radioelectronicsИзвестия высших учебных заведений России. РадиоэлектроникаJournal of the Russian Universities. Radioelectronics1993-89852658-4794Saint Petersburg Electrotechnical University10.32603/1993-8985-2023-26-6-74-93radioelectronics-819Research ArticleЭЛЕКТРОНИКА СВЧMICROWAVE ELECTRONICSМетодика разработки широкополосных отрицательных индуктивностей с малым отклонением для применений в СВЧ-диапазонеA Methodology to Design Broadband Negative Inductors with Tight Tolerance for Microwave ApplicationsБуянтуевБ. С.BuiantuevB. S.

Буянтуев Баир Саянович – магистр по направлению "Конструирование и технология электронных средств" (2016, СПбГЭТУ "ЛЭТИ"); начальник отдела разработки и модернизации РЭА, АО "НИТИ "Авангард". Автор 11 научных публикаций. Сфера научных интересов – нефостеровские элементы и их применения.

Кондратьевский пр., д. 72, Санкт-Петербург, 195271

Bair S. Buiantuev, Master in electronic design and technology (2016, Saint Petersburg Electrotechnical University); the Head of the Department for Design and Upgrade of Radio Electronic Equipment, JSC "NITI "Avangard". The author of 11 scientific publications. Area of expertise: non-Foster elements and their applications.

72, Kondratievsky Ave., St Petersburg 195271

ber89@mail.ruКалмыковН. С.KalmykovN. S.

Калмыков Никита Сергеевич – магистр по направлению "Конструирование и технология электронных средств" (2020, СПбГЭТУ "ЛЭТИ"), младший научный сотрудник кафедры микроволновой электроники. Автор 11 научных работ. Сфера научных интересов – нефостеровские элементы, СВЧ-фильтры.

ул. Профессора Попова, д. 5 Ф, Санкт-Петербург, 197022

Nikita S. Kalmykov, Master in electronic design and technology (2020, Saint Petersburg Electrotechnical University), a Junior Researcher at the Department of Microwave Electronics. The author of 11 scientific publications. Area of expertise: non-Foster elements and microwave filters.

5 F, Professor Popov St., St Petersburg 197022

nkalmykoff@gmail.comЯковенкоЕ. В.IakovenkoE. V.

Яковенко Егор Валерьевич – магистр по направлению "Электроника и наноэлектроника" (2023, СПбГЭТУ "ЛЭТИ"); инженер 2 категории, АО "МАРТ". Сфера научных интересов – нефостеровские элементы, частотно-перестраиваемые фильтры.

12-я линия В.О., д. 51 к. 2, Санкт-Петербург, 199178

Egor V. Iakovenko, Master in electronics and nanoelectronics (2023, Saint Petersburg Electrotechnical University); a second-class engineer at JSC "MART". Area of expertise: non-Foster elements and frequency-tunable filters.

51-2, 12th Line of Vasilievsky Island, St Petersburg 199178

jakovenkoegor7201@yandex.ruhttps://orcid.org/0000-0002-2477-0312ХолоднякД. В.KholodnyakD. V.

Холодняк Дмитрий Викторович – доктор технических наук (2016), доцент (2022), профессор, ведущий научный сотрудник, и.о. заведующего кафедрой микроволновой электроники. Автор более 200 научных работ. Сфера научных интересов – СВЧ-применения метаматериалов, высокотемпературных сверхпроводников, низкотемпературной совместно обжигаемой керамики и нефостеровских элементов.

ул. Профессора Попова, д. 5 Ф, Санкт-Петербург, 197022

Dmitry V. Kholodnyak, Dr. Sci. (Eng.) (2016), Professor, Leading Researcher, Acting Chair of the Department of Microwave Electronics. The author of 200 scientific publications. Area of expertise: microwave applications of metamaterials; high-temperature superconductors; low-temperature cofired ceramics, and non-Foster elements.

