An op-amp with an open-loop gain of 100 dB has unity gain bandwidth of 1 GHz. What is the bandwidth of this op-amp assuming it is a single pole system?

An op-amp with an open-loop gain of 100 dB has unity gain bandwidth of 1 GHz. What is the bandwidth of this op-amp assuming it is a single pole system?

• 1. 10 MHz
• 2. 10 kHz
• 3. 1 MHz
• 4. 10 Hz

_c = 10 kHz Gain = 100 dB f_T = 1 GHz 0 dB (Gain=1) -20 dB/decade

Conceptual Bode Plot of a Single-Pole Op-Amp

Step-by-Step Solution

Step 1: Convert Gain from dB to Linear Ratio
Open-loop gain (A_OL) in dB = 100 dB.
Using formula: dB = 20 log₁₀(Gain)
100 = 20 log₁₀(A_OL) → 5 = log₁₀(A_OL) → A_OL = 10⁵.

Step 2: Understand Unity Gain Bandwidth (UGBW)
For a single-pole system, the Gain-Bandwidth Product (GBW) is constant.
At unity gain (Gain = 1), the frequency is given as 1 GHz.
Therefore, GBW = 1 × 1 GHz = 10⁹ Hz.

Step 3: Calculate the Open-loop Bandwidth (BW)
The bandwidth is defined as the frequency where the DC gain starts to decrease.
GBW = A_OL × BW
10⁹ = 10⁵ × BW
BW = 10⁹ / 10⁵ = 10⁴ Hz.

Step 4: Final Unit Conversion
10⁴ Hz = 10,000 Hz = 10 kHz.

The correct value of the bandwidth is 10 kHz. (Option 2)

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