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

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