5 F, Professor Popov St., St Petersburg 197022

DVKholodnyak@etu.ruАО "НИТИ "Авангард"РоссияJSC "NITI "Avangard"Russian FederationСанкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)РоссияSaint Petersburg Electrotechnical UniversityRussian FederationАО "МАРТ"РоссияJSC "MART"Russian Federation2023271220232667493Copyright © Буянтуев Б.С., Калмыков Н.С., Яковенко Е.В., Холодняк Д.В., 20232023Буянтуев Б.С., Калмыков Н.С., Яковенко Е.В., Холодняк Д.В.Buiantuev B.S., Kalmykov N.S., Iakovenko E.V., Kholodnyak D.V.This work is licensed under a Creative Commons Attribution 4.0 License.https://re.eltech.ru/jour/article/view/819Введение

Введение. Нефостеровские элементы (НФЭ) имитируют в определенном диапазоне частот поведение гипотетических реактивных элементов с отрицательными значениями индуктивности или емкости и используются для компенсации частотной зависимости традиционных реактивностей, что позволяет создавать широкополосные СВЧ-устройства. Для реализации НФЭ применяются конверторы отрицательного импеданса (КОИ) – активные цепи, преобразующие импеданс нагрузки во входной импеданс противоположного знака. Ошибка преобразования, обусловленная неоптимальным выбором параметров КОИ, а также неидеальностью его элементов, ограничивает точность реализации значений и рабочую полосу частот НФЭ. Необходимость учета большого количества факторов, которые опосредованно и разнонаправленно влияют на конечный результат, и отсутствие универсальной методики значительно осложняют разработку НФЭ. Как следствие, характеристики НФЭ в широкой полосе частот заметно отличаются от целевых, что ограничивает возможности практических применений.

Цель работы

Цель работы. Предложить методику разработки отрицательных индуктивностей на основе КОИ, построенного по схеме Линвилла, которая позволила бы компенсировать ошибку преобразования и создавать широкополосные отрицательные индуктивности с малым отклонением от целевого значения.

Материалы и методы

Материалы и методы. Рассмотрено влияние параметров отдельных составляющих КОИ на частотные характеристики отрицательной индуктивности. На основании проведенного анализа и выявленных взаимосвязей предложена методика пошаговой разработки отрицательных индуктивностей с малым отклонением в широкой полосе частот. Показано, что при реализации отрицательных индуктивностей с большими абсолютными значениями целесообразно использовать в нагрузке КОИ отрезок длинной линии вместо сосредоточенной индуктивности, т.к. это позволяет обеспечить более широкую полосу частот при меньшем отклонении от целевого значения отрицательной индуктивности.

Результаты

Результаты. Для демонстрации возможностей, которые открывает применение предложенной методики, представлены результаты моделирования ряда отрицательных индуктивностей с фиксированным набором значений и отклонений в гигагерцовом диапазоне частот.

Заключение

Заключение. Полученные результаты показывают, что предложенная методика позволяет без применения численной оптимизации компенсировать ошибку преобразования и тем самым уменьшить отклонение значения отрицательной индуктивности от целевого в заданной полосе частот или расширить рабочую полосу частот при заданном допустимом отклонении отрицательной индуктивности.

Introduction

Introduction. Non-Foster elements (NFEs) mimic behavior of hypothetical negative inductors or capacitors in a certain frequency band. NFEs are used to compensate reactance of conventional inductors and capacitors that allows designing broadband microwave devices. To realize NFEs, active circuits referred to as negative impedance converters (NICs) are employed to convert the load impedance into the negative input impedance. The conversion error, caused by non-optimal choice of NIC parameters and non-idealities of NIC components, limits the accuracy and operating bandwidth of NFEs. The necessity to account for many factors, which indirectly and oppositely impact the final result, and unavailability of a universal design methodology complicate the design of NFEs significantly. As a result, broadband NFE characteristics differ from the target ones remarkably that limits practical applications.

Aim

Aim. Elaboration of a design methodology to compensate the Linvill’s NIC conversion error and realize high-accuracy broadband negative inductors.

Materials and methods

Materials and methods. Influence of NIC constituent parameters on the negative inductor frequency characteristics is considered. The performed analysis and the identified relationships allowed us to propose a step-by-step methodology to design negative inductors having tight tolerance over a broad frequency band. The use of a transmission line section instead of a lumped inductor in the NIC load when realizing negative inductors of high absolute values is shown to be advantageous as this allows providing better tolerance and wider bandwidth.

Results

Results. In order to demonstrate possibilities enabled by the proposed methodology, simulation results are presented for the GHz-range negative inductors with a set of inductance and tolerance values.

Conclusion

Conclusion. The results obtained show that the proposed methodology makes it possible to compensate the conversion error without any numerical optimization and therefore to reduce the deviation of the negative inductance from the target value in the given frequency range or to broaden the bandwidth for a given tolerable deviation of the negative inductance.

