EEVblog #1300 - "Parts Per" Notation EXPLAINED

[EEVblog]

"Per Mille" is a trap for young players.
"Parts Per" notation explained, along with percentage and ppm.

[johnlsenchak]

If  you  real  want to lose your mind   !

    One part per billion (ppb) denotes one part per 1000000000 parts, one part in 109, 1/1000000000 × 100% = 0.0000001% (or 1% = 10000000 ppb) and a value of 1 × 10−9.

    One part per trillion (ppt) denotes one part per 1000000000000 parts, one part in 1012, and a value of 1 × 10−12.

    One part per quadrillion (ppq) denotes one part per 1000000000000000 parts, one part in 1015, and a value of 1 × 10−15. Tevel are sometimes performed

[Neilm]

I first came across this notation reading an old research paper. The paper had been scanned into pdf and had been through an OCR and none of the calculations made sense. Fortunately I found a pdf of the paper before it had been OCRed and saw this notation and had to look up what it ment. Turned out the OCR had replaced the permille with the percent symbol.

[johnwa]

Interesting, I didn't know there was an "official" unit for per-unit notation. I agree that the name and prefixes sound a bit silly, but the basic concept is used quite a bit, especially in fields such as power engineering, and really makes much more sense from an engineering perspective.

The use of percentages probably stems from non-technical people being uncomfortable with decimal fractions. However, a consequence of this is formulas become littered with factors of 100 all over the place. (Also, the objection to decimals is rather spurious, given that the percentages themselves often have decimal fractions)

E.g: Efficiency (%) = 100 * Pout/Pin

or compound interest

 P' = P(1+r/100)^n

If the relevant quantities are simply treated as decimal fractions, the conversion factors disappear:

Efficiency = Pout/Pin

P' = P(1+r)^n


 This is generally what I do whenever I am building a calculation spreadsheet or program - any percentages as inputs are converted to per-unit as a first step, and then treated that way throughout. I am quite happy to view the results directly as decimals, but they can of course be converted back to percentages at the end if need be.

I don't know how standard this is, but I have often seen per-unit values identified by "PU" E.g: "The efficiency of the transformer is 0.8PU". Alternatively, you could write "The per-unit efficiency of the transformer is 0.8".

I hope this is a useful addendum to Dave's video. I really don't know why the power supply was specified like that though. If it was a marketer trying to make the numbers look bigger, they have really shot themselves in the foot this time!

Edit: This is of course the same idea a specifying amplifier gains, etc in volts/volt or whatever...

[hans]

The use of percentages probably stems from non-technical people being uncomfortable with decimal fractions. However, a consequence of this is formulas become littered with factors of 100 all over the place. (Also, the objection to decimals is rather spurious, given that the percentages themselves often have decimal fractions)

E.g: Efficiency (%) = 100 * Pout/Pin

Which is why it is better to write equations as:
Efficiency = 100% * Pout/Pin

That way it is clear that the 100% is used to represent it as a percentage, however, since 100% = 1.0, the efficiency calculated is still the correct fraction.
Things become a mess when you try to input these things in e.g. Excel or other computational programs. Excel/LibreOffice can use the percentage cell value formatter to do this conversion immediately, so no 100x factors in formulas needed. In addition, personally I found it's best practice to never convert anything 'presentation friendly' at an intermediate level, as un-doing these steps is prone to errors (e.g. you forget or apply the wrong conversion factor).

Sometimes fraction representation is funny if you look at really low-power stuff. Typical CPU load measurements are done in percentage to indicate how busy a CPU is. If you go into really low duty cycles (e.g. a short computational burst on a 10 minute period), you may see that a particular task will only run for 50ms every 600 seconds. That's a CPU load of only 0.008333%, or as I'd like to represent it: 83.33ppm. I'd prefer the latter, as the decimal point is put at a place that makes the number easier to read.

[Domagoj T]

Over here it's standard for expressing blood alcohol content. It's also used for grade in railway industry and probably more fields that don't come to mind right now.
PPM is used in medical field, but I have to admit I've never heard the "basis point" term.

[Bud]

Next time your country's central bank changes interest rates, check their press release 

[tszaboo]

When I was a young engineer, I got a task to design a current measuring device, with 0.05 PPM accuracy. I spent days, trying to do it, then I gave up. Told my boss it is impossible. But no, he insisted, it should be possible.Because 0.05 PPM = 0.05 parts per mille...

[johnwa]

Excel/LibreOffice can use the percentage cell value formatter to do this conversion immediately, so no 100x factors in formulas needed. In addition, personally I found it's best practice to never convert anything 'presentation friendly' at an intermediate level, as un-doing these steps is prone to errors (e.g. you forget or apply the wrong conversion factor).

Yeah, I have seen that, but I have never been too keen on the displayed value not equalling the actual numeric value in the cell. Though I guess it's no worse than displaying 1000V as 1kV.
 

That's a CPU load of only 0.008333%, or as I'd like to represent it: 83.33ppm. I'd prefer the latter, as the decimal point is put at a place that makes the number easier to read.

