23 lines
599 B
Markdown
23 lines
599 B
Markdown
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```
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Vout ──[ R]──●─────────── ADC
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=== C
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GND
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```
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For a one pole low pass filter where $\tau=RC$ and $\omega$ is angular velocity in radians:
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$$|H(j\omega)| = \frac{1}{\sqrt{1+{(\omega \tau)}^2}}$$
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The -3dB point is when $\omega \tau = 1$, i.e. magnitude response is $\frac{1}{\sqrt{2}} = 0.707$
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This cut off frequency is defined as $$\omega_{c} = \frac{1}{\tau}, \; f_{c} =\frac{1}{2 \pi \tau}$$
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For a Laplace transform derivation see [[Worked Example RC Low Pass]]
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---
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