нефостеровский элементотрицательная индуктивностьконвертор отрицательного импедансаNon-Foster elementnegative inductancenegative impedance converterГрант РНФ № 23-29-00991.The RSF Grant No. 23-29-00991.ReferencesFoster R. M. A Reactance Theorem // Bell Labs Technical J. 1924. Vol. 3, no. 2. P. 259–267. doi: 10.1002/j.1538-7305.1924.tb01358.xFoster R. M. A Reactance Theorem. Bell Labs Technical J. 1924, vol. 3, no. 2, pp. 259–267. doi: 10.1002/j.1538-7305.1924.tb01358.xSussman-Fort S. E., Rudish R. M. Non-Foster Impedance Matching of Electrically-Small Antennas // IEEE Trans. on Antennas and Propag. 2009. Vol. 57, no. 8. P. 2230–2241. doi: 10.1109/TAP.2009.2024494Sussman-Fort S. E., Rudish R. M. Non-Foster Impedance Matching of Electrically-Small Antennas. IEEE Trans. on Antennas and Propag. 2009, vol. 57, no. 8, pp. 2230–2241. doi: 10.1109/TAP.2009.2024494Zhu N., Ziolkowski R. W. Broad-Bandwidth, Electrically Small Antenna Augmented with an Internal Non-Foster Element // IEEE Antennas Wireless Propag. Let. 2012. Vol. 11. P. 1116–1120. doi: 10.1109/LAWP.2012.2219572Zhu N., Ziolkowski R. W. Broad-Bandwidth, Electrically Small Antenna Augmented with an Internal Non-Foster Element. IEEE Antennas Wireless Propag. Let. 2012, vol. 11, pp. 1116–1120. doi: 10.1109/LAWP.2012.2219572Elfrgani A. M., Rojas R. G. Stabilizing Non-Foster-Based Tuning Circuits for Electrically Small Antennas // Proc. IEEE Antennas Propag. Int. Symp. Memphis, TN, USA, Jul. 2014. IEEE, 2014. P. 464– 465. doi: 10.1109/APS.2014.6904563Elfrgani A. M., Rojas R. G. Stabilizing Non-Foster-Based Tuning Circuits for Electrically Small Antennas. Proc. IEEE Antennas Propag. Int. Symp. Memphis, TN, USA, Jul. 2014. IEEE, 2014, pp. 464– 465. doi: 10.1109/APS.2014.6904563Non-Foster Broadband Matching Networks for Electrically-Small Antennas / N. Ivanov, B. Buyantuev, V. Turgaliev, D. Kholodnyak // Proc. 2016 Loughborough Antennas and Propagation Conf. Loughborough, UK, Nov. 2016. IEEE, 2017. P. 1–4. doi: 10.1109/LAPC.2016.7807596Ivanov N., Buyantuev B., Turgaliev V., Kholodnyak D. Non-Foster Broadband Matching Networks for Electrically-Small Antennas. Proc. 2016 Loughborough Antennas and Propagation Conf., Loughborough, UK, Nov. 2016. IEEE, 2017, pp. 1–4. doi: 10.1109/LAPC.2016.7807596Ivanov N., Turgaliev V., Kholodnyak D. Performance Improvement of an Electrically-Small Loop Antenna Matched with Non-Foster Negative Inductance // Proc. 2017 IEEE MTT-S Int. Microwave Symp. Honolulu, HI, USA, Jun. 2017. IEEE, 2017. P. 348– 351. doi: 10.1109/MWSYM.2017.8059117Ivanov N., Turgaliev V., Kholodnyak D. Performance Improvement of an Electrically-Small Loop Antenna Matched with Non-Foster Negative Inductance. Proc. 2017 IEEE MTT-S Int. Microwave Symp., Honolulu, HI, USA, Jun. 2017. IEEE, 2017, pp. 348– 351. doi: 10.1109/MWSYM.2017.8059117Jacob M. M., Sievenpiper D. F. Non-Foster Matched Antennas for High-Power Applications // IEEE Trans. Antennas Propag. 2017. Vol. 65, no. 9. P. 4461–4469. doi: 10.1109/TAP.2017.2727513Jacob M. M., Sievenpiper D. F. Non-Foster Matched Antennas for High-Power Applications. IEEE Trans. Antennas Propag. 2017, vol. 65, no. 9, pp. 4461– 4469. doi: 10.1109/TAP.2017.2727513Improved Signal-to-Noise Ratio, Bandwidth-Enhanced Electrically Small Antenna Augmented With Internal Non-Foster Elements / T. Shi, M.-C. Tang, Z. Wu, H.-X. Xu, R. W. Ziolkowski // IEEE Trans. Antennas Propag. 