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Relaxation Oscillator

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data
    I am having a bit of trouble with a homework problem on relaxation oscillators, the schematic is shown below:

    https://webspace.utexas.edu/sz233/Relaxation%20Oscillator.png [Broken]

    The original problem states:
    derive a relationship for the period of oscillation for a relaxation oscillator in terms of R1, R2, RC, VCC
    and VEE.




    2. Relevant equations

    So I know from E&M that
    V=IR, and C=Q/V.
    also, I know that dq/dt = I



    3. The attempt at a solution
    from this, I deduce, possibly erroneously, that
    [tex] V_- = IR +\frac{1}{C} \int I(t)dt[/tex]
    so
    [tex] 0 = R \frac{dI}{dt} + \frac{1}{C} * I(t) [/tex]
    then
    [tex] \frac{dI}{I} = - \frac{1}{RC} dt[/tex]
    it follows that
    I = I0Exp[-t/RC]

    given that current doesn't change at the + or - poles on the amplifier, then this should be the same current that goes through V+ thus using the voltage divider formula,
    [tex]V_out = V_+ * \frac{R_2}{R_1 + R_2}[/tex]
    Now, how do I relate the Vout here with the current from above?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 27, 2009 #2
    Is there a reason for which the latex code doesn't appear? I pulled the notation direct from the sigma reference in the tool box menu
     
  4. Apr 28, 2009 #3
    thanks a bunch guys
     
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