Cuicut Output

[wheelman487]

I need help to create a circuit that creates the output below using only Capacitors inductors and Differentiating and/or integrating op amps only. Each input must go through at least one op amp. Not sure how to proceed, please help.
Thank you in advance

Wheelman487

A0 cos(ωt+Θ)+ A1(t-t0)³ + A2(t-t0)

 

[MrAl]

Hello,

Does this circuit have an input signal, and if so what is it? (For example Vin=sin(wt) )
Or is this supposed to be a generator circuit?
Also, it appears that A0, A1, and A2 are constants, is the phase shift (theta) constant too or can it vary?

 

[wheelman487]

Thanks for the reply
A0, A1, A2 are suppose to be gains, and theta are suppose to be constant. It will have an input signal which I also must figure out in order to obtain this output.
Thank you in advance
Wheelman487

 

[MrAl]

Hello again,

Oh, so you are saying that you can use any input signal you want, or will it be something set already?

One way to go about this is to take the Laplace transform of each term and that will show you how many integrators you need for each part or what else you need. I guess we could proceed that way if you like.
To see if this makes sense to you, the last term can be translated into A2/s^2, and that indicates that we'll need two integrators for that term. Does that make sense to you to do it this way or does it make no sense to you at all?

 

[wheelman487]

Thank You For the reply
It will be any input signal I want. My teacher told it would be easier to ignore the theta and t0 terms, and if I understand right your saying if I take the Laplace transform of each I could create the circuit using all integrators. I'm going to try this thank you.
This is the letter he sent us to make things easier see what you make of it.
Thank you in advance

Wheelman487

Ps thanks for your help and time


The t0 in the equations I gave are only there to represent generality as far as a TIME SHIFT (maybe the function generator didn't start it at time zero...)! If it helps, ignore the t0, and just look at the t term.

For example, if your output looks like

vo(t) = Ao*cos(wt+theta) +A1*(t-t0)^2 + A2*(t-t0)...

THE base equation is really

vo(t) = Ao*cos(wt) + A1*(t^2) +A2*(t)...

Note also that the theta or phi term in the output is just a general phase shift! the main part of that function is cos(wt)...

These outputs all will be repeating (periodic, but you can choose to use the same frequency for each!!). It doesn't matter much for the design, but will for the simulation and physical circuit construction.

AGAIN, you can pick the w (omega, frequency)...

ALSO...what is u(t)? What is delta(t)? They are functions with specific names and specific definitions. You have seen them before (in your circuit II course!), and will see them again. This definitely is not meant to be a trick, nor is it meant to complicate things further...

tpn

 

[MrAl]

Hello again,

u(t) is considered a step, while delta(t) is an impulse (usually represented by the curly delta symbol). If you have never encountered these before you may want to look into them also. It helps to know that u(t) is 1/s in the frequency domain.

As far as the circuit is concerned, we can start with the last term and that will get you going i think. That is:
Vo(t)=A2*(t)

Lets start by doing that one first as a separate circuit and that will show the procedure pretty well i think.

If you look at a table of Laplace Transforms you should find something like this:
t*u(t) => 1/s^2

which is 1/s*1/s, and if you recall, 1/s is an integration, so 1/s^2 is 1/s times 1/s which is a double integration which is two integrators one after the other:
Vin o---1/s---o---1/s---o Vout

so all that is left is to add the constant:
Vin o---a---o---1/s---o---1/s---o Vout

However, one of those 1/s has to be considered to be u(t) i guess, so we end up with the actual circuit:

Vin*u(t) o---a---o---1/s---o Vout

So do you think you can convert this to a circuit now? Do this one first and we can go from there but you'll probably get the rest after this anyway.