RTD linearization
in [Design]
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From: John Larkin on 22 Dec 2009 10:19 On Mon, 21 Dec 2009 23:17:47 -0800, "JosephKK"<quiettechblue(a)yahoo.com> wrote: >On Sat, 19 Dec 2009 16:38:01 -0800, John Larkin <jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: > >>On Sat, 19 Dec 2009 14:48:16 -0800, >>"JosephKK"<quiettechblue(a)yahoo.com> wrote: >> >>>On Sun, 13 Dec 2009 11:08:36 -0800, John Larkin <jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >>> >>>>On Sun, 13 Dec 2009 13:06:36 -0500, Spehro Pefhany >>>><speffSNIP(a)interlogDOTyou.knowwhat> wrote: >>>> >>>>>On Sun, 13 Dec 2009 09:28:53 -0800, the renowned John Larkin >>>>><jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >>>>> >>>>>>On Sun, 13 Dec 2009 12:20:05 GMT, nico(a)puntnl.niks (Nico Coesel) >>>>>>wrote: >>>>>> >>>>>>>John Larkin <jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >>>>>>> >>>>>>>>On Sat, 12 Dec 2009 12:46:37 -0800, Joerg <invalid(a)invalid.invalid> >>>>>>>>wrote: >>>>>>>> >>>>>>>>>John Larkin wrote: >>>>>>>>>> >>>>>>>>>> Does anybody remember the value of negative resistance that linearizes >>>>>>>>>> a 100 ohm platinum RTD? >>>>>>>>>> >>>>>>>>> >>>>>>>>>No uC at hand for this job? Maybe this helps: >>>>>>>>> >>>>>>>>>http://pdfserv.maxim-ic.com/en/an/AN3450.pdf >>>>>>>>> >>>>>>>>>But you don't have to use a Maxim opamp :-) >>>>>>>> >>>>>>>>I'm thinking I'll use 1K RTDs for the automation project, and lay out >>>>>>>>an interface board... easier than hand wiring. The little RS232 widget >>>>>>> >>>>>>>1k RTDs are easier to interface. I used one to control my floor >>>>>>>heating. 2k2 (IIRC) in series from 3.3V and then fed directly into an >>>>>>>ADC. In a limited temperature range, the output is quite linear so >>>>>>>there is not really a need for fancy math. >>>>>> >>>>>>I'm thinking along these lines... >>>>>> >>>>>>ftp://jjlarkin.lmi.net/RTD.jpg >>>>>> >>>>>>All the 1Ks will be 0.1%. >>>>> >>>>>I don't like this concept very much. Typically we'll run a 100R RTD at >>>>>< 1mA for a total Pd of < 100uW (much much less in some applications). >>>>>And usually the RTDs have a lot of added surface area because they're >>>>>glumped into some kind of protection tube. >>>>> >>>>>You have 1K RTDs running at 2.5mA for a power dissipation of around >>>>>6mW at 20C. That alone will result in an error of several degrees C >>>>>with an un-housed thin film sensor in moving air, more in static air, >>>>>natch. >>>>> >>>> >>>>Of course I've considered self-heating. >>>> >>>>I was planning to use the largish Minco ceramic-slab parts (we have >>>>1Ks in stock) and stick them in a plastic tube full of epoxy, to >>>>weatherize and reduce theta. The self-heat error should be small. I >>>>could epoxy them to a small strip of aluminum first, if I were >>>>compulsive. And I may as well calibrate the whole thing end-to-end >>>>against a good thermocouple. >>>> >>>>I do have some scope shots that quantify 1206 surface-mount RTD >>>>transient self-heating under different mounting scenarios. I could >>>>post them if there were great popular demand. >>>> >>>>John >>> >>>I would like to see them just as a matter of curiosity. >> >>ftp://jjlarkin.lmi.net/RTD_in_air.JPG >> >>ftp://jjlarkin.lmi.net/RTD_on_board.JPG >> >>ftp://jjlarkin.lmi.net/RTD_lotsa_copper.JPG >> >>John > >Thranx. I learned. One interesting thing is that the self-heating of this 1206 part is so low if you solder it to a lot of copper. We've verified that with infrared measurement of the hot-spot temp on conventional thick-film resistors. Since most surface-mount resistors are the same thickness of alumina, theta from the element to their end caps depends only on their l/w ratio, which also tends to be the same. So an 0603 resistor can handle as much power as a 1206, half a watt maybe, if you mount it right. Some people are making resistors on AlN substrates, and they have hard-to-believe power ratings. http://www.rftechniques.com/chip.html John
