Introduction
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Band Pass – which pass?
Bandpass filters are defined by a lower frequency limit and an upper frequency limit, this is the pass band for a band pass filter (say that a few times fast). The pass band for a high pass filter, in contrast, contain the frequencies above the cutoff frequency. Band pass filters are used extensively in communications systems. They do different things depending on whether you are transmitting or receiving.
On a transmitter, the bandpass filter restricts the transmission to the selected band so that it does not interfere with other transmissions. In this way, it helps to maximize the transmissions possible in a given frequency spectrum.
For a receiver, the bandpass filter removes the unwanted signals, so that the desired signal can be decoded. These undesired signals can be noise, or transmissions in other bands.
Is there only one?
A bandpass filter can take on many form factors. It can be active (using components like transistors and IC’s) or passive (using components like inductors, capacitors and resistors). The bandwidth, measured as the difference in frequencies between the 3dB or half power points, is one parameter that is selected by the designer. The number of poles, or the order of the filter, is also selectable. The order will affect the slope (how fast it falls off) of the filter cutoff limits. An ideal filter would be flat on the top (across the band) and vertical at the upper and lower cutoff frequencies. No filter is ideal and it is up to the designer to decide what is needed to achieve the desired outcome.
Different topologies are given different names. For example: Butterworth, Chebyshev, Cauer, Bessel and Gaussian. These names define a filter that has certain desirable features. The Butterworth filter, also known as the maximally flat magnitude filter was first described by a British Engineer and Physicist named Stephen Butterworth in 1930 in a paper called, “On the Theory of Filter Amplifiers.” The desirable characteristic of this filter is that the pass band is flat. A filter that has ripples in the pass band does not have a constant gain for all frequencies. This can have detrimental results for some systems.
The Chebyshev filter has a sharper roll-off than the Butterworth, but it also has more ripple in the pass band. Depending on what is most important for a particular application one characteristic will be more important to the designer than another.
Each of these filters can be designed with a different number of poles or order. A 6th order verses an 8th order filter will have different characteristics, including the flatness or ripple both in the pass band and the stop band and the steepness of the transition between these regions.
Does this resonate with you?
One metric of a filter is the center frequency or the resonant frequency. This is the point where the output gain is at its maximum value. You might be tempted to think this point would be half way between the upper and lower cutoff frequencies (the arithmetic average), but it is actually at the geometric mean value. That is located at fr^2=fc (upper) x fc (lower).
It is important to note that with passive components, the peak amplitude of the filter will always be lower than the input signal. That just expresses the fact that there are losses in passive components.
Other uses of band pass filters
For the most part bandpass filters are used in communications. But there are other fields that can make use of them as well. For example, in astronomy, bandpass filters are used to restrict the light to a specific spectrum. This can help to identify main sequence stars as well as redshifts.
In neuroscience, some cells in the visual cortex exhibit a filtering know as Gabor filtering. This filter is used to detect edges. It is also a bandpass filter.
In atmospheric sciences, they use bandpass filters on meteorological data to highlight cyclones. This is done by setting the upper and lower limits to 3 and 10 days. Then fluctuations from cyclones will remain while other sources will be filtered out.
Final thoughts
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#30: The Bandpass Filter
