=m*x*b method you described. Setpoints at 1.0-1.6 mean that calibrating at 0.21 is just too low for me to be comfortable.
With O2-rich mixes for OC tech dives, I think I’ll simply calibrate on pure oxygen and not worry about the low-point. For EAN50, I’d likely check with air-calibrated and O2-calibrated just to confirm and satisfy my craziness (and love of math and fiddling with crap). However, the final takeaway should really be: Calibrate using air and keep your brain open for obvious/apparent issues…you’ll be fine. Worrying even about temp and humidity is fairly minor.
OP has an answer they seem comfortable with, which is really what matters. For the rest of the (frankly useful) conversation, I think it's fairly safe to say that calibrating at a single, known point is more than good enough for reacreational mixes.
EAN21 is a plentiful and fairly-well-known gas and is close enough to the recreational mixes that you're normally fine....and close enough for current deco theory. A halfway decent sensor will be good enough to function. I caught my really bad sensor by just being cautious. I requested EAN32, the adjustment knob was far too far out of whack for my liking, and then it read low....much lower than is acceptable for gas supposedly EAN32. I tested with another analyzer (might've been yours) and it read right-at EAN32. Even on O2 it didn't get up to EAN32 on the readout. The cell was D-E-D.
As for the nitty gritty being discussed, I'm not sure I agree that the equation is y=m*b*x, either.
The formula for a basic linear equation is y=mx+b. In this case, it’s:
PO2=Multiplier*mV output by the cell + 0.
The 0 is the known-zero y-intercept. With an ideal cell, you only need those two points. The y-intercept clearly stays the same, but what changes is the linearity. The PO2=Multi*mV equation only functions on actually linear cells. Cells aren’t perfectly linear, especially around higher PO2 values….so the “fudge” commonly performed by CCR divers is the factor you called “linearity.” That essentially reduces the slop of the line to better approximate the near-or-over 1.0 pO2 values CCR divers run their units at.
That “linearity” fudge is a very safe way of correcting the line near the high-pO2 readings CCR divers want, much like ignoring it is safe for recreational EANx divers using pO2 of 0.21 as calibration gas for our mixes. It’s close, so it’s mostly fine.
The reason I’m disagreeing with y=m*x*b equation you provided is that it’s not what real cells follow….it’s a modified slope to make high-pO2 readings more accurate, and make extrapolations beyond pO2=1 more accurate. However, real cells aren’t linear, regardless of the slope you attribute to them. The best-fit line I could come up with was a second-order polynomial in the form of y=ax^2+bx. The “c” (times x^0) would be zero due to the known-zero y-intercept.
This really goes back to the beginning, though: Does any of this matter? Not to me. A single-point calibration using air is more than enough for me, especially with a periodic check at pure O2 to validate no severe limiting. Oxygen is easy enough to come by (most shops that fill N2 and any shop catering to CCR or Tech divers will have it, and we always keep it laying around). However, that cell going bad the way it did opened my eyes to needing to apply my brain and use logic to check for issues.
For CCR, I’ll do the linearity checks and math in the y=m*x*b method you described. Setpoints at 1.0-1.6 mean that calibrating at 0.21 is just too low for me to be comfortable.
With O2-rich mixes for OC tech dives, I think I’ll simply calibrate on pure oxygen and not worry about the low-point. For EAN50, I’d likely check with air-calibrated and O2-calibrated just to confirm and satisfy my craziness (and love of math and fiddling with crap). However, the final takeaway should really be: Calibrate using air and keep your brain open for obvious/apparent issues…you’ll be fine. Worrying even about temp and humidity is fairly minor.
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@stuartv i'm going to beat the horse one more time, to thank Victor for this one
@victorzamora
it was definitely my Cootwo when we found out how bad your cell was....
that's a better description of what i was trying to get at. with y=m*x*b, the assumption is that since the intercept is always 0, then the "+b" in normal formulas is always 0. Where I was trying to get with the linearity though is that you have to assume a true linear function when outside of two bounds of calibration, but within, it's easier to determine the slope of the line between the two points and ignore the intercept at 0 because it will always be 0. Second order polynomial is probably more close to real, but without doing a constant calibration across a pressure pot, I'm not sure how to program that into an analyzer based on two cal points... hrrm, food for thought for CCR computer calibration mayhaps?
