# Does anyone know how can I deduce this formula for frequency from this sawtooth generator?

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I know that this formula is correct, but I'm not sure how can I deduce it. Can anyone help me? Thanks in advance!

• You apply the low-side op-amp output voltage (-15 V or 15 V) to $R_3$ (-15 V) and $R_4$ (15 V) neglecting the diodes forward drops. You see that the (-) pin of the upper op-amp is a virtual ground so it's easy to deduce the currents circulating in $R_3$ (-15 V) / $R_4$ (15 V) . Knowing the thresholds brought by the Schmitt trigger, you determine the time it takes to charge $C_1$ to meet the first trigger threshold $t_1$ and the time $t_2$ it takes to discharge the cap. to the sec. threshold. The frequency is inverse of the sum of $t_1 + t_2$. No $C_1$ in your formula? – Verbal Kint May 22 at 9:45
• Can you be more specific? I'm not that advanced in electrical circuits:) – Andres Pasca May 22 at 9:50
• Is this homework? – Verbal Kint May 22 at 10:06
• Yes, it's a project for a class. – Andres Pasca May 22 at 10:09
• I see. Given the abundance of documents in the web, look up for integrator ramp generator for instance and op-amp Schmitt trigger. If only I had so many documents to browse when I was a student 35 years ago : ) – Verbal Kint May 22 at 10:19

As it's homework, we do the Socratic method here.

How fast does the capacitor round U8B slew?

When it's going +ve? When it's going -ve?

So how long does it take for each slew?

What voltage is the slew coming from? What voltage is it going to?

How do the values of R1 and R2 affect those voltages?

How does the length o time slewing relate to frequency?

If you've answered all of those questions, then you know more than the question setter. What is the formula in your question missing?

• is missing the capacitor? – Andres Pasca May 22 at 10:31
• @AndresPasca Yes, you can't figure out how fast the integrator slews without the capacitor value. – Neil_UK May 22 at 11:01
• The thing is that I have the frequency at which my signal should work, and I only need to size the components accordingly. The frequency is given from the beginning. – Andres Pasca May 22 at 11:50
• I found the mistake in the formula, but still I don't know how to deduce it. – Andres Pasca May 22 at 11:59
• Assume U8A's output is high, what current is required through R2 to send it to the other state? What voltage does this need on U8B's output? Do again for U8A output low. Those are the voltages U8B is required to slew through. How fast does U8B slew, when going up, when going down? What components control that slew rate? – Neil_UK May 22 at 12:24