08.Circuits and Systems - Fundamental Theory and by John G. Webster (Editor)

By John G. Webster (Editor)

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Use of an all-pass factor Ȑ(s) in T(Ϫs2) always penalizes the minimum gain level in the passband. Therefore one should avoid using any extra Blaschke product in step 3 if possible. • It is interesting to observe that, whenever ZG and ZL possess the same transmission zeros of Class A, it is not possible to satisfy the gain–bandwidth theorem simultaneously if they are inserted into F11 and F22 as all-pass functions. In this case, a proper form of F21 must be selected, which naturally includes these RHP zeros of load and generator, but not as all-pass products.

Utilizing hybrid or monolithic integrated circuit production technologies, it is possible to build this type of lumped circuit elements up to 10 GHz. Beyond these frequencies, however, physical sizes must be included in the design process. A straightforward method to construct matching equalizers with physical sizes is to employ equal delay transmission lines throughout the design. In this case, complex variable s ϭ ␴ ϩ jͶ is replaced with the Richard variable ␭ ϭ ⌺ ϩ j⍀. Here, transformed frequency ⍀ is given by ⍀ ϭ tanͶ␶, where ␶ specifies the equal delay length of transmission lines employed in the designs.

A. Kummert, Synthesis of two-dimensional lossless m-ports with prescribed scattering matrix, Circuits Syst. , 8: 97– 119, 1989. P. Landau and E. , 13: 123–132, 1985. R. Levy, A general equivalent circuit transformation for distributed networks, IEEE Trans. Circuit Theory, CT-12: 457–458, 1965. R. H. Levy and T. E. Rozzi, Precise design of coaxial low-pass filters, IEEE Trans. Microw. , MTT-16: 142–147, 1968. L. Y. G. L. Matthaei and E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures, New York: McGrawHill, 1964.

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