Аналитическое решение задачи синтеза трехзвенного ступенчатого чебышевского СВЧ-фильтра

The problem of synthesis of the three–link stepped Chebyshev's microwave filter is reduced to two independent fourth degree equations, including a single link wave impedance as unknown. The solution of Descartes – Euler is applied to these equations. It is proved, that in case of wave impedances of extreme links are equal, the problem of the filter synthesis has two solutions. Identical phase–frequency responses correspond to these solutions. It is proved, that for every one of links a product of the wave impedances, relating to these solutions, is equal to a square of the wave impedance of transmission line, including filter.

Ladder-Based Synthesis and Design of Low-Frequency Buffer-Based CMOS Filters

Buffer-based CMOS filters are maximally simplified circuits containing as few transistors as possible. Their applications, among others, include nano to micro watt biomedical sensors that process physiological signals of frequencies from 0.01 Hz to about 3 kHz. The order of a buffer-based filter is not greater than two. Hence, to obtain higher-order filters, a cascade of second-order filters is constructed. In this paper, a more general method for buffer-based filter synthesis is developed and presented. The method uses RLC ladder prototypes to obtain filters of arbitrary orders. In addition, a set of novel circuit solutions with ultra-low voltage and power are proposed. The introduced circuits were synthesized and simulated using 180-nm CMOS technology of X-FAB. One of the designed circuits is a fourth-order, low-pass filter that features: 100-Hz passband, 0.4-V supply voltage, power consumption of less than 5 nW, and dynamic range above 60 dB. Moreover, the total capacitance of the proposed filter (31 pF) is 25% lower compared to the structure synthesized using a conventional cascade method (40 pF).

Programmable Wavelength Filter with Double Ring Loaded MZI

We propose a novel filter circuit that incorporates a double ring resonator with a balanced Mach-Zehnder interferometer (MZI).The circuit has a response equivalent to a conventional ring loaded MZI filter, but with added flexibility in terms of configurability. The second-order filter can also be cascaded to realize higher-order filters. The circuit incorporates a two-stage input and output coupler to further reduce the effect of dispersion. A combination of local and global optimization strategies to program the filter, using tailored objective functions, have been tested in simulation and experiments. To our best knowledge, this is the first time a global optimization strategy is directly used in ARMA filter synthesis and simulation without any additional requirement. We further extend the optimization strategy into experiments and demonstrated its use in practical case for programmable filter circuits.

Development of a method for synthesis the FIR filters with a cascade structure based on genetic algorithm

The object of research is the process of digital signal processing. The subject of research is methods of synthesis of digital filters with a finite impulse response based on a genetic algorithm. Digital filtering is one of the tasks of digital signal processing. FIR filters are always stable and provide a constant group delay. There are various methods for synthesizing digital filters, but they are all aimed at synthesizing filters with a direct structure. One of the most problematic areas of a digital filter with a direct structure in digital processing is the high sensitivity of the filter characteristics to inaccuracies in setting the filter coefficients. Genetic algorithm-based filter synthesis methods use an ideal filter as the approximated filter. This approach has a number of disadvantages: it complicates the search for an optimal solution; computation time increases. The study used random search method, which is the basis of genetic algorithm (used for solving optimization problems); theory of digital filtering in filter analysis; numerical methods for modeling in a Python program. Prepared synthesis method FIR filter with the cascade structure, which is less sensitive to the effect of finite bit width. Computation time was reduced. This is due to the fact that the proposed method searches for the most suitable filter coefficients based on a genetic algorithm and has a number of features, in particular, it is proposed to use a piecewise-linear function as an approximated amplitude-frequency response. This makes it possible to reduce the number of populations of the genetic algorithm when searching for a solution. The synthesis of an FIR filter with a cascade structure based on a genetic algorithm showed that for a 24-order filter it took about 30–40 generations to get the filter parameters close to the optimal values. In comparison with classical methods of filter synthesis, the following advantages are provided: calculations of the coefficients of a filter with a cascade structure directly, the possibility of optimizing coefficients with limited bit depth.

Low-Pass Filtering Method for Poisson Data Time Series

Problems of digital processing of Poisson-distributed data time series from various counters of radiation particles, photons, slow neutrons etc. are relevant for experimental physics and measuring technology. A low-pass filtering method for normalized Poisson-distributed data time series is proposed. A digital quasi-Gaussian filter is designed, with a finite impulse response and non-negative weights. The quasi-Gaussian filter synthesis is implemented using the technology of stochastic global minimization and modification of the annealing simulation algorithm. The results of testing the filtering method and the quasi-Gaussian filter on model and experimental normalized Poisson data from the URAGAN muon hodoscope, that have confirmed their effectiveness, are presented.