The first thing you need to do is to understand how "ideal" non-inverting Schmitt trigger work.

Maybe this will help

For example if

The

and

In your circuit, you want the threshold voltage to be around

And now we can easily solve for R1 and R2.

You need to shift the Vref voltage up to:

Because with a single supply

Where

Maybe this will help

For example if

**Vcc = 5V**;**Vee = -5V**and**Vref = 0V ; R1 =10kΩ; R2 = 100kΩ**The

**VH = 10V * 10k/100k = 1V**and the threshold voltage are**V1 = Vref - VH/2 = 0V - 1V/2 = -0.5V**and

V2 = Vref + VH/2 = 0.5VV2 = Vref + VH/2 = 0.5V

In your circuit, you want the threshold voltage to be around

**V1 = 3.11V**and**V2 = 3.15V**. Therefore**Vh = V2 - V1 = 40mV**and because you are using single supply voltage (Vcc = 12V and Vee = 0)And now we can easily solve for R1 and R2.

**Vh = Vcc*(R1/R2)**

You need to shift the Vref voltage up to:

**Vref = V1 + VH/2 = 3.11V +40mV/2 = 3.13V**( exactly speaking Vref = R2/(R1 + R2) * V2)Because with a single supply

**V1**and**V2**are equal to :**V1 = Vref - (Vcc - Vref)* R1/R2****V2 = (R1 + R2)/R2 * Vref = Vref + (Vref -Vomin)* R1/R2**

Where

**Vomin**- comparator output voltage at low state
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