I have just started learning opamps in an introductory course. I am stuck at a question that asks to draw an opamp circuit such that Vo=2Vi + 3 dVi/dt

My guess would be to use differentiator circuit. But another type of opamp shud be attached to the input of the differentiator configuration to give the 2Vi.

Vo=output voltage. Vi=input voltage

Am i thinking right?
Thanks.

 

You could use a circuit with two stages:

Stage 1: feed \(V_{i}\) into the inverting inputs of a differentiator(where the product RC = 3) and an inverting amplifier (with a gain of -2).
The outputs are -RC(d\(V_{i}\)/dt) and -2\(V_{i}\).

Stage 2: feed the two outputs of stage 1 into the inverting input of an inverting summer. This sums the inputs and inverts them to give:
\(V_{o}\) = 2\(V_{i}\) + RC(d\(V_{i}\)/dt), where RC=3

NB: The non-inverting inputs of all three differential amps in both stages must be grounded.

 

By the way, if you're looking for examples check the ff. links:

Inverting amplifier: http://www.allaboutcircuits.com/vol_3/chpt_8/5.html
Inverting summer: http://www.allaboutcircuits.com/vol_3/chpt_8/8.html
Differentiators : http://www.allaboutcircuits.com/vol_3/chpt_8/11.html