СЕМЕЙСТВО АКТИВНЫХ RC-ФИЛЬТРОВ ВТОРОГО ПОРЯДКА (ФНЧ, ФВЧ, ПФ) С НЕЗАВИСИМОЙ ПОДСТРОЙКОЙ ОСНОВНЫХ ПАРАМЕТРОВ
Ключевые слова:
Активные RC-фильтры, фильтр низких частот, фильтр высоких частот, полосовой фильтр, частота полюса, добротность полюса, коэффициент передачи
Аннотация
Рассматривается банк схемотехнических решений активных RC-фильтров второго
порядка – фильтр нижних частот, фильтр верхних частот и полосовые фильтры, в кото-
рых обеспечивается независимая настройка основных параметров - частоты полюса, доб-
ротности полюса и коэффициента передачи. С этих позиций сформулированы требования
к трем специальным передаточным функциям многополюсника частотозадающей RC-
цепи, которая содержит два резистора и два конденсатора. С помощью выбора коэффи-
циентов числителя первой передаточной функции реализуется тип необходимого фильтра
(ФНЧ, ФВЧ, ПФ). Коэффициенты второй передаточной функции выбираются таким об-
разом, чтобы они влияли только на частоту полюса. Следует отметить, что в зависимо-
сти от набора коэффициентов полинома числителя передаточной функции, разработан-
ные схемы обладают свойством понижения частоты полюса или повышения частоты
полюса. При этом выбор параметров третьей передаточной функции обеспечивает необ-
ходимое затухание полюса. В введении приведено описание обобщенной архитектуры
звеньев активных RC-фильтров второго порядка, которая позволяет реализовать алго-
ритм поэтапной настройки основных параметров и может быть положена в основу син-
теза многих других модификаций активных RC-фильтров. Для корректной независимой
настройки должна соблюдаться следующая последовательность: частота полюса, вто-
рым этапом идёт настройка добротности полюса, и третьим этапом ˗ масштабный
коэффициент передачи. Рассмотрены этапы синтеза данного класса активных
RC-фильтров, приведены коэффициенты передаточных функций представленных схем 12
полосовых фильтров, фильтра верхний частот и фильтра нижних частот подтвержден-
ные 14 патентами РФ.
Литература
1. Slavsky G.N. Aktivnyye RC- i RCL- filʹtry i izbiratelʹnyye usiliteli [Active RC and RCL filters
and selective amplifiers]. Moscow: Communication. 1966. 216 p.
2. Moschytz G.S., Horn P. Active filter design handbook: for use with programmable pocket
calculators and minicomputers. Chichester England, New York, J. Wiley, 1981, 316 p.
3. Sallen R.P., Key E.L. A Practical Method of Designing RC Active Filters. IRE Trans, Circuit
Theory, 1955, pp. 78-85.
4. Huelsman L.P., Allen P.E. Introduction to the Theory and Design of Active Filters. McGraw-
Hill. New York, 1980, 429 p.
5. Denisenko D.Y., Prokopenko N.N., Pakhomov I.V., Ivanov Y.I. Generalized Structure of Active
RC Filters with Independent Tuning of Pole Frequency, Pole Q-Factor and Transfer Ratio,
Proceedings of 2021 IEEE East-West Design & Test Symposium, 2021, pp. 1-5. Available at:
https://doi.org/10.1109/EWDTS52692.2021.9581023.
6. Jung S., Song I., Cressler J.D. Systematic methodology for applying Mason's signal flow
graph to analysis of feedback circuits, 2014 IEEE International Symposium on Circuits and
Systems, 2014, pp. 2421-2424. Available at: https://doi.org/10.1109/ISCAS.2014.6865661.
7. Sheng Z., Jishi S., Shuibao Y., Xi C. Research on Integrated Technology of RC Active Filter
Optimization, 2010 International Conference on Intelligent Computation Technology and Automation,
2010, pp. 1177-1179. Available at: htps://doi.org/10.1109/ICICTA.2010.597.
8. Ezzedine H., Billonnet L., Jarry B., Guillon P. Design method and optimization of noise performances
for different types of planar microwave active filters, Proceedings of the IEEE - Russia
Conference. 1999 High Power Microwave Electronics: Measurements, Identification, Applications.
