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

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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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Cute Power Law circuit--selectable 1/3, 1/2, 2/3, 3/2, 2nd, and 3rd--for 30 cents Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2026-02-24 13:49 -0500

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