SUMMARYIt is shown that the shifted Jacobi polynomials are particularly useful in solving the approximation problem of both the general and the monotonic polynomial lowpass fitters. A new type of least squares monotonic filter is introduced.
We present a technique which resorts to the time domain capabilities of a vector network analyzer and to the network synthesia tools, in order to perform an in-fizture calibration of the S-purameter measurement system directly to the ports of the device under test. The effects of the cwtomer's nori ideal fiztures can be removed without requiring the insertion of standard components or particular loads, which can afect the calibration efectiveness. The inaccuracies due to the precision of the actual loads and to the connection repeatability are also avoided. Some simulation reeulte demonstrate the very g o d capability of the technique.Ezperimental tests were ab0 carried out on an actual microstrip transistor fizture, showing a very eatisfactoty launcher modeling and de-embedding.
The attenuation characteristics of lowpass and bandpass rational filters are approximated by optimizing a weighted error criterion. The analytical approach yields the solution in terms of kernel polynomials, and if the weight function has a particular form, the solution may be given explicitly in terms of the Szego-Bernstein polynomials; with other weight functions it is necessary to resort to numerical procedures. The solution exhibits a passband behaviour that depends on the chosen weight function; when the Szego-Bernstein polynomials are used both lowpass and bandpass filters may exhibit equiripple passband attenuation.
a , , , = 10 log [1+ E2]We make also the assumption that the number m and the position wi of the finite transmission zeros, the multiplicity noo of the attenuation peaks at infinity, and, in the bandpass case, the multiplicity no of
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