The voltage gain of an op amp is 200,000

The voltage gain of an op amp is 200,000. It has a critical frequency of 500 Hz. What is the midrange voltage gain in dB?

The correct answer and explanation is:

To find the midrange voltage gain in decibels (dB), use the following formula: Gain (dB)=20⋅log⁡10(Voltage Gain)\text{Gain (dB)} = 20 \cdot \log_{10}(\text{Voltage Gain})

Given:

• Voltage gain = 200,000

Gain (dB)=20⋅log⁡10(200,000)\text{Gain (dB)} = 20 \cdot \log_{10}(200{,}000)

First, calculate the logarithm: log⁡10(200,000)=log⁡10(2×105)=log⁡10(2)+log⁡10(105)\log_{10}(200{,}000) = \log_{10}(2 \times 10^5) = \log_{10}(2) + \log_{10}(10^5) =0.3010+5=5.3010= 0.3010 + 5 = 5.3010

Now multiply by 20: Gain (dB)=20⋅5.3010=106.02 dB\text{Gain (dB)} = 20 \cdot 5.3010 = 106.02 \text{ dB}

Correct Answer: 106.02 dB

Explanation:

In electronics, voltage gain is often expressed in decibels because this unit provides a logarithmic scale that helps compare values that vary across wide ranges. A midrange voltage gain refers to the amplification in the flat part of the op amp’s frequency response, before the gain starts to drop off due to bandwidth limitations. This is typically the region where the gain remains stable and consistent.

To convert a linear voltage gain to decibels, use the formula: Gain in dB=20⋅log⁡10(Av)\text{Gain in dB} = 20 \cdot \log_{10}(A_v)

where AvA_v is the voltage gain without units. This formula comes from how power relates to voltage in circuits and how logarithms help compress the scale for easier interpretation.

In this case, an op amp with a gain of 200,000 means the output signal is amplified 200,000 times compared to the input in the midrange frequency region. Calculating the logarithm and applying the formula results in a gain of 106.02 dB, which reflects a very high amplification. The critical frequency (500 Hz) marks the boundary where this gain starts to decline, but it does not affect the midrange gain value itself.