Abstract:
This article presents a new way to implement matching networks and filters
using the method of undetermined coefficients. A method is proposed for
approximating the transmission coefficient of the synthesized filter, taking
into account the required amplitude-frequency characteristics. To synthesize
the filter, an approximating function (AF) was used using orthogonal
Legendre polynomials, which is a mathematical description using a system
of equations. Filter properties whose implementation is based on modified
Legendre approximating functions usually depend on the interval on which
they are defined and have the property that they are orthogonal on this
interval. An example of seventh order filter synthesis using modified
Legendre approximating functions is given. The filter circuit is
implemented, the elements of the filter circuit are calculated based on the
selected approximating modified function. The criteria used were
minimization of the unevenness of the group delay time (GDT) and
minimization of the complex approximation error for given values of the AF
parameters. As a result, the number of filter elements, the group delay value
and the complex approximation error are significantly reduced.
