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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

  1. 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.

  2. 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: $$ A(dB) = 10 \log_{10} \left( \frac{100}{10} \right) $$

  3. Calculate the Power Ratio Calculate the ratio of ( P_{in} ) to ( P_{out} ): $$ \frac{P_{in}}{P_{out}} = \frac{100}{10} = 10 $$

  4. Calculate the Logarithm Now, find the logarithm: $$ \log_{10}(10) = 1 $$

  5. 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.
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