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Relaxation Oscillator

  • Thread starter limofunder
  • Start date
  • #1
15
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Homework Statement


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.




Homework Equations



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



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:

Answers and Replies

  • #2
15
0
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
 
  • #3
15
0
thanks a bunch guys
 

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