In an amplifier that has a power gain of 6 dB, what is the voltage gain in dB?

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Question:**

1. In an amplifier that has a power gain of 6 dB, what is the voltage gain in dB?

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**Explanation:**

In the text shown, the question involves a basic relationship between power gain and voltage gain in an amplifier, often calculated using decibels (dB). The document requires determining the voltage gain given a power gain of 6 dB.

**Calculation:**

Power gain in decibels (dB) is given by the formula:

\[ \text{Power Gain (dB)} = 10 \cdot \log_{10}\left(\frac{P_{\text{out}}}{P_{\text{in}}}\right) \]

Voltage gain in decibels (dB) is given by:

\[ \text{Voltage Gain (dB)} = 20 \cdot \log_{10}\left(\frac{V_{\text{out}}}{V_{\text{in}}}\right) \]

If the power gain is 6 dB, and assuming the input and output impedances are the same, the voltage gain can be calculated using the following relationship since:

\[ \text{Voltage Gain (dB)} = \text{Power Gain (dB)} / 2 \]

Thus, voltage gain = \( \frac{6}{2} = 3 \) dB.

This information would help students or individuals understand basic calculations and relationships involving decibels in amplifiers.

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There are no graphs or diagrams in the image, aside from a symbol that resembles a ground symbol often used in electrical diagrams.
Transcribed Image Text:--- **Question:** 1. In an amplifier that has a power gain of 6 dB, what is the voltage gain in dB? --- **Explanation:** In the text shown, the question involves a basic relationship between power gain and voltage gain in an amplifier, often calculated using decibels (dB). The document requires determining the voltage gain given a power gain of 6 dB. **Calculation:** Power gain in decibels (dB) is given by the formula: \[ \text{Power Gain (dB)} = 10 \cdot \log_{10}\left(\frac{P_{\text{out}}}{P_{\text{in}}}\right) \] Voltage gain in decibels (dB) is given by: \[ \text{Voltage Gain (dB)} = 20 \cdot \log_{10}\left(\frac{V_{\text{out}}}{V_{\text{in}}}\right) \] If the power gain is 6 dB, and assuming the input and output impedances are the same, the voltage gain can be calculated using the following relationship since: \[ \text{Voltage Gain (dB)} = \text{Power Gain (dB)} / 2 \] Thus, voltage gain = \( \frac{6}{2} = 3 \) dB. This information would help students or individuals understand basic calculations and relationships involving decibels in amplifiers. --- There are no graphs or diagrams in the image, aside from a symbol that resembles a ground symbol often used in electrical diagrams.
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According to the question, we need to calculate voltage gain in dB if power gain is 6dB.

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Should the correct answer be 3 decibals?

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