How to create a smooth change in voltage?

We are given two voltages A and B between 0 and 5V. So how do I generate a smooth/continuous analog change in voltage from A to B in a predefined time? The current with that varying voltage is 1 ma or less. The output voltage value is described by a simple quadratic (aX^2)+(bx)+c, at time x seconds.

If that not possible using an Arduino - what is the nearest solution to it? It seems that it would require an RC circuit?

When I mean smooth/continous I mean it doesn't move in "digital steps" or to use an analogy with resistance instead of voltage - it would be like the way resistance changes when a potentiometer is turned between two places, in a given time, by hand.

A potential solution would be to make a circuit that generate arbitrary voltage between 0 and 5v, some how, at a point in time. For each subsequent small change in time, the change in time is constant, generate the desired voltage from a sketch. If the change of time is small and constant, will putting in a high pass RC filter work? Though I'm not sure of a circuit that can create an arbitrary voltage, or arbitrary voltage resolution or how good the RC filter approximates the quadratic smoothness. I don't know the answer.

• If your only constraint is that the change be smooth, then an RC circuit would do the trick, with the proviso that the voltage will approach 5v asymptotically but never truly get there. Are there in fact other constraints, such as you want the voltage to increase linearly, so after half the time you have half the voltage? Nov 12 '16 at 19:30
• What kind of load will be attached to it? An RC filter will not work well with highish loads. You need to buffer it using an opamp. Alternatively add an DAC chip to your circuit. Nov 12 '16 at 19:46
• @MarkSmith The asympotitic behaviour is not really a problem (because I think you can use an opamp to rescale from between greater than 0 and less than 5 volts). .But I would prefer a solution without op-amps. Regarding the linear behaviour -I updated the question.
– Pete
Nov 12 '16 at 20:24
• @Gerben It sounds like the answer may be in your comment (use RC filter and OP amp).
– Pete
Nov 12 '16 at 20:28
• The quadratic requirement is quite significant - I can't think of any way to get that with an RC circuit, op-amp or no op-amp. Nov 12 '16 at 22:28