Filter
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Any circuit designed to remove or enhance certain frequencies in a signal.
Contents |
Uses for Filters
Categories of Filters
The broadest useful way to class a filter is according to its frequency response. Simply put, this describes which frequencies are boosted (passed) and which are damped down (rejected).
For each frequency response there is an ideal and a realisable response. Ideally, a filter would completely annihilate all frequencies it is intended to reject and leave all frequencies it is meant to pass untouched. This is not possible for mathematical as well as real-world reasons.
Low Pass
Low pass filters are intended to remove all high frequencies in a signal, leaving only the low frequencies.
High Pass
High pass filters are the opposite of low pass filters. They reject low frequencies. A DC blocking filter is an example of a high pass filter.
Band Pass
Band pass filters reject all frequencies outside a range. They would commonly be used in a radio station selecting circuit. They can be made using a cascade of low and high pass filters.
Notch or Band Reject
These remove all frequencies in a range. A common example is a filter used to remove the 50Hz or 60Hz mains hum from a circuit.
Properties of Filters
Bandwidth
The fundamental idea of bandwidth is very simple. If a filter is meant to pass everything between 100Hz and 500Hz then it has a bandwidth of 500Hz − 100Hz = 400Hz.
With realised filters it is slightly more complicated since there is no sharp boundary between pass and reject. To avoid this, the boundary is defined where the output is 
of the maximum output. These are often called the half power points since power is proportional to the square of voltage and the power at these points is half that at the maximum.
Rolloff
A real world filter does not completely remove its rejection band, nor does it leave its pass band completely untouched. Instead the frequency response is high in the pass band and slopes down to a low in the reject band. The steepness of this slope is called the rolloff of the filter.
A low rolloff means that there is not so much difference between the effect of the filter on the pass and the reject band. It also means there is a large transition band between the two which is somewhere between passed and rejected. A higher rolloff means higher discrimination between frequencies.
Quantitatively, rolloff would be measured as something like dB per decade. A rolloff of 20dB per decade means that in the transition band, a change in frequency by a factor of ten ("per decade") results in a change in output of 20dB. So if white noise is put through the filter, the 10Hz component might come out as 1V, while the 100Hz component might be reduced to .01V (20dB less).
Phase Response
Sensitivity
Filter Design
The design of filters fundamentally involves components that in some way depend on frequency. In almost all circuits, this means capacitors and inductors. (See Impedance) In some circuits semiconductors and other components are used.
Particularly under around 500kHz, capacitors are cheaper, smaller and simpler than inductors. Thus most filters for these frequencies are made from resistors and capacitors and are called RC filters. Theoretically, any RC circuit could have its resistors replaced with inductors and its capacitors replaced with resistors and have the same frequency response.
A simple filter made from a resistor and a capacitor does not have perfect rolloff (it is about 20dB per decade). For simple applications this doesn't matter. If it does, simply adding another RC filter to the output (cascading) will improve the rolloff (it just adds - two RC filters have a rolloff of 40dB per decade). In theory this can be done indefinitely but each stage weakens the signal a little. Thus complicated filters usually have one or more amplifiers in the circuit (almost always op-amps) and are called active filters.
