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Chapter 8: Problem 7

An amplifier has a gain of \(25 \mathrm{~dB}\). If the input voltage is \(15 \mathrm{mV}\) calculate the output voltage.

Short Answer

Expert verified
Answer: The output voltage of the amplifier is approximately 47.43 mV.

Step by step solution

01

Define and understand gain in decibels

Gain in decibels (dB) is a logarithmic scale to represent the ratio of two power levels, in our case, the ratio between the output voltage and the input voltage. Mathematically, gain in dB is given by the following formula: \[ Gain (dB) = 20\log_{10}(\frac{V_{out}}{V_{in}}) \] where \(V_{out}\) is the output voltage, \(V_{in}\) is the input voltage, and the factor 20 is required as we are dealing with voltages instead of power levels.
02

Convert gain in decibels to a dimensionless factor

Rearrange the gain formula so that it gives the ratio between output voltage and input voltage: \[ \frac{V_{out}}{V_{in}} = 10^{\frac{Gain (dB)}{20}} \] Now, we can substitute the given gain value to find the ratio: \[ \frac{V_{out}}{V_{in}} = 10^{\frac{25}{20}} = 10^{1.25} \]
03

Calculate the output voltage

We have the input voltage (\(V_{in} = 15 mV\)) and the ratio between output voltage and input voltage, and we can now calculate the output voltage by multiplying them: \[ V_{out} = V_{in} \times 10^{1.25} \] Substitute the given input voltage value: \[ V_{out} = 15 \times 10^{1.25} \approx 47.43 mV \] The output voltage of the amplifier is approximately \(47.43 \mathrm{mV}\).

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Most popular questions from this chapter

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