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An op amp has a gain bandwidth product of 2 MHz; at what frequency the gain becomes unity?1000 kHz2000 kHz(2000×2) kHz(1/2000) kHz

Question

An op amp has a gain bandwidth product of 2 MHz; at what frequency does the gain become unity?

  • 1000 kHz
  • 2000 kHz
  • (2000×2) kHz
  • (1/2000) kHz
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Solution

To solve the problem, we'll follow these steps:

1. Break Down the Problem

We need to find the frequency at which the gain of an operational amplifier (op-amp) becomes unity (1). Given that the gain bandwidth product (GBP) is 2 MHz, we know that:

GBP=Gain×Frequency GBP = Gain \times Frequency

When the gain is 1 (unity gain), the frequency can be calculated using the formula:

Frequency=GBPGain Frequency = \frac{GBP}{Gain}

2. Relevant Concepts

The gain bandwidth product (GBP) is a constant for a given op-amp, meaning that as you increase the gain, the bandwidth (range of frequencies) decreases, and vice versa.

3. Analysis and Detail

  • Given:
    • GBP = 2 MHz = 2×106 2 \times 10^6 Hz
    • Gain = 1 (for unity gain)

Using the formula:

Frequency=2×106Hz1=2×106Hz=2000kHz Frequency = \frac{2 \times 10^6 \, \text{Hz}}{1} = 2 \times 10^6 \, \text{Hz} = 2000 \, \text{kHz}

4. Verify and Summarize

By verifying the calculations, we see that at a gain of 1, the frequency is indeed equal to the gain bandwidth product since the GBP does not change.

Final Answer

The frequency at which the gain becomes unity is 2000 kHz.

This problem has been solved

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