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  • Cute Power Law circuit--selectable 1/3, 1/2, 2/3, 3/2, 2nd, and 3rd--for 30 cents

    From Phil Hobbs@pcdhSpamMeSenseless@electrooptical.net to sci.electronics.design on Tue Feb 24 13:49:34 2026
    From Newsgroup: sci.electronics.design

    Hi, All,

    I posted a conceptual power law circuit a week or so ago on the "cheap
    analog square function?" thread.

    Turns out that you can make it pretty simple and accurate by using dual matched (but not monolithic) PNPs such as the NSVT30010MXV6T1G from
    onsemi. These things have a maximum 2 mV offset; high, flat beta; come
    in SC70-6, and cost 10 cents @ qty 150 (LCSC).

    The circuit is pretty simple, just a current mirror with a twist.

    +5 0-------*-----------*
    | |
    | |
    Q1A \ | Q1B \ |
    V| V|
    |---* |---*
    /| | /| |
    3/2 / | | / | | 2/3
    | | | |
    0--*-----* *-----*--0
    | |
    | |
    Q2A \ | Q2B \ |
    V| V|
    |---* |---*
    /| | /| |
    3 / | | / | | 1/3
    | | | |
    0--*-----* *-----*--0<---0
    | | |
    | | R
    | Q3B \ | R
    | V| R
    | |---* R
    | /| | |
    Q3A \ | / | | GND
    V| | |
    |---------*-----*
    /| |
    / | |
    | |
    | |
    V I_OUT V I_IN


    If you move the resistor to the other positions, you get the indicated
    power law. You want the resistor to take a few times the maximum input current so that it effectively nails the top two stages still. Two
    packages get you the square or square root.

    It works very nicely in a feedback loop controlling one of our thermal
    Faraday actuators in Class H or filtered Class D. In that one, the
    heating power goes as V**2 and the RTD bridge gain goes as V, so a cube
    root is nice. (I'll post that shortly.)

    Datasheet thermal resistance is about 350 K/W to ambient, with the
    companion device receiving about half the delta-T. As long as the power dissipated isn't more than a few milliwatts per device, the thermal
    offset and slope errors stay within that 2 mV spec.

    <https://electrooptical.net/www/sed/BehavioralClassHCubeRootPNP.png> is
    an LTspice screenshot that shows the cube rooter controlling the pass
    element in a Class H circuit with a constant 1-V of headroom. (The
    variable switching supply is done behaviorally using an E source.)

    It's pretty handy--with a 10:1 voltage range on the heater, the loop
    bandwidth would want to change by 100 times without it!

    Cheers

    Phil Hobbs
    --
    Dr Philip C D Hobbs
    Principal Consultant
    ElectroOptical Innovations LLC / Hobbs ElectroOptics
    Optics, Electro-optics, Photonics, Analog Electronics
    Briarcliff Manor NY 10510

    http://electrooptical.net
    http://hobbs-eo.com

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