Non-linear functions ...
in [Design]
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From: Phil Hobbs on 25 Nov 2009 12:35 Robert Baer wrote: > Richard Rasker wrote: >> Hi all, >> >> I'm currently working with a mass air flow sensor (a Honeywell >> AWM3100V, see >> http://datasheet.octopart.com/AWM3100V-Honeywell-datasheet-57019.pdf), >> and >> I would like to convert the rather non-linear response curve of this >> device >> into a voltage which bears a linear relationship to the actual air flow. >> Ideally, I would like to see the air flow converted in millivolts, so >> that >> it can be fed into a 3.5 digit voltmeter directly. >> >> These are the values (F=flow): >> F (ccm) Vout (V) >> 0 1.00 >> 25 1.90 >> 50 2.67 >> 75 3.27 >> 100 3.75 >> 125 4.17 >> 150 4.50 >> 175 4.80 >> 200 5.00 >> >> The first problem was simple: finding a suitable mathematical function >> which >> fits the curve; I looked at something along the lines of >> Vout=c1*(1-e^(-F/c2))+1, and it turns out that c1=5 and c2=125 provides a >> near-perfect fit. The second problem was to find an inverse function >> -- no >> problem there either: F=-c2*ln(1-(Vout-1)/c1) -- leading to the third and >> rather trickier problem, which of course is to implement that inverse >> function in an actual circuit. >> I've been doing some trial-and-error experimenting with a simple circuit, >> based on a simple Si-diode with some bypass and series resistors in >> several >> configurations, but that doesn't produce satisfactory results -- the best >> curve I get is easily 10% off at the extremes, and that's even without >> temperature instability. All this is of course no surprise, as the >> exponential function of a forward-biased diode is something different >> than >> a logarithmic function, and a simple PN junction has a temperature >> coefficient of approximately 2 mV per degree Celsius. >> >> Does anyone know of designs which provide a better fit for this type of >> logarithmic function, and preferably a better temperature stability? >> >> Thanks in advance, best regards, >> >> Richard Rasker > But..but..but.. > Transistors have been used for ages (>40 years i think) to generate log > (and anti-log functions). > For temp tracking, use a superpair (by National) and use one for > reference (emulating log(k) where k is some non-zero constant) and > subtract. All the supermatch pairs are going away. 3N3811, LM394, MAT02, MAT04--all gone. MAT01 and MAT03 probably soon to follow. A pity, but what do you expect when they cost $10 apiece? Nowadays you have to instrument a less-good die, such as an HFA3046 or THAT340, which is quite doable but a much bigger pain, as well as more expensive overall. (You have to tweak out Ree' to do a decent job over wide current ranges anyway. I just did one of these.) Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal ElectroOptical Innovations 55 Orchard Rd Briarcliff Manor NY 10510 845-480-2058 hobbs at electrooptical dot net http://electrooptical.net
From: Fred Bartoli on 25 Nov 2009 12:38 Rich Grise a �crit : > On Tue, 24 Nov 2009 15:30:47 -0600, Tim Wescott wrote: >> On Tue, 24 Nov 2009 22:19:26 +0100, Richard Rasker wrote: >>> These are the values (F=flow): >>> F (ccm) Vout (V) >>> 0 1.00 >>> 25 1.90 >>> 50 2.67 >>> 75 3.27 >>> 100 3.75 >>> 125 4.17 >>> 150 4.50 >>> 175 4.80 >>> 200 5.00 >>> > ... >>> Does anyone know of designs which provide a better fit for this type of >>> logarithmic function, and preferably a better temperature stability? >> .-----. .----. .-----. >> | | | | | | >> problem o---->| ADC |----->| uP |----->| DAC |-----> answer >> | | | | | | >> '-----' '----' '-----' > > .-----. .-----. .-----. > | | | | | | > problem o---->| ADC |----->| LUT |----->| DAC |-----> answer > | | | | | | > '-----' '-----' '-----' > .-----. .-----. .-----. .-----. .-----. | | | OPE | | ABA | | OPE | | | slow problem o---->| ADC |-->| RA |-->| CUS |-->| RA |-->| DAC |-->answer | | | TOR | | | | TOR | | | '-----' '-----' '-----' '-----' '-----' -- Thanks, Fred.
From: krw on 25 Nov 2009 12:57 On Wed, 25 Nov 2009 10:30:08 -0700, Jim Thompson <To-Email-Use-The-Envelope-Icon(a)My-Web-Site.com> wrote: >On Wed, 25 Nov 2009 11:20:41 -0600, John Fields ><jfields(a)austininstruments.com> wrote: > >>On Tue, 24 Nov 2009 15:23:24 -0800, Rich Grise <richgrise(a)example.net> >>wrote: >> >>>On Tue, 24 Nov 2009 15:30:47 -0600, Tim Wescott wrote: >>>> On Tue, 24 Nov 2009 22:19:26 +0100, Richard Rasker wrote: >>>>> >>>>> These are the values (F=flow): >>>>> F (ccm) Vout (V) >>>>> 0 1.00 >>>>> 25 1.90 >>>>> 50 2.67 >>>>> 75 3.27 >>>>> 100 3.75 >>>>> 125 4.17 >>>>> 150 4.50 >>>>> 175 4.80 >>>>> 200 5.00 >>>>> >>>... >>>>> >>>>> Does anyone know of designs which provide a better fit for this type of >>>>> logarithmic function, and preferably a better temperature stability? >>>> >>>> .-----. .----. .-----. >>>> | | | | | | >>>> problem o---->| ADC |----->| uP |----->| DAC |-----> answer >>>> | | | | | | >>>> '-----' '----' '-----' >>> >>> .-----. .-----. .-----. >>> | | | | | | >>> problem o---->| ADC |----->| LUT |----->| DAC |-----> answer >>> | | | | | | >>> '-----' '-----' '-----' >>> >> >>Bingo! >> >>JF > >LUT best implemented with an FPGA ?? Not necessary if there's no other control to be done. As described above all that's needed is a ROM of some description. Of course if the ADC and DAC have some sort of funky interface (I2C and SPI are popular) an FPGA makes the work simpler, though a uC will be cheaper. Cheap FPGAs tend not to have much, if any, memory.