From: John Larkin on 22 Dec 2009 11:28 On Mon, 21 Dec 2009 23:38:08 -0800, "JosephKK"<quiettechblue(a)yahoo.com> wrote: >On Sat, 19 Dec 2009 17:39:19 -0800, John Larkin <jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: > >>On Sat, 19 Dec 2009 17:34:01 -0800, >>"JosephKK"<quiettechblue(a)yahoo.com> wrote: >> >>>On Sun, 13 Dec 2009 09:50:22 -0600, "RogerN" <regor(a)midwest.net> wrote: >>> >>>> >>>>"John Larkin" <jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote in message >>>>news:p1u7i5thbjmtjvqcj63b291l19rf7ktllp(a)4ax.com... >>>>> >>>>> >>>>> Does anybody remember the value of negative resistance that linearizes >>>>> a 100 ohm platinum RTD? >>>>> >>>>> John >>>> >>>>I thought RTD's were supposed to be linear. The 100 ohm resistance being at >>>>0 Degrees C and a change of .385 ohms (for a 100 Ohm RTD) per Degree C. I >>>>read a description of instrumentation for RTD's once. They said they used a >>>>1ma current source to the RTD and compared it to the voltage drop with 1ma >>>>in a 100 Ohm resistor. Low current, 1ma, was used to minimize the RTD >>>>heating up from power. I know there is a 3rd and sometimes 4th sense wire >>>>used to compensate for the lead resistance. I don't exactly remember the >>>>source but I read the information when looking up info for my Allen Bradley >>>>RTD input card for my PLC 5 rack. >>>> >>>>RogerN >>>> >>>Platinum RTDs are about total repeatability, a real mantra in the measurement >>>community. And 393 ppm/K is an exponential, like most all resistance tempcos. >> >>Exponential? How so? >> >>John > >Each degree of temperature change is a multiplier on the degree base before it. >so the recurrence relation results in an exponential. Thus it can be modeled >as r' = r(25) * k(1)e^[k(2)*t], an exponential. BTW just look at a R vs T plot. What are the coefficients? The curve slopes down. I've never seen the platinum RTD curve expressed as an exponential. The usual formulation is a polynomial. www.analogzone.com/acqt_052807.pdf http://www.omega.com/temperature/Z/pdf/z251.pdf John
From: Phil Hobbs on 22 Dec 2009 12:02 On 12/22/2009 11:28 AM, John Larkin wrote: > On Mon, 21 Dec 2009 23:38:08 -0800, > "JosephKK"<quiettechblue(a)yahoo.com> wrote: > >> On Sat, 19 Dec 2009 17:39:19 -0800, John Larkin<jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >> >>> On Sat, 19 Dec 2009 17:34:01 -0800, >>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>> >>>> On Sun, 13 Dec 2009 09:50:22 -0600, "RogerN"<regor(a)midwest.net> wrote: >>>> >>>>> >>>>> "John Larkin"<jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote in message >>>>> news:p1u7i5thbjmtjvqcj63b291l19rf7ktllp(a)4ax.com... >>>>>> >>>>>> >>>>>> Does anybody remember the value of negative resistance that linearizes >>>>>> a 100 ohm platinum RTD? >>>>>> >>>>>> John >>>>> >>>>> I thought RTD's were supposed to be linear. The 100 ohm resistance being at >>>>> 0 Degrees C and a change of .385 ohms (for a 100 Ohm RTD) per Degree C. I >>>>> read a description of instrumentation for RTD's once. They said they used a >>>>> 1ma current source to the RTD and compared it to the voltage drop with 1ma >>>>> in a 100 Ohm resistor. Low current, 1ma, was used to minimize the RTD >>>>> heating up from power. I know there is a 3rd and sometimes 4th sense wire >>>>> used to compensate for the lead resistance. I don't exactly remember the >>>>> source but I read the information when looking up info for my Allen Bradley >>>>> RTD input card for my PLC 5 rack. >>>>> >>>>> RogerN >>>>> >>>> Platinum RTDs are about total repeatability, a real mantra in the measurement >>>> community. And 393 ppm/K is an exponential, like most all resistance tempcos. >>> >>> Exponential? How so? >>> >>> John >> >> Each degree of temperature change is a multiplier on the degree base before it. >> so the recurrence relation