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Generally light emitted from a source contains several wavelengths. Similarly theΒ electrical voltage at the output of a sensor contains a mixture of dc and several acΒ components of different amplitudes and different frequencies. Filter circuits are usedΒ to pass desired frequencies and /or to eliminateΒ undesiredΒ frequencies. The frequenciesΒ transmitted by the filter form the pass band while the frequencies eliminated by theΒ filter form the stop band or rejection band.Β
We can think of four basic types of electrical filters- a low pass filter where frequenciesΒ below a certain cutoff frequency fcare passed. Similarly one can think of a high passΒ filter, band pass filter, band stop (or band rejection) filter. The cutoff frequencyΒ fc isΒ the frequency at which the output voltage falls to 1/β2 times its maximum value.Β
An inductor and/or a capacitoris an essential component of a filter. Generally aΒ resistance is included in a filter circuit to determine the time constant and hence theΒ cutoff frequency.
The input-output voltage relation for a certain high pass filter is given by $$\frac{V_o}{V_i} = \frac{\omega CR}{\sqrt{1 + \omega^2C^2R^2}}$$. The cut-off frequency $$f_c$$ for this filter will be
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