MIA-ME'99, 1999, pp. 1143-1148. Available at: https://doi.org/10.1109/MIAME.1999.827830.
9. Parmann L.D. Design and Analysis of Analog Filters: A Signal Processing Perspective.
Kluwer Academic Publishers, 2001, 439 p.
10. Shuhong Xu. Study on uncertain decision factors of logistics distribution using Mason theory,
2011 International Conference on Electric Information and Control Engineering, 2011, pp.
2691-2694. Available at: https://doi.org/10.1109/ICEICE.2011.5778217.
11. Lawrence P.H., Phillip E.A. Introduction to the Theory and Design of Active Filters. McGraw-
Hill, New York, 1980, 429 p.
12. Patent RF No. 2656728. Denisenko D.Yu, Ivanov Yu,I., Prokopenko N.N., Bugakova A.V. ARC-filʹtr
nizhnikh chastot s nezavisimoy nastroykoy osnovnykh parametrov [ARC low-pass filter with independent
adjustment of the main parameters.]. Application Date: 27.06.17. Publication Date:
06.06.18, 18 p. Available at: http://www.fips.ru/cdfi/fips.dll/ru?ty=29&docid=2694135.
13. Patent RF No. 2694135. Denisenko D.Yu., Butyrlagin N.V., Prokopenko N.N. ARC-filʹtr
verkhnikh chastot s nezavisimoy podstroykoy osnovnykh parametrov [High-pass ARC filter
with independent tuning of the main parameters]. Application Date: 11.09.2018. Publication
Date: 06.06.18, 18 p. Available at: https://patents.s3.yandex.net/RU2694135C1_20190709.pdf.
14. Patent RF No. 2694134. Denisenko D.Yu., Bugakova A.V., Prokopenko N.N., Svizev G.A. Polosovoy
ARC-filʹtr na dvukh operatsionnykh usilitelyakh s povysheniyem chastoty polyusa i nezavisimoy
podstroykoy osnovnykh parametrov [Bandpass ARC filter on two operational amplifiers with pole
frequency increase and independent tuning of the main parameters]. Application Date: 11.09.18.
Publication Date: 09.07.19, 18 p. Available at: https://patents.s3.yandex.net/
RU2694134C1_20190709.pdf.
15. Patent RF No. 2688237. Denisenko D.Yu., Bugakova A.V., Prokopenko N.N., Zhebrun E.A.
Polosovoy ARC-filʹtr na dvukh operatsionnykh usilitelyakh s ponizheniyem chastoty polyusa i
nezavisimoy podstroykoy osnovnykh parametrov [Bandpass ARC filter on two operational
amplifiers with pole frequency reduction and independent tuning of the main parameters]. Application
Date: 11.09.2018. Publication Date: 21.05.19, 17 p. Available at:
https://patents.s3.yandex.net/RU2688237C1_20190521.pdf.
16. Patent RF № 2701095. Denisenko D.Yu., Bugakova A.V., Ignashin A.A., Prokopenko N.N.
Nizkochuvstvitelʹnyy polosovoy filʹtr s nezavisimoy podstroykoy osnovnykh parametrov
[Low-sensitivity band-pass filter with independent tuning of the main parameters]. Application
Date: 11.03.2019. Publication Date: 24.09.19, 14 p. Available at: https://patents.s3.
yandex.net/RU2701095C1_20190924.pdf.
17. Patent RF № 2704530. Denisenko D.Yu., Bugakova A.V., Zhebrun E.A, Prokopenko N.N.
Shirokopolosnyy polosovoy filʹtr s nezavisimoy podstroykoy chastoty polyusa, zatukhaniya polyusa
i koeffitsiyenta peredachi [Broadband bandpass filter with independent adjustment of the pole frequency,
pole attenuation and transmission coefficient]. Application Date: 07.03.2019. Publication
Date: 29.10.19, 14 p. Available at: https://patents.s3.yandex.net/RU2704530C1_20191029.pdf.
18. Patent RF № 2697944. Denisenko D.Yu., Butyrlagin N.V., Svizev G.A., Prokopenko N.N. Polosovoy
filʹtr vtorogo poryadka s nezavisimoy podstroykoy osnovnykh parametrov [Second-order band-pass
filter with independent adjustment of the main parameters]. Application Date: 25.02.2019. Publication
Date: 21.08.19, 13 p. Available at: https://patents.s3.yandex.net/RU2697944C1_20190821.pdf.
