# Analog Linearization Technique

#### vdd

Joined Nov 8, 2006
11
Hi All,
I have sensor circuit(proximity) whose o/p is as shown in the plot attached.
I want linear o/p with respect to distance. Can you suggest some analog linearisation technique(preferably low cost) or is there any other technique where we can achieve Linearization of the o/p voltage.

Regards,
vdd

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#### n9352527

Joined Oct 14, 2005
1,198
Quite difficult. The easiest way I can think of is to limit the region of signal that you are interested in and apply a piecewise linear compensation. You would get some error, worse on some parts of the curve and better on others. Try plotting the log of the signal and see whether it is any easier in piecewise sense.

I have no idea whether there is anyone working with high-order analogue linearisations, probably not. Complex filters might be able to do it, but I imagine playing with them is not that easy.

Digital linearisation is another idea, easy to do and pretty flexible.

#### vdd

Joined Nov 8, 2006
11
Hi n9352527,
The digital linearization technique you are talking about is using ADC, microcontroller(with look up table in EPROM)and DAC........RIGHT?
or any other digital linearization technique.
How about its size and cost?.
I want whole thing in small size .
Can u help?

Regards,
vdd

#### beenthere

Joined Apr 20, 2004
15,819
Hi,

Are you fixed on this sensor? Is there another proximity detector that might have a linear detection signal?

#### Papabravo

Joined Feb 24, 2006
12,767
Just so I'm clear. Do you want the voltage output of the network connected to the sensor to be a linear function of distance or do you want a polynomial approximation that will convert the sensor voltage to distance?

#### vdd

Joined Nov 8, 2006
11
Just so I'm clear. Do you want the voltage output of the network connected to the sensor to be a linear function of distance or do you want a polynomial approximation that will convert the sensor voltage to distance?
Hello Papabravo ,
I want the solution for the former part of your question .

#### vdd

Joined Nov 8, 2006
11
Hi,

Are you fixed on this sensor? Is there another proximity detector that might have a linear detection signal?
Hello beenthere,
I am working on a Analog inductive proximity sensor and as per my knowledge due to the magnetic properties of the ferromagnetic targets the o/p of the sensor is substantially non-linear .
Can you provide me a technique with op-amp whose transfer function can be designed to give linear output.

Thanks,
vdd

#### Papabravo

Joined Feb 24, 2006
12,767
Hello Papabravo ,
I want the solution for the former part of your question .
I know of no such solution or technology. The vast bulk of opamp circuits are linear. There are certain elementary nonlinearities like deadband, limiter, and rectifier. AFAIK there is no general purpose analog method of linearizing such a characteristic.

With a sufficiently fast A/D converter, a Digital Signal Processor, and a D/A converter you might have a chance. It's not analog and it won't be particularly inexpensive. So I guess you're SOL.

#### beenthere

Joined Apr 20, 2004
15,819
Hi,

I'm not aware of any op amp with such a transfer function. If you were dealing with a changing frequency, some feedback network might be devised, but not for an analog voltage.

#### Papabravo

Joined Feb 24, 2006
12,767
If you can accurately determine the function of the sensor and can program a piecewise linear version of the inverse of the sensor function with an opamp and diodes then cascade the sensor and the inverse function generator then

Rich (BB code):
y = f^-1(f(x)) = x
I have absolutely no idea what happens if the implemented inverse function drifts away from the true inverse, or what happens if the sensor characteristic changes.

Do you know how to build a piecewise linear diode function generator?

#### hgmjr

Joined Jan 28, 2005
9,029
Hi All,
I have sensor circuit(proximity) whose o/p is as shown in the plot attached.
I want linear o/p with respect to distance. Can you suggest some analog linearisation technique(preferably low cost) or is there any other technique where we can achieve Linearization of the o/p voltage.

Regards,
vdd
vdd,

Can you explain the reason you would like the output to be linear?

hgmjr

#### vdd

Joined Nov 8, 2006
11
If you can accurately determine the function of the sensor and can program a piecewise linear version of the inverse of the sensor function with an opamp and diodes then cascade the sensor and the inverse function generator then

Rich (BB code):
y = f^-1(f(x)) = x
I have absolutely no idea what happens if the implemented inverse function drifts away from the true inverse, or what happens if the sensor characteristic changes.

Do you know how to build a piecewise linear diode function generator?
hello papabravo,
I am not at all aware of piecewise linear diode function generator
I would be very happy if you elaborate on the same.

thanks,
vdd

#### Papabravo

Joined Feb 24, 2006
12,767
It's an old analog computer technique. I've never used it myself, but there was a description in my textbook:
Scott, Norman R.,Analog and Digital Computer Technology, McGraw-Hill, 1960, pp.70-88

The example that they give is for a parabola generator.

The crux of the technique is to use a diode in series with a resistor and a voltage source on the inputs to a summing amplifier. It doesn't look like a very prctical technique unless size and cost are no object.

#### beenthere

Joined Apr 20, 2004
15,819
Hi,

It's not very practical. If you can get hold of the spec sheets for an ICL8038 waveform generator, you'll find the sine wave generator is really a parabolic waveform generator. It's very elaborate and has no output capability.

#### Papabravo

Joined Feb 24, 2006
12,767
It did not occur to me until now that the inverse of the sensor function is going to have near vertical slopes at the extremes. I think that will make any opamp solution well nigh impossible.

#### beenthere

Joined Apr 20, 2004
15,819
Hi,

But trivial for a microprocessor with an A to D and look-up tables.

#### Papabravo

Joined Feb 24, 2006
12,767
Hi,

But trivial for a microprocessor with an A to D and look-up tables.
Don't forget the DAC, the output needs to be analog. And we appear to have come full circle. It's too bad this solution was eliminated from the get go by the op's requirements.

#### vdd

Joined Nov 8, 2006
11
vdd,

Can you explain the reason you would like the output to be linear?

hgmjr
hi,
I want my output to be function of the distance so linearity is what I am looking for.

#### vdd

Joined Nov 8, 2006
11
Hi ,
I am really fixed on this thing.
Let me explain my application in brief.
I have a inductive proxi switch and I want to convert this into analog Inductive sensor.
So right now i am sensing the current which flows through the oscillator when the target approaches the sensor . This is ok and the plot is as shown in my earlier thread. Now the difficult task is to convert this voltage into the range of 1 to !0 Volts . As the plot is non-linear it has become very difficult for me to convert this into linear 1-10V.
Also I cannot use the digital technique because of size.

(Note-I have also used log amplifier to convert this exp. plot into linear one but with minimum success)

Thanks
vdd.

#### hgmjr

Joined Jan 28, 2005
9,029
Hi ,
I am really fixed on this thing.
Let me explain my application in brief.
I have a inductive proxi switch and I want to convert this into analog Inductive sensor.
So right now i am sensing the current which flows through the oscillator when the target approaches the sensor . This is ok and the plot is as shown in my earlier thread. Now the difficult task is to convert this voltage into the range of 1 to !0 Volts . As the plot is non-linear it has become very difficult for me to convert this into linear 1-10V.
Also I cannot use the digital technique because of size.

(Note-I have also used log amplifier to convert this exp. plot into linear one but with minimum success)

Thanks
vdd.
Are you planning to output the distance measurement to a display? If so, what kind of display are you planning to use? If not, what are you planning to feed the linearized output to once it is generated?

hgmjr