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Expenential decay linearizer

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mahfuzmatyaacob

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Hey guys,

Im working on a small project to linearize exponential decay (discharge voltage or maybe charging voltage). The circuit need to linearize it according to a math func (probably). Any idea u guys might wanna share?

Thanks!
 
Would you care to offer a precise definition of what it means to "linearize" an exponential waveform? It sounds like a really silly idea. Why would you want to do such a thing?
 
Papabravo said:
Would you care to offer a precise definition of what it means to "linearize" an exponential waveform? It sounds like a really silly idea. Why would you want to do such a thing?

It is a test fixture for embedded A/D. The discharge voltage is used as the input. But since A/D needs an increasing ramp voltage, the discharge is converted into linearized increasing ramp. (discharge region is used instead of charging because of the time constant)
 
As I remember if you take and op amp in the inverting mode, put a capacitor from the - input to ground and connect a resistor to a + supply the output from the op amp will be a linear increasing rampas the capacitor charges. If once the capacitor is charged and then the resistor lead that was connected to the + supply is grounded the output of the op amp would be a linear ramp going down. Perhaps some modifications of this circuit would solve the problem.
 
k7elp60 said:
As I remember if you take and op amp in the inverting mode, put a capacitor from the - input to ground and connect a resistor to a + supply the output from the op amp will be a linear increasing rampas the capacitor charges. If once the capacitor is charged and then the resistor lead that was connected to the + supply is grounded the output of the op amp would be a linear ramp going down. Perhaps some modifications of this circuit would solve the problem.

I already have the circuitry for discharge voltage. The thing is how to convert each point of voltage discharge to an increasing ramp voltage. Im thinking of using programmable ALU (writting ln function since discharge is in exponential) to convert the voltage decay to a constant increasing voltage. Hows that?
 
You haven't posted your circuit, so this idea may not be relevant. What about converting your single slope ADC to a dual-slope ADC so the non-linearity cancels out?
 
Would a logarithmic amplifier do the job?
 
Papabravo said:
Would a logarithmic amplifier do the job?

Logarithmic amplifier? Well im not used to it so im know sure how that thing operates. Can the logarithmic amp be setted to a certain formula that enable the discharge to be linearized as in a factor of ln?
 
Yes. The output of a logarithmic amplifier is the logarithm of the input. So, says me, if you feed an exponential signal in you'll get the exponent out which is a linear function of the time t. N'est pas?
 
Papabravo said:
Yes. The output of a logarithmic amplifier is the logarithm of the input. So, says me, if you feed an exponential signal in you'll get the exponent out which is a linear function of the time t. N'est pas?

Guess i should have use it then... Providing an exponential decay input to get the desired linearized output.. Logarithmic amp, sounds interesting.. WIll have a check on that device. Still need to figure out the design... :(
 
If you take a 555 timer and inject a constant current source into its its threshold and discharge pins, you will see linear ramp appear on that pin. The straightness of the ramp depends on the flatness of the current source's I-V characteristic.

I used the attached system in a ramp ADC running close to 44kHz. The ramp will appear on the collector of Q1. The trigger can be the output of another 555 if you want. I'd also adjust C1 and C2 to get right time constant.

The main limit is that it will only drive high-impedance loads. Our load was about 100kOhms. When we lowered it below 50k, the ramp seemed to destabilize.
 

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DigiTan, he has already made it clear that his goal is not to generate a linear ramp per se. His goal is to linearize the exponential discharge of a capacitor.

I agree that a log amp is the way to do it.
 
Roff said:
DigiTan, he has already made it clear that his goal is not to generate a linear ramp per se. His goal is to linearize the exponential discharge of a capacitor.

I agree that a log amp is the way to do it.

Yeah, u got it right Roff... Anyway, Thanks DigiTan...

I do agree that a log amp is suitable, but can it be programmed to do certain formula conversion? I dont think so.. For example, the Q1 is the highest input value (exponentially decaying to 0V). So, the conversion need to be -ln (input_value/Q1).. This will generate a linearized waveform from an exponential decay input.. Each input_value is actually the value of the exponential decay voltage.
 
DigiTan said:
If you take a 555 timer and inject a constant current source into its its threshold and discharge pins, you will see linear ramp appear on that pin. The straightness of the ramp depends on the flatness of the current source's I-V characteristic.

I used the attached system in a ramp ADC running close to 44kHz. The ramp will appear on the collector of Q1. The trigger can be the output of another 555 if you want. I'd also adjust C1 and C2 to get right time constant.

The main limit is that it will only drive high-impedance loads. Our load was about 100kOhms. When we lowered it below 50k, the ramp seemed to destabilize.

Thanks for sharing it, but the circuit u posted is for generating a linear ramp from a constant source. My question was to change an exponential decay voltage to a linear increasing voltage. The dischrage is in exponential, so in order to linearized it, i have to have a circuit that have a -ln function. PIC would be my choice, but logarithmic amp could also do. Its juz that it might b in terms of analog, where u cant program to a certain logarithmic function like PIC does.. Thats what im thinking :(
 
Am I missing the point here?

I understand that the idea is to create a linear ramp from an exponential decay.

But why? What is so magical about the original exponential decay?

If you need a linear ramp, then make one using the appropriate techniques.

This makes as much sense as saying:

"I have a steam engine and want to convert it into a diesel engine"

Just my two Ringits worth.

JimB
 
You want an exponential input and a linear output. When the voltage is low the gain is low and then the voltage is high the gain should be very high. When the slope is positive and the reverse of that when the slope is negative.

On the negative slope, as the voltage approaches zero the gain approaches infinity. This is a recipe for instability. On the positive slope side the gain is infinity at the reference voltage. It will oscillate.

This sounds like a school project not a real world thing. If you want a linear ramp, make one.
 
JimB said:
Am I missing the point here?

I understand that the idea is to create a linear ramp from an exponential decay.

But why? What is so magical about the original exponential decay?

If you need a linear ramp, then make one using the appropriate techniques.

This makes as much sense as saying:

"I have a steam engine and want to convert it into a diesel engine"

Just my two Ringits worth.

JimB

Linearized ramp is to be used as a test fixture in embedded A/D test. That is why it need to be converted from exponential decay voltage (capacitor discharge to be exact). So, the circuit its just a converter, converting the exponential to linear ramp, so that it can be use in A/D testing.
 
I think we all understand your desire for RC exponential to linear ramp.
Most of us know how to make a linear ramp.
None of us know how to make exponential to linear with out errors.
With “analog computers” there is +, -, log, x^2, AxB and some more. Log is not very accurate. Squared is ok. How good do you want your ramp? As the exponential approaches Vref or GND the error will get bad.

Search “analog computers” and see what functions there are. Then using these functions try to get from exponential to linear. I would use EXCEL to do the math. You could use spice but I like EXCEL better for math.

I think you are not getting an answer, just questions because this is not simple, accurate or temperature stable. AND a linear ramp is so easy to make.
 
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