question about "Linearization"

Discussion in 'General Electronics Chat' started by reckz, Nov 13, 2008.

  1. reckz

    Thread Starter New Member

    Nov 11, 2008
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    What is Linearization. In circuit analysis, why do we use it and what techniques are used to achieve a sensor linearization?

    Thanks.
     
  2. thingmaker3

    Retired Moderator

    May 16, 2005
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    "Linearization" is to make more linear. The mire non-linear circuit, the more more distortion it will produce.
     
  3. scubasteve_911

    Senior Member

    Dec 27, 2007
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    Linearization has many applications.. A lot of times, a system is made linear through a transform, so that it can be controlled whereas a non-linear system is very difficult to control from a stability perspective.

    Another use is to make a non-linear response from a sensor, a linear response. A thermister typically has a non-linear response. One would find the function that governs the response, then transform it to a linear one, so that you may gather meaningful data.

    The techniques used are:

    curve fitting (interpolation), many types, polynomial, etc. least-squares, vandermonde, etc.
    regression
    lookup tables

    Steve
     
  4. reckz

    Thread Starter New Member

    Nov 11, 2008
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    thanks both of you folks for providing the information.

    Steve, about the lookup tables - what is the general concept of developing such a table. For example a Linearization table having Voltage vs Temperature. How does this table related each voltage value to a corresponding temperature reading, I guess I am interested to know the high level concept of the algorithm that goes into developing such a table.
     
  5. scubasteve_911

    Senior Member

    Dec 27, 2007
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    I generate most of my lookup tables in excel, or from a interpolated function. The following link should help you out.

    http://en.wikipedia.org/wiki/Lookup_table

    The advantages of using lookup tables are when the function requires a high degree polynomial to interpolate, and the many multiplications and summations would take too much time and memory, and be subject to rounding errors, etc. Also, lookup tables are the fastest way to get your result.

    Steve
     
  6. reckz

    Thread Starter New Member

    Nov 11, 2008
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    thanks for the info - this helped explaining some of the questions I had.
     
  7. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Sorry but I don't think Steve's definition fits.

    There are at least three distinct uses of the word.

    Firstly if a transfer curve (output v input) is not a straight line (non linear) linearisation involves substituting a linear function (straight line) for a small section of the transfer curve, to make calculations/ formulae easier.

    For exmple the transfer curve for a FET is parabolic or worse, but can be approximated by a straight line in it's 'linear' region of operation.

    This is not quite the same as 'correction tables' that used to be common on the back of meters and such to acount for the fact that they were non ideal, not exactly 'linear'.

    Secondly 'linearisation' occurs when feedback is applied to an amplifier. This refers to the control of gain v frequency one obtains by the use of feedback.

    Thirdly, Linearisation is used in many fields of numerical maths to indicate the substitution of a linear function for a more complicated function. This is often done in Finite Element analysis where repeated applications of a simple function will converge to the solution with any required degree of accuracy.
     
    Last edited: Nov 14, 2008
  8. scubasteve_911

    Senior Member

    Dec 27, 2007
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    Hey,

    I illuded to this when I mentioned control systems, but this is not what the OP desires. He is looking for ways to make a sensor's response linear.

    Steve
     
  9. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Steve, you are correct, I didn't read the bit about the sensor properly.

    The simplest way to linearize a sensor is to limit the range of operation so that the output of the sensor approximates to a linear function over the small range.
     
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