From: Jon Kirwan on 25 Nov 2009 13:15 On Wed, 25 Nov 2009 15:16:41 +0100, Fred Bartoli <" "> wrote: >Richard Rasker a �crit : >> Jon Kirwan wrote: >> >>> On Tue, 24 Nov 2009 22:19:26 +0100, Richard Rasker wrote: >>> >>>> I'm currently working with a mass air flow sensor (a Honeywell AWM3100V, >>>> see http://datasheet.octopart.com/AWM3100V-Honeywell-datasheet-57019.pdf), >>>> and I would like to convert the rather non-linear response curve of this >>>> device into a voltage which bears a linear relationship to the actual air >>>> flow. Ideally, I would like to see the air flow converted in millivolts, >>>> so that it can be fed into a 3.5 digit voltmeter directly. >>>> >>>> These are the values (F=flow): >>>> F (ccm) Vout (V) >>>> 0 1.00 >>>> 25 1.90 >>>> 50 2.67 >>>> 75 3.27 >>>> 100 3.75 >>>> 125 4.17 >>>> 150 4.50 >>>> 175 4.80 >>>> 200 5.00 >>>> >>>> The first problem was simple: finding a suitable mathematical function >>>> which fits the curve; I looked at something along the lines of >>>> Vout=c1*(1-e^(-F/c2))+1, and it turns out that c1=5 and c2=125 provides a >>>> near-perfect fit. The second problem was to find an inverse function -- no >>>> problem there either: F=-c2*ln(1-(Vout-1)/c1) -- leading to the third and >>>> rather trickier problem, which of course is to implement that inverse >>>> function in an actual circuit. >>>> >... ><snip> >... >> >>> Third was to consider recommending a micro, which is a rather common >>> approach to conditioning sensors these days. >> >> I know. But I'm one of those old school die-hards who prefers hooking up a >> dozen or so components to a meter in an hour or so instead of spending a >> multiple of that time programming a controller to do the same. >> > >OK, then instead of using your log approach, one could notice the >extreme similarity between your sensor response Vout=c1*(1-e^(-F/c2))+1 >and an RC step response Vout=Vo*(1-e^(-t/tau)) which only differs from >your sensor response by a 1 constant. You can easily put this to work, >without having to bother with the inherent log amp thermal problems, and >use feedback to recover the flow value... > > > R C RC = C2 > ___ || > -1 >----. C1 >--|___|--+--||---. > | | || | > .---. | === > Vout >--| + |---. .--------+ GND > '---' | | | > .-----. | > \+ -/ +-|| > comparator \ / ->|| > V +-||---. > | | | > | === | > .--o--. GND | > GND -|D S Q|-------------' > | | > Clk >---|> -| ___ > | R Q|---|___|--+-----> Flow > '--o--' | > --- > --- > | > === > GND > > >Note that this will be a sampled system, so you have to adapt the clock >frequency to your wanted frequency bandwidth. Yes, I was imagining the RC response when I'd earlier responded. And this approach, though not so cleanly. Jon
From: Spehro Pefhany on 25 Nov 2009 14:38
On Wed, 25 Nov 2009 10:30:08 -0700, Jim Thompson <To-Email-Use-The-Envelope-Icon(a)My-Web-Site.com> wrote: >On Wed, 25 Nov 2009 11:20:41 -0600, John Fields ><jfields(a)austininstruments.com> wrote: > >>On Tue, 24 Nov 2009 15:23:24 -0800, Rich Grise <richgrise(a)example.net> >>wrote: >> >>>On Tue, 24 Nov 2009 15:30:47 -0600, Tim Wescott wrote: >>>> On Tue, 24 Nov 2009 22:19:26 +0100, Richard Rasker wrote: >>>>> >>>>> These are the values (F=flow): >>>>> F (ccm) Vout (V) >>>>> 0 1.00 >>>>> 25 1.90 >>>>> 50 2.67 >>>>> 75 3.27 >>>>> 100 3.75 >>>>> 125 4.17 >>>>> 150 4.50 >>>>> 175 4.80 >>>>> 200 5.00 >>>>> >>>... >>>>> >>>>> Does anyone know of designs which provide a better fit for this type of >>>>> logarithmic function, and preferably a better temperature stability? >>>> >>>> .-----. .----. .-----. >>>> | | | | | | >>>> problem o---->| ADC |----->| uP |----->| DAC |-----> answer >>>> | | | | | | >>>> '-----' '----' '-----' >>> >>> .-----. .-----. .-----. >>> | | | | | | >>> problem o---->| ADC |----->| LUT |----->| DAC |-----> answer >>> | | | | | | >>> '-----' '-----' '-----' >>> >> >>Bingo! >> >>JF > >LUT best implemented with an FPGA ?? > > ...Jim Thompson If speed isn't important, a micro is cheaper, will use less power, and will be pretty much self-contained (maybe just an external bypass capacitor). ROM in a FPGA uses a lot of internal resources. But if you need the answer FAST it might be the answer. |