# Difference between revisions of "RC Filters"

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=== Short Topical Videos === | === Short Topical Videos === | ||

− | * [http://youtu.be/ | + | * [http://youtu.be/TBhdzzdT3cU RC Filters (by Karol Sanchez)] |

+ | * [http://www.youtube.com/watch?v=OBM5T5_kgdI Passive RC low pass filters (by Afrotechmods)] | ||

+ | * [http://www.youtube.com/watch?v=4CcIFycCnxU Passive RC high pass filters (by Afrotechmods)] | ||

+ | |||

===Reference Material=== | ===Reference Material=== | ||

+ | * Horowitz & Hill, ''The Art of Electronics, 2nd Ed.'', Ch. 1 | ||

+ | |||

<latex> | <latex> | ||

\documentclass[11pt]{article} | \documentclass[11pt]{article} | ||

Line 9: | Line 14: | ||

\begin{document} | \begin{document} | ||

− | \section*{ | + | \section*{RC Filters} |

− | \ | + | |

− | \ | + | RC filters use resistors ($R$) and capacitors ($C$) 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: |

+ | \begin{align} | ||

+ | Z_R &= R \\ | ||

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

+ | \end{align} | ||

+ | 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} | ||

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

+ | \end{equation} | ||

+ | |||

+ | 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: | ||

+ | \begin{align} | ||

+ | |Z_R| &= |Z_C| \\ | ||

+ | |R| &= \left|\frac1{j\omega C}\right| \\ | ||

+ | \omega_{-3dB} &= \frac1{RC} \\ | ||

+ | \end{align} | ||

+ | |||

\subsection*{Low-Pass Filter} | \subsection*{Low-Pass Filter} | ||

+ | \begin{figure} | ||

+ | \includegraphics[width=2in]{rc_lowpass.png} | ||

+ | \caption{A passive RC low-pass filter} | ||

+ | \end{figure} | ||

+ | |||

\subsection*{High-Pass Filter} | \subsection*{High-Pass Filter} | ||

+ | \begin{figure} | ||

+ | \includegraphics[width=2in]{rc_hipass.png} | ||

+ | \caption{A passive RC hi-pass filter} | ||

+ | \end{figure} | ||

</latex> | </latex> |

## 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*