Measurement and result interpretation

Discussion in 'General Electronics Chat' started by fila, Sep 13, 2012.

  1. fila

    Thread Starter Member

    Feb 14, 2011
    64
    5
    I would like to know how to interpret the results of a measurement. Suppose you are designing a circuit. At point A in the circuit the voltage must have a value x_0.
    You build the circuit and take N measurements (x_1, x_2, ..., x_N) at that point and obtain the average value x_{avg}.

    Now we have to analyze the result. First we calculate the (absolute) difference between the desired value and the measured value

    |{\Delta}x| = |x_0 - x_{avg}|.

    That gives us some information about the quality of the design. But that isn't good enough.

    Let's say that x_0 = 5 V and x_{avg} = 4.9 V. We calculate |Δx| = 0.1 V. Another example is x_0 = 0.2 V, x_{avg} = 0.1 V gives also |Δx| = 0.1 V.

    But now if we calculate the relative difference

    x_{relative} = \frac{|{\Delta}x|}{x_0}

    the first example gives us x_{relative} = 2 %, and the second example x_{relative} = 50 %.

    Based on these examples how would you interpret the results? Are there any general rules or standards in the world of electronics about these values (absolute difference, relative difference)?
     
  2. #12

    Expert

    Nov 30, 2010
    16,257
    6,757
    In electronics, the % difference from the intended is usually the important number.

    1-(dX/Xo) x100= % error
     
  3. fila

    Thread Starter Member

    Feb 14, 2011
    64
    5
    How small would it have to be (error) to conclude that the design is good?
     
  4. #12

    Expert

    Nov 30, 2010
    16,257
    6,757
    Depends on your goal. I used to work 1% meters. For that, "good" was less than 1%.
    In early TV's, 20% was often considered good enough.
     
  5. Papabravo

    Expert

    Feb 24, 2006
    10,136
    1,786
    If you compute the variance of the samples it will tell you the range of likely values with high probability. The square root of the variance is the standard deviation. 99% of all the measurements will be within 3 standard deviations of the mean. If you establish what you expect that range to be and the measurements confirm that, then you have some evidence for calling it good.
     
  6. Moon968

    New Member

    Apr 14, 2014
    10
    0
    To achieve the most exact results possible and to identify measurement errors multiple readings are unavoidable.
     
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