Calculate attenuation in dB.
Understand the Problem
The question is asking how to calculate attenuation in decibels (dB), which typically involves using a formula related to the ratio of output power to input power in a transmission medium.
Answer
$10 \, dB$
Answer for screen readers
The attenuation is $10 , dB$.
Steps to Solve
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Identify the Attenuation Formula To calculate attenuation in decibels, we use the formula: $$ A(dB) = 10 \log_{10} \left( \frac{P_{in}}{P_{out}} \right) $$ where ( A(dB) ) is the attenuation in decibels, ( P_{in} ) is the input power, and ( P_{out} ) is the output power.
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Plug in the Values Determine the values for ( P_{in} ) and ( P_{out} ). For example, if ( P_{in} = 100 ) mW and ( P_{out} = 10 ) mW, substitute these into the formula: $$ A(dB) = 10 \log_{10} \left( \frac{100}{10} \right) $$
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Calculate the Power Ratio Calculate the ratio of ( P_{in} ) to ( P_{out} ): $$ \frac{P_{in}}{P_{out}} = \frac{100}{10} = 10 $$
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Calculate the Logarithm Now, find the logarithm: $$ \log_{10}(10) = 1 $$
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Complete the Attenuation Calculation Finally, substitute back into the attenuation formula: $$ A(dB) = 10 \cdot 1 = 10 , dB $$
The attenuation is $10 , dB$.
More Information
Attenuation in decibels helps to quantify how much the signal has weakened in a transmission medium. A value of 10 dB means the output power is 10 times less than the input power.
Tips
- Confusing input and output power values, which can lead to incorrect calculations. Always ensure ( P_{in} ) is greater than ( P_{out} ) when calculating attenuation.
- Forgetting to use logarithms correctly; ensure you are calculating ( \log_{10} ) specifically for decibels.
