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Low-Pass Butterworth Filter Design
In this article we will describe the design of a simple low-pass Butterworth filter using normalized prototype circuits. The procedure is simple, and it is quite valuable to know, since the same procedure can later be used to design high-pass, band-pass, and band-stop filters as well (these types will be discussed in a future article). Using this method, an individual with no prior filter design experience can design a low-pass filter to his or her specifications in a short matter of time. Furthermore, if you are viewing this article on your computer, you can enter your own design values into the interactive example design so that by the time you finish reading the article your design will be complete!
The design method that is described in this article takes advantage of the fact that several different low pass prototype filters have been designed over the years. Examples of this type of filter include the Chebychev, Elliptical, and Butterworth designs (many others exist as well). Each design has characteristics that provide different design tradeoffs. For example, the Butterworth filter has a smooth passband response and more gradual out-of-band attenuation, whereas the Chebyshev filter has a "rippled" passband response and a steeper out-of-band attenuation. This article describes the design of a Butterworth filter.
The procedure for designing a filter based on a normalized prototype is quite simple.
- First, you determine the order of filter that will be needed to fulfill your design requirements.
- Then, tables or formulas list the element values that will produce a lowpass filter of that order with a cutoff frequency of 1 radian/second, with source and load terminations of 1 Ohm connected to it. These are the normalized prototype values
- Formulas are used to scale those values to the actual source and load impedances and to the actual design cutoff frequency.
