Circuit Output

Discussion in 'Homework Help' started by wheelman487, Dec 6, 2010.

  1. wheelman487

    Thread Starter New Member

    Dec 6, 2010
    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


    A0 cos(ωt+Θ)+ A1(t-t0)³ + A2(t-t0)

    this was a letter my teacher sent us to make it easier

    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...

  2. tyblu

    Active Member

    Nov 29, 2010
    This is a generalized op-amp mayhem circuit. First, break it up into modules:
    A0*cos(ωt+Θ)+ A1*(t-t0)³ + A2*(t-t0) = S
    Let B0 = A0*cos(ωt+Θ), B1 = A1*(t-t0)³, B2 = A2*(t-t0)

    Now: B0 + B1 + B2 = S
    Realize this circuit using a 3-input adder (op amp + resistors).

    Going into the B's:
    Each has a simple multiplication. Realize this using a 2-input (i/p) multiplier.
    B0 has a cosine function in it. Not sure about doing this operation on a non-sinusoidal waveform, but for a regular sine wave this is just a phase shift or time delay. A delay can be as simple as an RC circuit; note that passive delays will put frequency limits on your circuit.

    Going into the "t-t0"'s:
    These operations are supposed to be implemented on the change in time since t0, which can be accumulated with integrators. Ensure you set the max accumulated time to stay below the amp saturation point.

    The cubed part is another multiplier.

    If you're interested, the book "Art of Electronics" has many practical example circuits.
  3. wheelman487

    Thread Starter New Member

    Dec 6, 2010
    Thank you so much for your reply. I'm going to try and find that book. Again thank you for the help