Difference between revisions of "RC Filters"

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|R| &= \left|\frac1{j\omega C}\right| \\
 
|R| &= \left|\frac1{j\omega C}\right| \\
 
\omega_{-3dB} &= \frac1{RC} \\
 
\omega_{-3dB} &= \frac1{RC} \\
 +
\end{align}
  
 
\subsection*{Low-Pass Filter}
 
\subsection*{Low-Pass Filter}

Revision as of 15:32, 30 August 2012

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Reference Material

RC Filters

RC filters uses 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 construction 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

Rc lowpass.png


A passive RC low-pass filter

High-Pass Filter

Rc hipass.png


A passive RC hi-pass filter