Non-linear functions ...
in [Design]
|
From: Fred Bartoli on 26 Nov 2009 03:51 Spehro Pefhany a �crit : > On Wed, 25 Nov 2009 16:10:31 +0100, Fred Bartoli <" "> wrote: > >> Hmmm, even simpler... >> You could use the 555 with an external mos switch with it's source >> shifted, say 1V (guess why) and omit the constant subtraction from your >> Vout input. >> >> >> R C RC = C2 >> ___ || >> C1 >--|___|--+--||---. >> | || | >> | === >> Vout >----------. .--------+ GND >> | | | >> .-----. | >> \+ -/ +-|| >> comparator \ / ->|| >> V +-||---. >> | | | >> | +1V | >> .--o--. | >> GND -|D S Q|-------------' >> | | >> Clk >---|> -| ___ >> | R Q|---|___|--+-----> Flow >> '--o--' | >> --- >> --- >> | >> === >> GND > > Very nice, Fred! > > These should be very close to practical values: > > 24K9 10n > ___ || > 6.02V >--|___|--+--||---. > | || | > | === > Vout >---------. .--------+ GND > | | | > .-----. | > \+ -/ +-|| > comparator \ / ->|| > V +-||---. > | | | > | 1V | > .--o--. | > GND -|D S Q|-------------' > | | > 100Hz Clk >---|> -| ___ > | R Q|---|___|--+-----> Flow > '--o--' | 200mV full scale > --- > --- > | > === > GND > > Thanks for calculating the values I was to lazy to compute. Now I can reveal the whole world the last simplification bit (ahem) : that is, if you make sure the duty cycle is far enough from 100%, which sure would be with a 100Hz clock, then you can just delete the 1V reference and make it a simple resistor (with a small bypass cap) so that the 6.02V reference with the 24K9/Rsource divider just gives you the wanted 1V at the capacitor top. Adjust the source bypass cap to optimize the circuit behavior WRT the mosfet charges. A value from the low tens of pF to maybe 1nF. Also, please applause the effort I made in disclosing the resistor's secret value (just had a cup of coffee :-). That would be: 24K9 10n ___ || 6.02V >--|___|--+--||---. | || | | === Vout >---------. .--------+ GND | | | .-----. | \+ -/ +-|| comparator \ / ->|| optim. V +-||---. .---||-----. | | | | ___ | | '--------+--|___|---+ .--o--. | 4K96 | GND -|D S Q|-------------' === | | GND 100Hz Clk >---|> -| ___ | R Q|---|___|--+-----> Flow '--o--' | 200mV full scale --- --- | === GND -- Thanks, Fred.
From: Richard Rasker on 26 Nov 2009 06:50 Fred Bartoli <" "> wrote: > Spehro Pefhany a écrit : >> On Wed, 25 Nov 2009 16:10:31 +0100, Fred Bartoli <" "> wrote: >> >>> Hmmm, even simpler... [snip great, simple antilog circuit] > Thanks for calculating the values I was to lazy to compute. > > Now I can reveal the whole world the last simplification bit (ahem) : > that is, if you make sure the duty cycle is far enough from 100%, which > sure would be with a 100Hz clock, then you can just delete the 1V > reference and make it a simple resistor (with a small bypass cap) so > that the 6.02V reference with the 24K9/Rsource divider just gives you > the wanted 1V at the capacitor top. > Adjust the source bypass cap to optimize the circuit behavior WRT the > mosfet charges. A value from the low tens of pF to maybe 1nF. > > Also, please applause the effort I made in disclosing the resistor's > secret value (just had a cup of coffee :-). > > That would be: > 24K9 10n > ___ || > 6.02V >--|___|--+--||---. > | || | > | === > Vout >---------. .--------+ GND > | | | > .-----. | > \+ -/ +-|| > comparator \ / ->|| optim. > V +-||---. .---||-----. > > | | | | ___ | > | '--------+--|___|---+ > > .--o--. | 4K96 | > GND -|D S Q|-------------' === > | | GND > 100Hz Clk >---|> -| ___ > | R Q|---|___|--+-----> Flow > '--o--' | 200mV full scale > --- > --- > | > === > GND > Absolutely wonderful, I'm truly amazed how even elegant, simple circuits can often be optimized and refined even further! Now talking about optimization: from this design, it would appear that one could swap the MOSFET and 4K96 resistor -- which would mean that the internal discharge FET (using an ICM7555) can be used, doing away with an external MOSFET altogether. I'll build this beastie tomorrow, and I'm sure to let you know how it turns out! Thanks once again, best regards, Richard Rasker -- http://www.linetec.nl
