# How to find the free running oscillation frequency of a Sigma Delta Circuit?

Thread Starter

#### Precooledear

Joined May 16, 2019
6
I've been trying to find the equation that would tell me the free running oscillation frequency of this circuit.

I know it has to do with this, but I'm not sure on how the derivation of the equation came to be.

From lab manual

Is there any type of reference anyone know of that can help me derive this?

#### DickCappels

Joined Aug 21, 2008
6,661
You have a current source driving an integrator (the driven resistor into the summing node) and two thresholds.That should give you the basic relationship, then throw in a tiny bit for delay in the comparator stage and you have it.

Thread Starter

#### Precooledear

Joined May 16, 2019
6
You have a current source driving an integrator (the driven resistor into the summing node) and two thresholds.That should give you the basic relationship, then throw in a tiny bit for delay in the comparator stage and you have it.
Do you mean as a behavior model? Can you show me the exact mathematics on it?

#### DickCappels

Joined Aug 21, 2008
6,661
Can you see how it works? What are the two switching thresholds? ( hint: you need the opamp specsheet and the power supply voltage.

Thread Starter

#### Precooledear

Joined May 16, 2019
6
During the experiment we used the TL082 op amps with the power supply at around +-10V

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#### Jony130

Joined Feb 17, 2009
5,186
Thread Starter

#### Precooledear

Joined May 16, 2019
6
we ran it at an input of 200Hz but we were supposed to do this type of calculation before the experiment. I just don't understand the derivation of this formula. Based on the experiment sheet vin = Vc and Vout = Vr

Thread Starter

#### Precooledear

Joined May 16, 2019
6
Thank you so much @Jony130 this is exactly what I needed. Thank you to @DickCappels I can see how your method can be used for simulation/experimental calculations.