# Frequency of oscillator (exercise)

I tried to evaluate the frequency of the following oscillator:

The loop gain $\beta(j\omega)A(j\omega)$ is:

To find frequency I must impose the condition:

$$\angle \beta(j\omega_0)A(j\omega_0)=0$$

but I don't know if the term $1-(RC\omega_0)^2$ is positive or negative. The angle is different in the two cases.

• Choose the lower $\omega$ where it is + (which has more gain ) such that the numerator= demominator and R2/R1 fine tunes that ratio =1.00 for a perfect sinewave if more than 1 then it starts to saturate where gain is automatically reduced. This assumes a split supply otherwise Vin+ shud be Vcc/2 instead of gnd. Essentiall'y 2xRC gives 180 deg lag and R2/R1 amp gives the other 180 inversion for Barhausen Criteria with unity gain Nov 7, 2016 at 17:56
• In your equation a minus sign is missing (gain is -R2/R1). Where is the problem? For w=1/RC the terms [1-(RCwo)²] are equal to zero and the equation reduces to (-R2/R1)x(-1)=+R2/R1 which can be made to be unity.
– LvW
Jan 8, 2017 at 10:45