文档介绍：Fundamentals of Measurement Technology(13)
Prof. Wang Boxiong
Types of filters
Low-pass filters
Fig. Low-pass filters
Types of filters
RC lower-pass filter
()
()
where the frequency
corresponds to the point of amplitude attenuation of –3dB, and is the upper cut-off frequency.
Types of filters
For simple first-order systems, the attenuation is quite gradual with frequency,6dB/octave. By adding more “stages”(see (a))the sharpness of cutoff may be increased. But the disadvantage: loading effects should be take into account.
Fig. Amplitude and phase characteristics of the first-order low-pass filters
Types of filters
Many electrical filters are active devices based on op-amp technology. Passive filters have very low noise, require no power supplies, and have a wide dynamic range; Active filters are much more adjustable and versatile, can cover very wide frequency ranges, have very high input and very low output impedances, and can be configured for simple switching from low-pass to high-pass bination for band-pass or band-reject behavior.
Types of filters
(b) illustrates a “state-variable filter” with electrically adjustable parameters. The state-variable filter provides three simultaneous outputs: a low-pass, a high-pass, and a band-pass:
()
()
()
Types of filters
Fig. Sharper-cutoff low-pass filters(1)
Types of filters
Fig. Sharper-cutoff low-pass filters(2)
Types of filters
Many methods can be adopted in filter design to raise the filter order. four basic designing methods: Butterworth, Chebyshev, Bessel, Cauer or elliptical filters. With the increase in filter order, the transition band e steeper, the attenuation increases, thus the filtering effect strengthened.
Theoretically, it is possible to cascade several works to enhance filter order and to accelerate the attenuation. In practice, loading effect between different cascaded stages