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Lucy Liang edited subsection_Equivalent_Noise_Bandwidth_ENBW__.tex
over 8 years ago
Commit id: 36d0d26face0d9bb21d1c01ba9cdd0a425276841
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diff --git a/subsection_Equivalent_Noise_Bandwidth_ENBW__.tex b/subsection_Equivalent_Noise_Bandwidth_ENBW__.tex
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A bandwidth describes a range of frequencies for which signals with frequencies within the range are allowed to pass through. Ideally, the range will be exactly as set, and all signals will be equally amplified in that range when there is a gain. But in reality, almost all instruments do not have an exact cutoff at the set frequency boundaries, which will result in a signal that is less than expected.
In order to make a more accurate calculation, an equation that corrects for the actual bandwidth has been derived
(\href{http://media4.physics.indiana.edu/~courses/p451/background_info/TeachSpin_Manual_Noise_Fundamentals.pdf}{TeachSpin Manual 7.3}) to be:
\begin{equation}
\label{eq:ENBW}
ENBW=f_c \frac{\pi}{4\sigma}=f_c \frac{\pi Q}{2}
\end{equation}
where $f_c$ is the corner frequency, and $Q$ is the quality factor of the filter.