What practical modification is commonly made to an ideal differentiator circuit to improve stability, and what is its effect?

What practical modification is commonly made to an ideal differentiator circuit to improve stability, and what is its effect?

• A. It increases the DC offset but doesn't affect stability.
• B. A resistor in series with input capacitor or a small capacitor in parallel with the feedback resistor; this limits high-frequency gain and improves stability.
• C. It has no effect on stability.
• D. It is achieved by doubling the resistor values in the feedback network.

Answer: (B)

An ideal differentiator has a gain that rises with frequency, which makes it very sensitive to noise and can cause instability in a real op-amp with finite bandwidth and phase lag. The practical fix is to add a small resistor in series with the input capacitor or a small capacitor in parallel with the feedback resistor. These additions introduce a high-frequency break in the response, so the gain stops increasing beyond a certain frequency. This caps the high-frequency gain, improves phase margin, and reduces the tendency to oscillate or amplify noise. In effect, the differentiator still provides differentiation over a useful mid-band, but its high-frequency behavior is tempered for stability.

An ideal differentiator has a gain that rises with frequency, which makes it very sensitive to noise and can cause instability in a real op-amp with finite bandwidth and phase lag. The practical fix is to add a small resistor in series with the input capacitor or a small capacitor in parallel with the feedback resistor. These additions introduce a high-frequency break in the response, so the gain stops increasing beyond a certain frequency. This caps the high-frequency gain, improves phase margin, and reduces the tendency to oscillate or amplify noise. In effect, the differentiator still provides differentiation over a useful mid-band, but its high-frequency behavior is tempered for stability.