Fair enough, I guess you could always use scientific notation if you wanted to.

When I was a young engineer, I got a task to design a current measuring device, with 0.05 PPM accuracy. I spent days, trying to do it, then I gave up. Told my boss it is impossible. But no, he insisted, it should be possible.Because 0.05 PPM = 0.05 parts per mille...

You should be thankful he didn't ask for it to have 100% reliability as well... 

[tszaboo]

When I was a young engineer, I got a task to design a current measuring device, with 0.05 PPM accuracy. I spent days, trying to do it, then I gave up. Told my boss it is impossible. But no, he insisted, it should be possible.Because 0.05 PPM = 0.05 parts per mille...

You should be thankful he didn't ask for it to have 100% reliability as well... 

Oh, that was my current boss. There was a destructive test, with pass fail output. I asked him for the confidence level requirement for the test, he said 99%. So I told him, I need to destroy most of the production units to have that confidence.

[Howardlong]

What happens when you don't know what ppm means...

https://www.bbc.co.uk/news/uk-england-sussex-52379192

https://assets.publishing.service.gov.uk/media/5e9d5b4cd3bf7f0316b6a63a/AAIB_Special_Bulletin_S1-2020_G-POWN.pdf

"The EASA Part-66 B1 licensed AMO engineer was not familiar with the term ‘ppm’."

[Monkeh]

What happens when you don't know what ppm means...

https://www.bbc.co.uk/news/uk-england-sussex-52379192

https://assets.publishing.service.gov.uk/media/5e9d5b4cd3bf7f0316b6a63a/AAIB_Special_Bulletin_S1-2020_G-POWN.pdf

"The EASA Part-66 B1 licensed AMO engineer was not familiar with the term ‘ppm’."

That's fairly disturbing on multiple points. I look forward to the full report.

[thm_w]

The  task  states  that  fuel  should  be  mixed  with  Kathon  biocide  at  a  concentration  of  100  parts  per  million  (ppm)  by  volume  and  then  the  aircraft  pressure-refuelled  using  the  onboard  automatic  control  functionality  in  accordance  with  AMM Task 12-11-28-650-003-A, Pressure Refuel with Automatic Control.  The Kathon-dosed fuel should remain in the aircraft fuel tanks for 24 hours.The EASA Part-66 B1 licensed AMO engineer11 was not familiar with the term ‘ppm’.  It was not written in expanded form anywhere in the AMM Task or glossary, and the AMM task did not provide instructions about how to perform the calculation of how much Kathon to use.  He therefore searched the internet for a definition and conversion calculator.  The AMO engineer knew that he would be uploading 6,200 kg of fuel into each wing tank and, using  an  internet  calculator,  he  calculated  a  quantity  of  30  kg  of  Kathon  for  each  wing  tank.  There was 150 kg of Kathon available in the AMO stores and so he made a material requisition for 60 kg of Kathon.

So somehow he calculated 30kg per 6200kg, when it should be ~0.8kg.

I looked at a number of online calculators and couldn't find any that would give the wrong result. They will tell you 100mg/L, 100mg/kg, 0.1ml/L, etc which are all correct. None of these are close to 0.5% he used. I think there is a bigger screw up here than not knowing what ppm is, on top of not looking up a term you aren't familiar with..

[THDplusN_bad]

Thanks, Dave.

yes, ‰ is a common symbol in the Medical field (i.e. for blood testing for alcohol) and in Economic studies and the like. It is not so common in Engineering Term, I agree.

But then, I was not really surprised to see ppm used for accuracy and drift specs for real high-end T&M equipment such as the model 2002 DMM from Keithley - much easier to understand than counting zeros after the decimal point or comma...

Cheers,

THD+N bad

[EEVblog]

But then, I was not really surprised to see ppm used for accuracy and drift specs for real high-end T&M equipment such as the model 2002 DMM from Keithley - much easier to understand than counting zeros after the decimal point or comma...

Yes, it's the same reason why the nanofarad was introduced. It was just getting silly saying 0.001uF or 10000pF etc
I can remember "the great nanofarad" debate in the electronics magazine on whether or not they should start using the nF on schematics.

[PathLoss]

As an Aside... Dealing with orders of magnitude analysis (and more) in your brain - with or without the prefixes:

* Fermi Estimate:

https://brilliant.org/wiki/fermi-estimate/

Excerpt: "A Fermi estimate is one done using back-of-the-envelope calculations and rough generalizations to estimate values which would require extensive analysis or experimentation to determine exactly."

* Fermi problem - Wikipedia:

https://en.wikipedia.org/wiki/Fermi_problem

Excerpt: "In physics or engineering education, a Fermi problem, Fermi quiz, Fermi question, Fermi estimate, or order estimation is an estimation problem designed to teach dimensional analysis or approximation of extreme scientific calculations, and such a problem is usually a back-of-the-envelope calculation. The estimation technique is named after physicist Enrico Fermi as he was known for his ability to make good approximate calculations with little or no actual data. Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds."