Analog Computer Power Raiser Design with OpAmp, Transistor & PTC temperature compensation

Analog Power Raiser is an Analog Computer that raises one input signal to the power of another input signal. How does this Analog computer work? What are the roles of its subcircuits and circuit components? This unique circuit is designed, presented and analyzed here as my 200th circuit video in my analog circuits playlist • Electrical Engineering... . This interesting analog circuit is designed with nine operational amplifiers, eight NPN BJT Bipolar Junction Transistors, two 1k ohm PTC TempCo resistors with positive temperature coefficients and two potentiometers to compute V1^V2 utilizing a smart technique of computing exp(V2*log(V1)) where exp() is the Antilog function (AntiLog Amplifier). V1 and V2 are the input voltage signals in this circuit and Vo=V1^V2 is the output voltage of the circuit. As discussed in detail in this video, this unique circuit uses Shockley PN junction equation Vbe=VT*log(collectorCurrent/SaturationCurrent) and matched pair of PN junctions of BJT transistors to remove the dependency on saturation current that is exponentially dependent on silicon process and junction temperature. Circuit also uses PTC Temperature Compensating resistor PT146 to then compensate the linear dependency on temperature to a good extent. The first subcircuit has two op amps and a pair of matched NPN BJT transistors to function as a Log Amplifier to compute natural logarithm of one input signal. Then the second subcircuit functions as a four-quadrant analog multiplier to compute the product of V2 and Log(V1) to generate V2*Log(V1) which is then fed as input to the third subcircuit that finally computes the antilog or Exp(V2*Log(V1)) = V1^V2 as the final output voltage of this unique Analog computer.

[@arturperreira5680]

Thanks for your great work , keep spreading the word.

[@STEMprof]

My pleasure. Thank you for encouraging comment. Glad that you liked this Analog Computer circuit. Here are few more examples: Analog Logarithm Computer with Op Amp ua-cam.com/video/RpKEq5WyoLg/v-deo.html
Analog Exponential (Anti-Log) computer ua-cam.com/video/kk2c7Gk3nW4/v-deo.html
Analog Multiplier Circuit (4-quadrant) ua-cam.com/video/VP53A2zpVMQ/v-deo.html
I hope these videos are interesting as well. 🙋‍♂️

[@user-qi6yy8uv7v]

Intresting! Thanks

[@STEMprof]

You are welcome! Glad that you liked this interesting Analog Computer :)

[@LydellAaron]

This is a fascinating circuit. How wide of a result voltage rail can you do if you tried with wide op amps?
Will the circuit do negative voltage power as a division fraction?

[@STEMprof]

Thank you. Glad that you liked this circuit. You can try larger voltage rail valued as large as Op Amp and NPN BJT transistors can properly operate. And yes, negative power also works as long as abs(Ln(V1))

[@shakaibsafvi97]

Excellent Video.... very very interesting... I could never have figured this out...
I can do a multiplication circuit...
raised to the power... absolutely not.... cheers !

[@STEMprof]

You're welcome. Glad that you liked this circuit video. As a special case when voltage V2 is constant, this unique circuit can also realizes signal to power n. 🙂

[@STEMprof]

Analog Power Raiser is an Analog Computer that raises one input signal to the power of another input signal. For more Analog Computer & Op Amp Circuit examples:
Analog Logarithm Computer with Op Amp ua-cam.com/video/RpKEq5WyoLg/v-deo.html
Analog Exponential (Anti-Log) computer ua-cam.com/video/kk2c7Gk3nW4/v-deo.html
Analog Multiplier Circuit (4-quadrant) ua-cam.com/video/VP53A2zpVMQ/v-deo.html
Analog Computer to Raise Signal to power n ua-cam.com/video/IUTlBH1UraE/v-deo.html
Analog Computer: Signal Division Calculator ua-cam.com/video/2axI5l3cf6c/v-deo.html
Op Amp Analog Computer Differential Equation Solver: ua-cam.com/video/ENq39EesfPw/v-deo.html
For more analog signal processing examples see: ua-cam.com/play/PLrwXF7N522y4c7c-8KBjrwd7IyaZfWxyt.html
I hope these Circuit design and analysis videos are helpful.

[@dcorp80]

😮

[@STEMprof]

😄👍

[@voice4voicelessKrzysiek]

I'm sorry I didn't do these calculations for years and I understand that you operate with approximate values but it still puzzles me how did you go straight from tempco to resistance value? Isn't it the proper formula: (1 + 3.5 * 10e-3 * delta T) * R?

[@STEMprof]

@voice4voicelessKrzysiek No Problem. Yes, starting from the formula TempCo Resistance = (1 + 3.5 * 10e-3 * delta T) * R = (1 + 3.5 * 10e-3 * (T-300) ) * 1kohm = (1 - 3.5*10e-3 *300 + 3.5 * 10e-3 * T ) * 1kohm that then simplifies to (1 - 1 + 3.5 * 10e-3 * T ) * 1kohm = 3.5 * 10e-3 * T ) * 1kohm and therefore TempCo Resistance = 3.5*T where T is the Temperature in degree Kelvin. I hope this explanation is helpful.

[@voice4voicelessKrzysiek]

@@STEMprof Yeah, thank you, I got it. Losing my agility in mathematical thinking in my old age 🤣

[@STEMprof]

Glad that the explanation is helpful. 🙋‍♂️