19. Patent RF № 2701038. Denisenko D.Yu., Ovsepyan E. V., Titov A. E., Prokopenko N.N.
Polosovoy filʹtr na dvukh operatsionnykh usilitelyakh s nezavisimoy podstroykoy osnovnykh
parametrov, [Band-pass filter on two operational amplifiers with independent adjustment of
the main parameters]. Application Date: 27.02.2019. Publication Date: 24.09.19, 15 p. Available
at: https://patents.s3.yandex.net/RU2701038C1_20190924.pdf.
20. Patent RF № 2718709. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Polosovoy filʹtr s
nezavisimoy podstroykoy osnovnykh parametrov [Bandpass filter with independent adjustment
of the main parameters]. Application Date: 22.11.2019. Publication Date: 14.04.2020,
12 p. Available at: https://patents.s3.yandex.net/RU2718709C1_20200414.pdf.
21. Patent RF № 2718830. Denisenko D.Yu., Prokopenko N. N., Titov A.E. Polosovoy filʹtr vtorogo
poryadka s nezavisimoy podstroykoy osnovnykh parametrov [Second-order band-pass filter with
independent adjustment of the main parameters]. Application Date: 25.11.2019. Publication Date:
14.04.2020, 15 p. Available at: https://patents.s3.yandex.net/RU2718830C1_20200414.pdf.
22. Patent RF № 2722602. Denisenko D.Yu., Prokopenko N.N, Titov A.E. Aktivnyy polosovoy
filʹtr vtorogo poryadka s nezavisimoy podstroykoy osnovnykh parametrov [Second-order active
band-pass filter with independent adjustment of the main parameters]. Application Date:
10.12.2019. Publication Date: 02.06.2020, 14 p. Available at: https://patents.s3.yandex.net/
RU2722602C1_20200602.pdf.
23. Patent RF № 2720558. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Polosovoy filʹtr na
dvukh operatsionnykh usilitelyakh s nezavisimoy podstroykoy osnovnykh parametrov
[Bandpass filter on two operational amplifiers with independent adjustment of the main parameters].
Application Date: 11.12.2019. Publication Date: 12.05.2020, 14 p. Available at:
https://patents.s3.yandex.net/RU2720558C1_20200512.pdf.
24. Patent RF № 2722752. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Polosovoy filʹtr s
nezavisimoy podstroykoy chastoty polyusa, zatukhaniya polyusa i koeffitsiyenta peredachi
[Band-pass filter with independent adjustment of the pole frequency, pole attenuation and
transmission coefficient]. Application Date: 11.12.2019. Publication Date: 03.06.2020, 14 p.
Available at: https://patents.s3.yandex.net/RU2722752C1_20200603.pdf.
25. Patent RF № 2721404. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Aktivnyy RC-filʹtr s
nezavisimoy podstroykoy osnovnykh parametrov [Active RC filter with independent adjustment
of the main parameters]. Application Date: 12.12.2019. Publication Date: 19.05.2020,
13 p. Available at: https://patents.s3.yandex.net/RU2721404C1_20200519.pdf.
and selective amplifiers]. Moscow: Communication. 1966. 216 p.
2. Moschytz G.S., Horn P. Active filter design handbook: for use with programmable pocket
calculators and minicomputers. Chichester England, New York, J. Wiley, 1981, 316 p.
3. Sallen R.P., Key E.L. A Practical Method of Designing RC Active Filters. IRE Trans, Circuit
Theory, 1955, pp. 78-85.
4. Huelsman L.P., Allen P.E. Introduction to the Theory and Design of Active Filters. McGraw-
Hill. New York, 1980, 429 p.
5. Denisenko D.Y., Prokopenko N.N., Pakhomov I.V., Ivanov Y.I. Generalized Structure of Active
RC Filters with Independent Tuning of Pole Frequency, Pole Q-Factor and Transfer Ratio,
Proceedings of 2021 IEEE East-West Design & Test Symposium, 2021, pp. 1-5. Available at:
https://doi.org/10.1109/EWDTS52692.2021.9581023.