@victorzamora
it was definitely my Cootwo when we found out how bad your cell was....
that's a better description of what i was trying to get at. with y=m*x*b, the assumption is that since the intercept is always 0, then the "+b" in normal formulas is always 0. Where I was trying to get with the linearity though is that you have to assume a true linear function when outside of two bounds of calibration, but within, it's easier to determine the slope of the line between the two points and ignore the intercept at 0 because it will always be 0. Second order polynomial is probably more close to real, but without doing a constant calibration across a pressure pot, I'm not sure how to program that into an analyzer based on two cal points... hrrm, food for thought for CCR computer calibration mayhaps?
This has made a very interesting afternoon read.
Can we all agree that a single adjustment analyzer, you can set it for whatever you would like, but a good way to check the validity of your cells is to reference another (different O2 content) gas source to verify that the same reading has been presented?
While we are at it, only 2 gases containing O2 are universally accepted. Atmospheric Air and pure Oxygen?
So go ahead and adjust the analyzer to read the *correct* readout (either by voodoo, manufacturers suggestions, "calibrated gas", etc) and every once in a while (or not), if it is available, as a second step to verify your analyzer is working properly, verify against a second "calibrated" gas that contains some fraction of O2?
_R
Can we all agree that a single adjustment analyzer, you can set it for whatever you would like, but a good way to check the validity of your cells is to reference another (different O2 content) gas source to verify that the same reading has been presented?
While we are at it, only 2 gases containing O2 are universally accepted. Atmospheric Air and pure Oxygen?
So go ahead and adjust the analyzer to read the *correct* readout (either by voodoo, manufacturers suggestions, "calibrated gas", etc) and every once in a while (or not), if it is available, as a second step to verify your analyzer is working properly, verify against a second "calibrated" gas that contains some fraction of O2?
_R
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@_Ralph the linearity of the cells is critical when evaluating gas mixes quite a ways away from the reference gas i.e. when analyzing 50%, you want to calibrate to 21% and O2 since that will draw a line very close to 50% and give you a good chance of getting it accurately.
Yes, the two best reference gases are atmospheric, and pure O2. O2 being the better of the two since O2 will be less variable than atmospheric. O2 will also show if a cell is limited or not within the intended analysis range
If you only have one reference gas to check against, 100% O2 will be the best reference gas. Farther away from the intended gas but over it, is better imo than closer but under because of cell limiting. I.e. I would place more value on a calibration value at 100% when trying to analyze EAN32, than I would for atmospheric.
A 90% linearity value can cause EAN32 to read as EAN28. May not be a huge thing, at at least for decompression purposes it is more conservative so long as you don't go and add O2 until the mix reads at EAN32 when it actually would be blended as EAN36. In that case, MOD is the only risk for you.
Yes, the two best reference gases are atmospheric, and pure O2. O2 being the better of the two since O2 will be less variable than atmospheric. O2 will also show if a cell is limited or not within the intended analysis range
If you only have one reference gas to check against, 100% O2 will be the best reference gas. Farther away from the intended gas but over it, is better imo than closer but under because of cell limiting. I.e. I would place more value on a calibration value at 100% when trying to analyze EAN32, than I would for atmospheric.
A 90% linearity value can cause EAN32 to read as EAN28. May not be a huge thing, at at least for decompression purposes it is more conservative so long as you don't go and add O2 until the mix reads at EAN32 when it actually would be blended as EAN36. In that case, MOD is the only risk for you.
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I just find, checking against 50% a little off .... Atmosphere and 100% are the only two gases with oxygen content that is a more or less constant. A bottle of 50% doesn't mean it is 50.0%. That is all I was getting at with the two gasses.
_R
_R
tarponchik
Contributor
@tbone1004
"Yes, the two best reference gases are atmospheric, and pure O2. O2 being the better of the two since O2 can have more variability than the atmospheric air."
Here, I am confused: How can a more variable substance be a better calibration standard?
"A 90% linearity value can cause EAN32 to read as EAN28."
If I got your math right, this can happen only if you use O2 as your calibration standard because the aging sensor gives non-linear readings at high O2 percentage. If you use air, the error will be much lower. Look at the graph in your manual again: the cell is clearly aging "from the top".
"Yes, the two best reference gases are atmospheric, and pure O2. O2 being the better of the two since O2 can have more variability than the atmospheric air."
Here, I am confused: How can a more variable substance be a better calibration standard?
"A 90% linearity value can cause EAN32 to read as EAN28."
If I got your math right, this can happen only if you use O2 as your calibration standard because the aging sensor gives non-linear readings at high O2 percentage. If you use air, the error will be much lower. Look at the graph in your manual again: the cell is clearly aging "from the top".
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