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Small change
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hpretl committed Aug 22, 2024
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11 changes: 4 additions & 7 deletions _sec_mosfet_diode.qmd
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Expand Up @@ -164,15 +164,12 @@ $$
\overline{V_\mathrm{n}^2}(f) = \frac{4 k T \gamma \gm}{(\gm + \gds)^2 + (2 \pi f \Cgs)^2}.
$$ {#eq-mosfet-diode-noise-psd}
If we are interested in the PSD of the noise then @eq-mosfet-diode-noise-psd gives us the result. If we are interested in the rms value (the total noise) we need to integrate this equation.
::: {.callout-info}
$$
\int_0^\infty {\frac{a}{b^2 + (c f)^2} df} = \frac{\pi a}{2 b c}
If we are interested in the PSD of the noise then @eq-mosfet-diode-noise-psd gives us the result. If we are interested in the rms value (the total noise) we need to integrate this equation, using the following identity:
$$
:::
\int_0^\infty {\frac{a}{b^2 + c^2 f^2} df} = \frac{\pi a}{2 b c}
$$ {#eq-integral-identity}
Using the integral help from the previous info box, we can easily get at
Using the integral help in @eq-integral-identity, we can easily transform @eq-mosfet-diode-noise-psd to
$$
V_\mathrm{n,rms}^2 = \int_0^\infty \overline{V_\mathrm{n}^2}(f) df = \frac{k T \gamma \gm}{(\gm + \gds) \Cgs}.
$$ {#eq-mosfet-diode-noise-rms}
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