Question

Calculate the gain limiting frequency for the circuit

(a) 15.64Hz

(b) 23.356Hz

(c) 33.89Hz

(d) None of the mentioned

The question was posed to me during an online interview.

This question is from Differentiator topic in section Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

To calculate the gain-limiting frequency for a differentiator circuit, we need to know the transfer function of the differentiator and use the cutoff frequency formula for an operational amplifier circuit in this configuration.

Differentiator Circuit Transfer Function:

For an ideal differentiator, the transfer function is given by:

$$H(s)=-sRC$$

Where:

• $R$ is the resistance,
• $C$ is the capacitance,
• $s$ is the complex frequency ($s=j\omega$).

Gain Limiting Frequency (Cutoff Frequency):

The gain limiting frequency is the frequency at which the output voltage begins to decrease (roll off). For a differentiator, the gain starts to reduce beyond the frequency ωc\omega_cωc​ (cutoff frequency), which is the point where the circuit’s gain becomes limited.

The cutoff frequency is given by:

fc=12πRCf_c = \frac{1}{2 \pi RC}fc​=2πRC1​

Where:

• $R$ is the resistance,
• $C$ is the capacitance.

However, to calculate the exact limiting frequency for your specific differentiator circuit, I would need the values of $R$ and $C$. Since they are not provided in your question, it is likely that this question involves typical values or assumptions about the circuit.

Given the options, we would choose the answer based on typical values of $R$ and $C$ in differentiators. If you have specific values for $R$ and $C$, I can calculate it directly for you.