In this chapter, we will discuss different methods to synthesize the transfer function of an analog filter, i.e., determine the required filter order and the coefficients in the transfer function, for different types of requirements. The coefficients, which determine the positions of the poles and zeros, will later be used to determine the component values in the filter realizations. Here, we will focus on frequency selective filters, which can be used to separate signals and noise that lie in different frequency bands. Moreover, in this chapter we will focus on transfer functions that can be realized with lumped circuit elements, i.e., the transfer functions are rational functions ofs.
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Notes
- 1.
S. Butterworth, UK, 1930.
- 2.
The order of a rational function is the greater of the degree of the numerator and denominator polynomials. For a causal filter, the degree of the numerator is equal to or less than the degree of the denominator.
- 3.
In some literature, the factorε 2 is included in the characteristic function.
- 4.
Adolf Hurwitz, (1859–1919), Germany.
- 5.
Pafnuty L. Chebyshev, (1821–1894), St. Petersburg, Russia.
- 6.
\(\rm{a\\cosh(x)} = \rm{In} (x+\sqrt{x^2-1})and \ a\\sinh(x)=In (x+\sqrt{x^2+1})\).
- 7.
This product is an alternative formulation of the Heisenberg uncertainty principle.
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Wanhammar, L. (2009). Synthesis of Analog Filters. In: Analog Filters Using MATLAB. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-92767-1_2
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DOI: https://doi.org/10.1007/978-0-387-92767-1_2
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