6. Jung S., Song I., Cressler J.D. Systematic methodology for applying Mason's signal flow
graph to analysis of feedback circuits, 2014 IEEE International Symposium on Circuits and
Systems, 2014, pp. 2421-2424. Available at: https://doi.org/10.1109/ISCAS.2014.6865661.
7. Sheng Z., Jishi S., Shuibao Y., Xi C. Research on Integrated Technology of RC Active Filter
Optimization, 2010 International Conference on Intelligent Computation Technology and Automation,
2010, pp. 1177-1179. Available at: htps://doi.org/10.1109/ICICTA.2010.597.
8. Ezzedine H., Billonnet L., Jarry B., Guillon P. Design method and optimization of noise performances
for different types of planar microwave active filters, Proceedings of the IEEE - Russia
Conference. 1999 High Power Microwave Electronics: Measurements, Identification, Applications.
MIA-ME'99, 1999, pp. 1143-1148. Available at: https://doi.org/10.1109/MIAME.1999.827830.
9. Parmann L.D. Design and Analysis of Analog Filters: A Signal Processing Perspective.
Kluwer Academic Publishers, 2001, 439 p.
10. Shuhong Xu. Study on uncertain decision factors of logistics distribution using Mason theory,
2011 International Conference on Electric Information and Control Engineering, 2011, pp.
2691-2694. Available at: https://doi.org/10.1109/ICEICE.2011.5778217.
11. Lawrence P.H., Phillip E.A. Introduction to the Theory and Design of Active Filters. McGraw-
Hill, New York, 1980, 429 p.
12. Patent RF No. 2656728. Denisenko D.Yu, Ivanov Yu,I., Prokopenko N.N., Bugakova A.V. ARC-filʹtr
nizhnikh chastot s nezavisimoy nastroykoy osnovnykh parametrov [ARC low-pass filter with independent
adjustment of the main parameters.]. Application Date: 27.06.17. Publication Date:
06.06.18, 18 p. Available at: http://www.fips.ru/cdfi/fips.dll/ru?ty=29&docid=2694135.
13. Patent RF No. 2694135. Denisenko D.Yu., Butyrlagin N.V., Prokopenko N.N. ARC-filʹtr
verkhnikh chastot s nezavisimoy podstroykoy osnovnykh parametrov [High-pass ARC filter
with independent tuning of the main parameters]. Application Date: 11.09.2018. Publication
Date: 06.06.18, 18 p. Available at: https://patents.s3.yandex.net/RU2694135C1_20190709.pdf.
14. Patent RF No. 2694134. Denisenko D.Yu., Bugakova A.V., Prokopenko N.N., Svizev G.A. Polosovoy
ARC-filʹtr na dvukh operatsionnykh usilitelyakh s povysheniyem chastoty polyusa i nezavisimoy
podstroykoy osnovnykh parametrov [Bandpass ARC filter on two operational amplifiers with pole
frequency increase and independent tuning of the main parameters]. Application Date: 11.09.18.
Publication Date: 09.07.19, 18 p. Available at: https://patents.s3.yandex.net/
RU2694134C1_20190709.pdf.
15. Patent RF No. 2688237. Denisenko D.Yu., Bugakova A.V., Prokopenko N.N., Zhebrun E.A.
Polosovoy ARC-filʹtr na dvukh operatsionnykh usilitelyakh s ponizheniyem chastoty polyusa i
nezavisimoy podstroykoy osnovnykh parametrov [Bandpass ARC filter on two operational
amplifiers with pole frequency reduction and independent tuning of the main parameters]. Application
Date: 11.09.2018. Publication Date: 21.05.19, 17 p. Available at:
https://patents.s3.yandex.net/RU2688237C1_20190521.pdf.
16. Patent RF № 2701095. Denisenko D.Yu., Bugakova A.V., Ignashin A.A., Prokopenko N.N.
Nizkochuvstvitelʹnyy polosovoy filʹtr s nezavisimoy podstroykoy osnovnykh parametrov
[Low-sensitivity band-pass filter with independent tuning of the main parameters]. Application
Date: 11.03.2019. Publication Date: 24.09.19, 14 p. Available at: https://patents.s3.
yandex.net/RU2701095C1_20190924.pdf.