results in an exponential. Thus it can be modeled >> as r' = r(25) * k(1)e^[k(2)*t], an exponential. BTW just look at a R vs T plot. > > What are the coefficients? The curve slopes down. > > I've never seen the platinum RTD curve expressed as an exponential. > The usual formulation is a polynomial. > > www.analogzone.com/acqt_052807.pdf > > http://www.omega.com/temperature/Z/pdf/z251.pdf > > > > John > A curve whose normalized slope is constant is an exponential--for instance, tempco of resistance is generally defined as (1/R)dR/dT, which is d/dT(ln R). If that were really some constant alpha, then ln R would be proportional to T, so R would be something times exp(alpha T). Of course, there's nothing that says the tempco is constant, IOW not all curves are exponential. The RTD curve is a simple rational function of T--it really linearizes beautifully with a bit of negative resistance, with theoretical deviations are of the order of 0.01K over wide temperature ranges. Cheers Phil Hobbs
From: Spehro Pefhany on 22 Dec 2009 14:51 On Tue, 22 Dec 2009 12:02:35 -0500, Phil Hobbs <pcdhSpamMeSenseless(a)electrooptical.net> wrote: >On 12/22/2009 11:28 AM, John Larkin wrote: >> On Mon, 21 Dec 2009 23:38:08 -0800, >> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >> >>> On Sat, 19 Dec 2009 17:39:19 -0800, John Larkin<jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >>> >>>> On Sat, 19 Dec 2009 17:34:01 -0800, >>>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>>> >>>>> On Sun, 13 Dec 2009 09:50:22 -0600, "RogerN"<regor(a)midwest.net> wrote: >>>>> >>>>>> >>>>>> "John Larkin"<jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote in message >>>>>> news:p1u7i5thbjmtjvqcj63b291l19rf7ktllp(a)4ax.com... >>>>>>> >>>>>>> >>>>>>> Does anybody remember the value of negative resistance that linearizes >>>>>>> a 100 ohm platinum RTD? >>>>>>> >>>>>>> John >>>>>> >>>>>> I thought RTD's were supposed to be linear. The 100 ohm resistance being at >>>>>> 0 Degrees C and a change of .385 ohms (for a 100 Ohm RTD) per Degree C. I >>>>>> read a description of instrumentation for RTD's once. They said they used a >>>>>> 1ma current source to the RTD and compared it to the voltage drop with 1ma >>>>>> in a 100 Ohm resistor. Low current, 1ma, was used to minimize the RTD >>>>>> heating up from power. I know there is a 3rd and sometimes 4th sense wire >>>>>> used to compensate for the lead resistance. I don't exactly remember the >>>>>> source but I read the information when looking up info for my Allen Bradley >>>>>> RTD input card for my PLC 5 rack. >>>>>> >>>>>> RogerN >>>>>> >>>>> Platinum RTDs are about total repeatability, a real mantra in the measurement >>>>> community. And 393 ppm/K is an exponential, like most all resistance tempcos. >>>> >>>> Exponential? How so? >>>> >>>> John >>> >>> Each degree of temperature change is a multiplier on the degree base before it. >>> so the recurrence relation results in an exponential. Thus it can be modeled >>> as r' = r(25) * k(1)e^[k(2)*t], an exponential. BTW just look at a R vs T plot. >> >> What are the coefficients? The curve slopes down. >> >> I've never seen the platinum RTD curve expressed as an exponential. >> The usual formulation is a polynomial. >> >> www.analogzone.com/acqt_052807.pdf >> >> http://www.omega.com/temperature/Z/pdf/z251.pdf >> >> >> >> John >> > >A curve whose normalized slope is constant is an exponential--for >instance, tempco of resistance is generally defined as (1/R)dR/dT, which >is d/dT(ln R). If that were really some constant alpha, then ln R would >be proportional to T, so R would be something times exp(alpha T). > >Of course, there's nothing that says the tempco is constant, IOW not all >curves are exponential. The RTD curve is a simple rational function of >T--it really linearizes beautifully with a bit of negative resistance, >with theoretical deviations are of the order of 0.01K over wide >temperature ranges. > >Cheers > >Phil Hobbs Maybe 0.1�C over the full temperature range of an RTD (-200 ~ 850�C). R = -2311 ohms. About +/-0.02� for 0 ~ 400�C. R = -2515 ohms And almost nothing for 0 ~ 100�C R = -2687 ohms
