Question

Determine the high frequency model op-amp with single break frequency

I had been asked this question in a dream while sleeping

This interesting question is from High Frequency Op-Amp Equivalent Circuit in chapter Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

To determine the high-frequency model of an operational amplifier (op-amp) with a single break frequency, we need to understand the behavior of the op-amp at high frequencies. The typical high-frequency model of an op-amp includes the following elements:

1. Open-loop gain (A): The op-amp's open-loop gain, which is frequency-dependent, decreases at high frequencies.

2. Break frequency (f_b): The break frequency is where the gain starts to fall off due to internal capacitances. In the case of a simple single-pole model, this is where the op-amp's bandwidth starts to limit its performance.

High-Frequency Model of an Op-Amp

For an op-amp with a single break frequency, the model typically includes:

• Open-loop gain (A_0): The open-loop gain of the op-amp at low frequencies.
• Bandwidth (f_b): The frequency at which the open-loop gain begins to roll off. This is often referred to as the unity gain bandwidth or GBP (Gain Bandwidth Product), which remains constant for an op-amp.
• Capacitance (C): The internal capacitance that causes the gain to roll off at high frequencies.

At high frequencies, the gain of the op-amp decreases as a function of frequency. This can be represented by the following equation for the open-loop gain $A(f)$ of the op-amp:

A(f)=A01+jffbA(f) = \frac{A_0}{1 + j\frac{f}{f_b}}A(f)=1+jfb​f​A0​​

Where:

• A0A_0A0​ is the low-frequency open-loop gain,
• fbf_bfb​ is the break frequency (or the pole frequency) at which the gain begins to roll off,
• $f$ is the frequency of operation,
• $j$ is the imaginary unit.

Conclusion:

At high frequencies, the op-amp behaves as if its open-loop gain is inversely proportional to the frequency, starting to fall off beyond the break frequency fbf_bfb​. This frequency-dependent behavior is a result of internal capacitances (often the input capacitance and the compensation capacitor), and the op-amp typically exhibits a single-pole roll-off characterized by a break frequency.