17. Patent RF № 2704530. Denisenko D.Yu., Bugakova A.V., Zhebrun E.A, Prokopenko N.N.
Shirokopolosnyy polosovoy filʹtr s nezavisimoy podstroykoy chastoty polyusa, zatukhaniya polyusa
i koeffitsiyenta peredachi [Broadband bandpass filter with independent adjustment of the pole frequency,
pole attenuation and transmission coefficient]. Application Date: 07.03.2019. Publication
Date: 29.10.19, 14 p. Available at: https://patents.s3.yandex.net/RU2704530C1_20191029.pdf.
18. Patent RF № 2697944. Denisenko D.Yu., Butyrlagin N.V., Svizev G.A., Prokopenko N.N. Polosovoy
filʹtr vtorogo poryadka s nezavisimoy podstroykoy osnovnykh parametrov [Second-order band-pass
filter with independent adjustment of the main parameters]. Application Date: 25.02.2019. Publication
Date: 21.08.19, 13 p. Available at: https://patents.s3.yandex.net/RU2697944C1_20190821.pdf.
19. Patent RF № 2701038. Denisenko D.Yu., Ovsepyan E. V., Titov A. E., Prokopenko N.N.
Polosovoy filʹtr na dvukh operatsionnykh usilitelyakh s nezavisimoy podstroykoy osnovnykh
parametrov, [Band-pass filter on two operational amplifiers with independent adjustment of
the main parameters]. Application Date: 27.02.2019. Publication Date: 24.09.19, 15 p. Available
at: https://patents.s3.yandex.net/RU2701038C1_20190924.pdf.
20. Patent RF № 2718709. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Polosovoy filʹtr s
nezavisimoy podstroykoy osnovnykh parametrov [Bandpass filter with independent adjustment
of the main parameters]. Application Date: 22.11.2019. Publication Date: 14.04.2020,
12 p. Available at: https://patents.s3.yandex.net/RU2718709C1_20200414.pdf.
21. Patent RF № 2718830. Denisenko D.Yu., Prokopenko N. N., Titov A.E. Polosovoy filʹtr vtorogo
poryadka s nezavisimoy podstroykoy osnovnykh parametrov [Second-order band-pass filter with
independent adjustment of the main parameters]. Application Date: 25.11.2019. Publication Date:
14.04.2020, 15 p. Available at: https://patents.s3.yandex.net/RU2718830C1_20200414.pdf.
22. Patent RF № 2722602. Denisenko D.Yu., Prokopenko N.N, Titov A.E. Aktivnyy polosovoy
filʹtr vtorogo poryadka s nezavisimoy podstroykoy osnovnykh parametrov [Second-order active
band-pass filter with independent adjustment of the main parameters]. Application Date:
10.12.2019. Publication Date: 02.06.2020, 14 p. Available at: https://patents.s3.yandex.net/
RU2722602C1_20200602.pdf.
23. Patent RF № 2720558. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Polosovoy filʹtr na
dvukh operatsionnykh usilitelyakh s nezavisimoy podstroykoy osnovnykh parametrov
[Bandpass filter on two operational amplifiers with independent adjustment of the main parameters].
Application Date: 11.12.2019. Publication Date: 12.05.2020, 14 p. Available at:
https://patents.s3.yandex.net/RU2720558C1_20200512.pdf.
24. Patent RF № 2722752. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Polosovoy filʹtr s
nezavisimoy podstroykoy chastoty polyusa, zatukhaniya polyusa i koeffitsiyenta peredachi
[Band-pass filter with independent adjustment of the pole frequency, pole attenuation and
transmission coefficient]. Application Date: 11.12.2019. Publication Date: 03.06.2020, 14 p.
Available at: https://patents.s3.yandex.net/RU2722752C1_20200603.pdf.
25. Patent RF № 2721404. Denisenko D.Yu., Prokopenko N.N., Titov A.E. Aktivnyy RC-filʹtr s
nezavisimoy podstroykoy osnovnykh parametrov [Active RC filter with independent adjustment
of the main parameters]. Application Date: 12.12.2019. Publication Date: 19.05.2020,
13 p. Available at: https://patents.s3.yandex.net/RU2721404C1_20200519.pdf.
Опубликован
2023-02-27
Выпуск
Раздел
РАЗДЕЛ III. ЭЛЕКТРОНИКА, НАНОТЕХНОЛОГИИ И ПРИБОРОСТРОЕНИЕ
