Circuit Optimization

Discussion in 'Math' started by ErnieM, Feb 16, 2012.

  1. ErnieM

    Thread Starter AAC Fanatic!

    Apr 24, 2011
    Circuit Optimization

    I am working out a circuit for a micro controller device. I am reading two voltages thru an analog to digital converter, performing a conversion calculation on the results and using the result to adjust some other parameter.

    The conversion is of the form:

    T = K (\frac {X}{Y}-1)

    K is a constant
    X is a measured voltage dependent upon an external resistor
    Y is a measured voltage reference

    We can also say the following about X and Y:

    Y \leq X\leq 5

    0 \leq Y\leq 5

    I chose this scheme for a number of reasons, not the least of which is the exact value of the driving 5 volt supply voltage cancels out of the equation.

    Now my goal is to select a Y to minimize errors when computing T. To predict that I am equating the magnitude of the change due to X to the magnitude of the change due to Y:

    Compute derivatives:

    \frac {dT}{dX} = \frac {K}{Y}

    \frac {dT}{dY} = -K \frac {X}{Y^2}

    Equate the magnitudes:

    \frac {K}{Y}=K \frac {X}{Y^2}


    At this point I start waving my hands trying to explain why setting the constant term Y to 2.5 will result in the least errors in the system, but all I can say is it "feels" right.

    Does someone catch my drift here and can offer a firm mathematical basis for selecting Y?