Question

If a voltage amplifier has a gain of $60 \mathrm{db}$ and an output voltage of $5 \mathrm{~V}$, what is the input voltage? 

   If a voltage amplifier has a gain of $60 \mathrm{db}$ and an output voltage of $5 \mathrm{~V}$, what is the input voltage?
Essentials of Electrical and Computer Engineering
Essentials of Electrical and Computer Engineering
David V. Kerns, Jr.,… 1st Edition
Chapter 8, Problem 19 ↓

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The gain in dB can be calculated using the formula: \[ \text{Gain (dB)} = 20 \log_{10} \left( \frac{V_{\text{out}}}{V_{\text{in}}} \right) \] where \( V_{\text{out}} \) is the output voltage and \( V_{\text{in}} \) is the input voltage.  Show more…

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If a voltage amplifier has a gain of $60 \mathrm{db}$ and an output voltage of $5 \mathrm{~V}$, what is the input voltage?
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Key Concepts

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Voltage Amplifier
A voltage amplifier is an electronic device that increases the amplitude of an input voltage signal, producing a larger output voltage while typically maintaining the same waveform characteristics.
Decibel (dB) Scale
The decibel (dB) scale is a logarithmic unit used to express ratios, particularly for power and voltage levels. It allows very large or small ratios to be represented more conveniently and is defined in terms of logarithms.
Conversion of dB to Voltage Ratio
The conversion between decibel gain and the voltage ratio is given by the formula 20 log10(Vout/Vin). This relationship enables one to determine how many times greater the output voltage is compared to the input voltage based on the dB value.
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