From: Richard Rasker on 26 Nov 2009 07:38 Przemek Klosowski 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 >> >> 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. >> > > A second degree polynomial fit is not too bad either. > > V = -7.6087e-05*F^2 + 3.4724e-02 *F + 1.0566 > > BTW, your c1/c2 didn't work for me; shouldn't it be > 128,125 rather than 5,125? I think you made a miscalculation then, or misinterpreted the formula; the sensor's Vout exhibits an e-power curve which asymptotically approaches +6 volts, which means that c1 must be 5. An example with F=75ccm: Vout = 5(1-e^(-75/125))+1 ~= 5(1-0.55)+1 = 5*0.45+1 = 3.25V Richard Rasker -- http://www.linetec.nl
From: Fred Bartoli on 26 Nov 2009 07:51 Richard Rasker a écrit : > Fred Bartoli <" "> wrote: > >> Spehro Pefhany a écrit : >>> On Wed, 25 Nov 2009 16:10:31 +0100, Fred Bartoli <" "> wrote: >>> >>>> Hmmm, even simpler... > > [snip great, simple antilog circuit] > >> Thanks for calculating the values I was to lazy to compute. >> >> Now I can reveal the whole world the last simplification bit (ahem) : >> that is, if you make sure the duty cycle is far enough from 100%, which >> sure would be with a 100Hz clock, then you can just delete the 1V >> reference and make it a simple resistor (with a small bypass cap) so >> that the 6.02V reference with the 24K9/Rsource divider just gives you >> the wanted 1V at the capacitor top. >> Adjust the source bypass cap to optimize the circuit behavior WRT the >> mosfet charges. A value from the low tens of pF to maybe 1nF. >> >> Also, please applause the effort I made in disclosing the resistor's >> secret value (just had a cup of coffee :-). >> >> That would be: >> 24K9 10n >> ___ || >> 6.02V >--|___|--+--||---. >> | || | >> | === >> Vout >---------. .--------+ GND >> | | | >> .-----. | >> \+ -/ +-|| >> comparator \ / ->|| optim. >> V +-||---. .---||-----. >> >> | | | | ___ | >> | '--------+--|___|---+ >> >> .--o--. | 4K96 | >> GND -|D S Q|-------------' === >> | | GND >> 100Hz Clk >---|> -| ___ >> | R Q|---|___|--+-----> Flow >> '--o--' | 200mV full scale >> --- >> --- >> | >> === >> GND >> > > > Absolutely wonderful, I'm truly amazed how even elegant, simple circuits can > often be optimized and refined even further! > Now talking about optimization: from this design, it would appear that one > could swap the MOSFET and 4K96 resistor -- which would mean that the > internal discharge FET (using an ICM7555) can be used, doing away with an > external MOSFET altogether. > Of course you're absolutely right (I guess one cup of coffee wasn't enough this morning). Now you've really squizzed the last remaining bit of optimization out of this. -- Thanks, Fred.
From: Jim Thompson on 26 Nov 2009 10:07
On Wed, 25 Nov 2009 18:31:39 -0500, Spehro Pefhany <speffSNIP(a)interlogDOTyou.knowwhat> wrote: >On Wed, 25 Nov 2009 16:10:31 +0100, Fred Bartoli <" "> wrote: > >> >>Hmmm, even simpler... >>You could use the 555 with an external mos switch with it's source >>shifted, say 1V (guess why) and omit the constant subtraction from your >>Vout input. >> >> >> R C RC = C2 >> ___ || >> C1 >--|___|--+--||---. >> | || | >> | === >> Vout >----------. .--------+ GND >> | | | >> .-----. | >> \+ -/ +-|| >> comparator \ / ->|| >> V +-||---. >> | | | >> | +1V | >> .--o--. | >> GND -|D S Q|-------------' >> | | >> Clk >---|> -| ___ >> | R Q|---|___|--+-----> Flow >> '--o--' | >> --- >> --- >> | >> === >> GND > >Very nice, Fred! > >These should be very close to practical values: > > 24K9 10n > ___ || > 6.02V >--|___|--+--||---. > | || | > | === > Vout >---------. .--------+ GND > | | | > .-----. | > \+ -/ +-|| > comparator \ / ->|| > V +-||---. > | | | > | 1V | > .--o--. | > GND -|D S Q|-------------' > | | > 100Hz Clk >---|> -| ___ > | R Q|---|___|--+-----> Flow > '--o--' | 200mV full scale > --- > --- > | > === > GND > > > Indeed! VERY NICE! I nominate Fred's solution as the "Most Clever SED Posting of 2009" !! ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | |