# Is there an exponentiation configuration for MOSFETs or Opamps?

I am working on a problem that can be made really simple if the output of the transistor were to be a fixed power of the input. For ex., if the input is 8 V and power is 0.333, then the output voltage is 2 V.

An opamp circuit would be fine as well. Essentially, the circuit should be minimal (1 transistor or 1 opamp) and the output should be exponentiation.

• You can get an exp(x) function by using an op amp and one transistor or one diode (I believe the transistor option is superior, but I can't remember why), along with a few passives. – Hearth Feb 2 '19 at 16:37
• Re-reading the question though, it sounds like you want a polynomial of the input, not an exponential. That's also possible, though complicated. Certainly not a one-transistor or one-opamp job; look up analog multipliers. – Hearth Feb 2 '19 at 16:39
• @Hearth I don't remember the physics explanation, but the lore I've heard is that a diode-connected transistor acts more like an ideal diode than a diode does, being good over several more decades of current. – TimWescott Feb 2 '19 at 16:46
• So are you looking for a one-transistor exponentiation circuit so that you can use it to build a more complicated power-of-whatever circuit? Or are you conflating exponentiation with $x^3$? – TimWescott Feb 2 '19 at 16:49
• Also: How do you want it to handle negative inputs? – Hearth Feb 2 '19 at 16:58

Look up the square root diode function circuit, but modify for higher current maybe using a 3x Darlington emitter follower. This drives an unity inverter Op Amp 1st stage with emitter follower feedback for current gain to drive the 2nd stage inverting square root circuit for non-INV sqrt. sqrt function where $$\Vout=k\sqrt{Vin}=k\sqrt{Pd*Rin} \$$, where R input resistor accepts the high current to achieve the constant power or quadratic voltage of base-emitters before saturation, where it becomes more linear. Here the intermediate input R receives the current and the op amp Vin+ ref =0 but needs two inv. stages to make a non inverting function from a high impedance source.
￼ ￼ Here is one example where labelled R values are equal for k=1 but others must be chosen not to allow output currents to saturate the Op Amp or the Vce=0 which limits the decades of range unless you inject clever offsets that cancel/avoid this.