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Chapter 8: Problem 1

Calculate the voltage gain in decibels of an amplifier where the input signal is \(0.5 \mathrm{~V}\) and the output signal is \(2.2 \mathrm{~V}\).

Short Answer

Expert verified
Question: Calculate the voltage gain in decibels of an amplifier with an input signal of 0.5 V and an output signal of 2.2 V. Answer: The voltage gain in decibels of the amplifier is approximately 12.86 dB.

Step by step solution

01

Identify the given values

In this exercise, we are given the input voltage (\(0.5 \mathrm{~V}\)) and output voltage (\(2.2 \mathrm{~V}\)). We will use these values to calculate the voltage gain.
02

Calculate the ratio of output to input voltage

We need to find the ratio of the output voltage to the input voltage. This can be done by dividing the output voltage (\(V_{out}\)) by the input voltage (\(V_{in}\)): \(\frac{V_{out}}{V_{in}} = \frac{2.2 \mathrm{~V}}{0.5 \mathrm{~V}}\).
03

Solve for the output-to-input voltage ratio

Divide the output voltage by the input voltage to get the ratio: \(\frac{V_{out}}{V_{in}} = \frac{2.2 \mathrm{~V}}{0.5 \mathrm{~V}} = 4.4\)
04

Calculate the voltage gain in decibels

Now we can calculate the voltage gain in decibels using the formula \(G_v = 20 \log_{10} \left( \frac{V_{out}}{V_{in}} \right)\). Substitute the calculated ratio (4.4) into the formula: \(G_v = 20 \log_{10}(4.4)\)
05

Solve for the voltage gain in decibels

Calculate the voltage gain in decibels using a calculator or logarithm table: \(G_v = 20 \log_{10}(4.4) \approx 12.86\)
06

Write the final answer

The voltage gain in decibels of the amplifier is approximately \(12.86 \mathrm{dB}\).

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