Microwave Filters for Communication Systems: Fundamentals, Design and Applications

CHAPTER 6

SYNTHESIS OF A GENERAL CLASS OF THE CHEBYSHEV FILTER FUNCTION

In this chapter, we review some important scattering parameter relations that are relevant for the synthesis of filter networks. This is followed by a discussion of the general kind of Chebyshev function and its application in generating the transfer and reflection polynomials for equiripple filter characteristics with an arbitrary distribution of the transmission zeros. In the final part of this chapter, the special cases of predistorted and dual-band filtering functions are discussed.

6.1 POLYNOMIAL FORMS OF THE TRANSFER AND REFLECTION PARAMETERS S₂₁(s) AND S₁₁(s) FOR A TWO-PORT NETWORK

For the great majority of the filter circuits, we shall initially consider two-port networks; a “source port” and a “load port” (Fig. 6.1).

For a two-port network, the scattering matrix is represented by a 2 × 2 matrix

where b₁ and b₂ are the power waves propagating away from ports 1 and 2, respectively, and a₁ and a₂ are the power waves incident at ports 1 and 2, respectively.

Figure 6.1 Two-port network.

If the network is passive, lossless, and reciprocal, its 2 × 2 S-parameter matrix yields two conservation of energy equations

and one unique orthogonality equation¹

where the S parameters are now assumed to be functions ...