From: pcdhSpamMeSenseless@electrooptical.net   
      
   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.   
      
    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   
      
   --- SoupGate-Win32 v1.05   
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