# Difference between revisions of "RC Filters"

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Z_C &= \frac1{j\omega C} \\ | Z_C &= \frac1{j\omega C} \\ | ||

\end{align} | \end{align} | ||

− | where $j\equiv\sqrt{-1}$. Regardless of whether you are | + | where $j\equiv\sqrt{-1}$. Regardless of whether you are constructing a low-pass or high-pass filter, RC filters have a characteristic frequency at which their frequency response evolves most rapidly. This timescale is given by the product $RC$. In a great triumph of SI units, |

\begin{equation} | \begin{equation} | ||

1\ s = 1\Omega \cdot 1 F. | 1\ s = 1\Omega \cdot 1 F. |

## Latest revision as of 10:11, 21 January 2014

### Short Topical Videos[edit]

- RC Filters (by Karol Sanchez)
- Passive RC low pass filters (by Afrotechmods)
- Passive RC high pass filters (by Afrotechmods)

### Reference Material[edit]

- Horowitz & Hill,
*The Art of Electronics, 2nd Ed.*, Ch. 1

## RC Filters

RC filters use resistors () and capacitors () to make circuits that have frequency-dependent responses to input waveforms. They are passive circuits that operate on the same principle as the voltage divider, but make use of the imaginary, frequency-dependent impedances of capacitors. Recall that the impedances of resistors and capacitors are given by:

where . Regardless of whether you are constructing a low-pass or high-pass filter, RC filters have a characteristic frequency at which their frequency response evolves most rapidly. This timescale is given by the product . In a great triumph of SI units,

The frequency response of filters is typically given by the cutoff frequency at which a signal is attenuated by 3dB. For RC filters (both low-pass and high-pass), this happens when the magnitude of the impedance of the resistor and the capacitor are equal:

### Low-Pass Filter

*A passive RC low-pass filter*

### High-Pass Filter

*A passive RC hi-pass filter*