# In an opamp differentiator, how does high gain produce oscillations?

The gain of an ideal differentiator increases 20dB/dec - this means the gain increases as frequency increases. I'm wondering how high gain produces oscillations.

I've read so many times that negative feedback stabilizes the op amp but never quite get why the opamp needs stabilizing. I understand high gain is useless because a small input signal can saturate the output of opamp. Also I understand how the negative feedback reduces offset voltage, but that's it.

I don't get how high gain produces oscillations.

Any help?

• Comments are not for extended discussion; this conversation has been moved to chat. – Voltage Spike Jun 10 at 22:26

Here I made a simple simulation in LTspice assuming Vin = 0V:

And the output voltage looks like this:

And the frequency of this oscillation is equal to:

$$F = \sqrt{F_T \times F_{RC}} = \sqrt{1MHz \times \frac{0.16}{10\textrm{nF} \times 10\textrm{k}\Omega}} \approx 40\textrm{kHz}$$

Adding a resistor in series with the capacitor may fix the circuit because now at high frequency the feedback network phase shift is 0 degrees.

• Nice result, (+1) and, did you try putting 1 ohm (or more) in series with C1 to see if it stops oscillating? That would be a nice touch. – Andy aka Apr 4 at 16:56
• @Andyaka 5 ohm kills oscillations. – G36 Apr 4 at 17:18
• that's quite high for a differentiator. Never thought it would be that high. – Andy aka Apr 4 at 17:53