Self-equalized Filter Research Articles

New Triple-Resonance Configuration Using Stubbed Waveguide Dual-Mode Cavities

This letter presents new configurations of stubbed waveguide cavities for the realization of pseudo-elliptic and self-equalized filters. The basic structure consists of a main TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">102</sub> /TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">201</sub> dual-mode cavity that is loaded with a pair of waveguide stubs. The two stubs are located at the top and bottom walls of the cavity while always being parallel and in-line to each other. Such a two-stub arrangement can be seen as a TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">110</sub> mode cavity, which is embedded into the main dual-mode cavity. By properly setting the polarization of the stubs with respect to the main cavity as well as finely adjusting the difference between the lengths of the stubs, triple-resonance structures with selected topologies and controllable coupling mechanisms can be implemented. The resulting third-order filtering functions comprise three poles and two zeros, the latter being either group delay equalization zeros or finite frequency transmission zeros depending on the polarization of the stubs. The experimental results of a fifth-order filter with two finite frequency transmission zeros using one stubbed waveguide cavity between two standard cavities validate the new configuration.

Optimized Synthesis of Self-Equalized Microwave Filters

In this paper, a new methodology for synthesizing self-equalized filters is introduced. The methodology consists of optimizing the polynomial transfer and reflection functions considering amplitude and phase constraints simultaneously. The algorithm gives access to a more general class of functions than generalized Chebyshev (also called quasi-elliptic) functions. Two self-equalized filters are designed using this new methodology, and their performances are compared to general Chebyshev filters in order to put into evidence the interest of the proposed optimization algorithm. The first design leads to reduced group-delay variations, and the second one leads to a simplification of the hardware, reducing the number of resonators.

General Coupling Matrix Synthesis Method for Microwave Resonator Filters with Arbitrary Topology

This letter presents a new approach to synthesize the resonator filters of an arbitrary topology. This method employs an optimization method based on the relation between the polynomial coefficients of the transfer function and those of the S 21 from the coupling matrix. Therefore, this new method can also be applied to self-equalized filters that were not considered in the conventional optimization methods. Two microwave filters, a symmetric 4-pole filter with four transmission zeros (TZs) and an asymmetric 8-pole filter with seven TZs, are synthesized using the present method for validation. Excellent agreement between the response of the transfer junction and that of the synthesized S 21 from the coupling matrix is shown.

New Building Blocks for Modular Design of Elliptic and Self-Equalized Filters

This paper introduces building blocks for modular design of elliptic, pseudoelliptic, and self-equalized filters. The first building block is of second order and generates two transmission zeros (TZs), which are either on the real or imaginary axis. Moving the zeros from the real axis (linear phase response) to the imaginary axis (attenuation poles) requires changing the sign of one coupling coefficient. The second building block is a structure of order three, called extended doublet, which allows the generation of two TZs practically anywhere in the complex plane. An important property of this block is its ability to move the two TZs from the real axis to the imaginary axis of the complex s-plane without changing the signs of its coupling coefficients. The third building block is of third order and generates two TZs, which can be moved from the real to the imaginary axis by changing the sign of one coupling coefficient. Simple waveguide structures to implement these blocks are introduced for validation, although this general approach is feasible for all resonator filter types. Higher order filters are designed modularly by cascading an arbitrary number of these building blocks. A novel concept, which allows the independent control of each pair of TZs in higher order filters, is then introduced. It is shown that the new concept allows a filter of order N to generate N TZs without directly coupling the source to the load even when the coupling coefficients are all assumed frequency independent. The same approach can be used to design and reduce the sensitivity of higher order elliptic and pseudoelliptic filters using other building blocks such as doublets or a mixture of building blocks of different orders and properties. Measured results and extensive computer simulation are presented to demonstrate the validity of the concept and the performance of the designed filters.

Synthesis of coupled-resonators group-delay equalizers

A systematic synthesis and design procedure for coupled-resonators cavity group-delay equalizers is presented. The procedure consists of solving the approximation problem by optimization and performing cascade synthesis. The error function for the optimization is computed from the given filter's group delay and the zeros and poles of the input impedance of the equalizer. Convergence of the optimization is fast and insensitive to the initial guess even when the number of resonators is large. Two examples, together with experimental results, are presented; comparisons between the externally equalized and self-equalized filters are made. The effect of the isolation of the cascading devices (circulator or 3-dB hybrid) on the ripple of the final group-delay response is also extensively investigated. The good agreement between the theoretical simulation and the experimental results demonstrates the powerful nature and effectiveness of the proposed design procedure.