From: Phil Hobbs on 22 Dec 2009 15:01
On 12/22/2009 2:51 PM, Spehro Pefhany wrote: > On Tue, 22 Dec 2009 12:02:35 -0500, Phil Hobbs > <pcdhSpamMeSenseless(a)electrooptical.net> wrote: > >> On 12/22/2009 11:28 AM, John Larkin wrote: >>> On Mon, 21 Dec 2009 23:38:08 -0800, >>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>> >>>> On Sat, 19 Dec 2009 17:39:19 -0800, John Larkin<jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote: >>>> >>>>> On Sat, 19 Dec 2009 17:34:01 -0800, >>>>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>>>> >>>>>> On Sun, 13 Dec 2009 09:50:22 -0600, "RogerN"<regor(a)midwest.net> wrote: >>>>>> >>>>>>> >>>>>>> "John Larkin"<jjlarkin(a)highNOTlandTHIStechnologyPART.com> wrote in message >>>>>>> news:p1u7i5thbjmtjvqcj63b291l19rf7ktllp(a)4ax.com... >>>>>>>> >>>>>>>> >>>>>>>> Does anybody remember the value of negative resistance that linearizes >>>>>>>> a 100 ohm platinum RTD? >>>>>>>> >>>>>>>> John >>>>>>> >>>>>>> I thought RTD's were supposed to be linear. The 100 ohm resistance being at >>>>>>> 0 Degrees C and a change of .385 ohms (for a 100 Ohm RTD) per Degree C. I >>>>>>> read a description of instrumentation for RTD's once. They said they used a >>>>>>> 1ma current source to the RTD and compared it to the voltage drop with 1ma >>>>>>> in a 100 Ohm resistor. Low current, 1ma, was used to minimize the RTD >>>>>>> heating up from power. I know there is a 3rd and sometimes 4th sense wire >>>>>>> used to compensate for the lead resistance. I don't exactly remember the >>>>>>> source but I read the information when looking up info for my Allen Bradley >>>>>>> RTD input card for my PLC 5 rack. >>>>>>> >>>>>>> RogerN >>>>>>> >>>>>> Platinum RTDs are about total repeatability, a real mantra in the measurement >>>>>> community. And 393 ppm/K is an exponential, like most all resistance tempcos. >>>>> >>>>> Exponential? How so? >>>>> >>>>> John >>>> >>>> Each degree of temperature change is a multiplier on the degree base before it. >>>> so the recurrence relation results in an exponential. Thus it can be modeled >>>> as r' = r(25) * k(1)e^[k(2)*t], an exponential. BTW just look at a R vs T plot. >>> >>> What are the coefficients? The curve slopes down. >>> >>> I've never seen the platinum RTD curve expressed as an exponential. >>> The usual formulation is a polynomial. >>> >>> www.analogzone.com/acqt_052807.pdf >>> >>> http://www.omega.com/temperature/Z/pdf/z251.pdf >>> >>> >>> >>> John >>> >> >> A curve whose normalized slope is constant is an exponential--for >> instance, tempco of resistance is generally defined as (1/R)dR/dT, which >> is d/dT(ln R). If that were really some constant alpha, then ln R would >> be proportional to T, so R would be something times exp(alpha T). >> >> Of course, there's nothing that says the tempco is constant, IOW not all >> curves are exponential. The RTD curve is a simple rational function of >> T--it really linearizes beautifully with a bit of negative resistance, >> with theoretical deviations are of the order of 0.01K over wide >> temperature ranges. >> >> Cheers >> >> Phil Hobbs > > Maybe 0.1�C over the full temperature range of an RTD (-200 ~ 850�C). > R = -2311 ohms. > > About +/-0.02� for 0 ~ 400�C. > R = -2515 ohms > > And almost nothing for 0 ~ 100�C > R = -2687 ohms > > > I can see we share some of the same odd taste in recreations. Depends a bit on whether you like the European or US curves, of course. They have shinier platinum over there, like everything else--just ask them. ;) But then at that level it also depends on residual stress in the metal, CTE mismatch with the substrate.... Still, from a mathematical perspective, it's pretty. Cheers Phil Hobbs |