# Relaxation Oscillator

1. Apr 27, 2009

### limofunder

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
$$V_- = IR +\frac{1}{C} \int I(t)dt$$
so
$$0 = R \frac{dI}{dt} + \frac{1}{C} * I(t)$$
then
$$\frac{dI}{I} = - \frac{1}{RC} dt$$
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,
$$V_out = V_+ * \frac{R_2}{R_1 + R_2}$$
Now, how do I relate the Vout here with the current from above?

Last edited by a moderator: May 4, 2017
2. Apr 27, 2009

### limofunder

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. Apr 28, 2009

### limofunder

thanks a bunch guys