2019. Vol. 67, no. 4. P. 2763–2768. doi: 10.1109/TAP.2019.2894331Shi T., Tang M.-C., Wu Z., Xu H.-X., Ziolkowski R. W. Improved Signal-to-Noise Ratio, Bandwidth-Enhanced Electrically Small Antenna Augmented With Internal Non-Foster Elements. IEEE Trans. Antennas Propag. 2019, vol. 67, no. 4, pp. 2763–2768. doi: 10.1109/TAP.2019.2894331Batel L., Pintos J.-F., Rudant L. Superdirective and Broadband Compact Antenna Array Using Non-Foster Elements // Proc. 2019 Int. Workshop on Antenna Technol. (iWAT), Miami, FL, USA, May 2019. IEEE, 2019. P. 17–20. doi: 10.1109/IWAT.2019.8730643Batel L., Pintos J.-F., Rudant L. Superdirective and Broadband Compact Antenna Array Using Non-Foster Elements. Proc. 2019 Int. Workshop on Antenna Technol. (iWAT), Miami, FL, USA, May 2019. IEEE, 2019, pp. 17–20. doi: 10.1109/IWAT.2019.8730643Design of Compact Superdirective and Reconfigurable Array Antenna Associated with Non-Foster Elements for IoT / S. Souai, A. Diallo, J. -M. Ribero, T. Aguili // Proc. 2020 Int. Workshop on Antenna Technol. (iWAT), Bucharest, Romania, Feb. 2020. IEEE, 2020. P. 1–4. doi: 10.1109/iWAT48004.2020.1570607198Souai S., Diallo A., Ribero J.-M., Aguili T. Design of Compact Superdirective and Reconfigurable Array Antenna Associated with Non-Foster Elements for IoT. Proc. 2020 Int. Workshop on Antenna Technol. (iWAT), Bucharest, Romania, Feb. 2020. IEEE, 2020, pp. 1–4. doi: 10.1109/iWAT48004.2020.1570607198Lee Y.-H., Cho S.-Y., Chung J.-Y. SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit // Appl. Sci. 2020. Vol 10, no. 13. P. 4464. doi:10.3390/app10134464Lee Y.-H., Cho S.-Y., Chung J.-Y. SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit. Appl. Sci. 2020, vol 10, no. 13, pp. 4464. doi:10.3390/app10134464Methodology for broadband matching of electrically small antenna using combined non-Foster and passive networks / S. Almokdad, R. Lababidi, M. Le Roy, S. Sadek, A. Perennec, D. Le Jeune // Analog Integr Circ Sig Process. 2020. Vol. 104. P. 251–263. doi:10.1007/s10470-020-01672-3Almokdad S., Lababidi R., Le Roy M., Sadek S., Perennec A., Le Jeune D. Methodology for Broadband Matching of Electrically Small Antenna Using Combined Non-Foster and Passive Networks. Analog Integr Circ Sig Process. 2020, vol. 104, pp. 251–263. doi:10.1007/s10470-020-01672-3Albarracín-Vargas F., González-Posadas V., Segovia-Vargas D. Small Printed Antenna Array Based on Non-Foster Networks // Proc 17th Int. Congr. on Artif. Mat. for Novel Wave Phenomena (Metamaterials 2023), Crete, Greece, Sept. 2023. IEEE, 2023. P. X-332–X-334. doi: 10.1109/Metamaterials58257.2023.10289315Albarracín-Vargas F., González-Posadas V., Segovia-Vargas D. Small Printed Antenna Array Based on Non-Foster Networks. Proc 17th Int. Congr. on Artif. Mat. for Novel Wave Phenomena (Metamaterials 2023), Crete, Greece, Sept. 2023. IEEE, 2023, pp. X-332–X-334. doi: 10.1109/Metamaterials58257.2023.10289315A Novel Design Methodology for Non-Foster Elements with Application in Broadband Self-Oscillating Antennas / B. Buiantuev, L. Vincelj, D. Kholodnyak, S. Hrabar // Proc. of 14th Eur. Conf. on Antennas and Propag. (EuCAP 2020), Copenhagen, Denmark, March 2020. IEEE, 2020. P. 1–4. doi: 10.23919/EuCAP48036.2020.9135388Buiantuev B., Vincelj L., Kholodnyak D., Hrabar S. A Novel Design Methodology for Non-Foster Elements with Application in Broadband Self-Oscillating Antennas. Proc. of 14th Eur. Conf. on Antennas and Propag. (EuCAP 2020), Copenhagen, Den-mark, March 2020. IEEE, 2020, pp. 1–4. doi: 10.23919/EuCAP48036.2020.9135388Non-Foster Self-Oscillating Single-Loop Antenna / S. Hrabar, D. Kholodnyak, B. Buiantuev, D. Dobrijevic, M. Jakovcev, A. Zeljko, M. Martinic, I. Krois // Proc. of 14th Int. Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials 2020), New York, USA, October 2020. IEEE, 2020. P. X-124–X-126. doi: 10.1109/Metamaterials49557.2020.9285087Hrabar S., Kholodnyak D., Buiantuev B., Dobrijevic D., Jakovcev M., Zeljko A., Martinic M., Krois I. Non-Foster Self-Oscillating Single-Loop Antenna. Proc. of 14th Int. Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials 2020), New York, USA, October 2020. IEEE, 2020, pp. X-124–X-126. doi: 10.1109/Metamaterials49557.2020.9285087Vincelj L., Krois I., Hrabar S. Toward Self-Oscillating Non-Foster Unit Cell for Future Active Metasurfaces // IEEE Trans. Antennas Propag. 2020. Vol. 68, no. 3. P. 1665–1679. doi: 10.1109/TAP.2019.2951529Vincelj L., Krois I., Hrabar S. Toward Self-Oscillating Non-Foster Unit Cell for Future Active Metasurfaces. IEEE Trans. Antennas Propag. 2020, vol. 68, no. 3, pp. 1665–1679. doi: 10.1109/TAP.2019.2951529Hrabar S. First Ten Years of Active Metamaterial Structures with "Negative" Elements // EPJ Applied Metamaterials. 2018. Vol. 5, no. 9. P. 1–12. doi: 10.1051/epjam/2018005Hrabar S. First Ten Years of Active Metamaterial Structures with "Negative" Elements. EPJ Applied Metamaterials. 2018, vol. 5, no. 9, pp. 1–12. doi: 10.1051/epjam/2018005Temporal Metamaterials with Non-Foster Networks / Y. Kiasat, V. Pacheco-Peña, B. Edwards, N. Engheta // Proc. 2018 Conf. on Lasers and Electro-Optics, San Jose, CA, USA, Мay 2018. IEEE, 2018. P. 1–2. doi: 10.1364/CLEO_AT.2018.JW2A.90Kiasat Y., Pacheco-Peña V., Edwards B., Engheta N. Temporal Metamaterials with Non-Foster Networks. Proc. 2018 Conf. on Lasers and Electro-Optics, San Jose, CA, USA, Мay 2018. IEEE, 2018, pp. 1–2. doi: 10.1364/CLEO_AT.2018.JW2A.90Study and Optimization of a Non-Foster Circuit for the Design of Wideband Metasurfaces / C. Fisné, C. Мartel, A. Franc, N. Raveu // Proc. 2019 Int. Conf. on Electromagn. in Adv. Appl., Granada, Spain, Sep. 2019. IEEE, 2019. P. 0761–0764. doi: 10.1109/ICEAA.2019.8879230Fisné C., Мartel C., Franc A., Raveu N. Study and Optimization of a Non-Foster Circuit for the Design of Wideband Metasurfaces. Proc. 2019 Int. Conf. on Electromagn. in Adv. Appl., Granada, Spain, Sep. 2019. IEEE, 2019, pp. 0761–0764. doi: 10.1109/ICEAA.2019.8879230Kalmykov N., Buiantuev B., Kholodnyak D. Broadband Metasurfaces Loaded with Non-Foster Elements // J. of Phys.: Conf. Ser. 2021. Vol. 2015, 012061. P. 1–7. doi: 10.1088/1742-6596/2015/1/012061Kalmykov N., Buiantuev B., Kholodnyak D. Broadband Metasurfaces Loaded with Non-Foster Elements. J. of Phys.: Conf. Ser. 2021, vol. 2015, 012061, pp. 1–7. doi: 10.1088/1742-6596/2015/1/012061A Wideband IM3 Cancellation Technique Using Negative Impedance for LNAs with Cascode Topology / W. Cheng, A. J. Annema, G. J. M. Wienk, B. Nauta // Proc. 2012 IEEE Radio Freq. Integr. Circuits Symp. Montreal, QC, Canada, Jun. 2012. IEEE, 2021. P. 13–16. doi: 10.1109/RFIC.2012.6242221Cheng W., Annema A. J., Wienk G. J. M., Nauta B. A Wideband IM3 Cancellation Technique Using Negative Impedance for LNAs with Cascode Topology. Proc. 2012 IEEE Radio Freq. Integr. Circuits Symp. Montreal, QC, Canada, Jun. 2012. IEEE, 2021, pp. 13–16. doi: 10.1109/RFIC.2012.6242221A 6–18 GHz GaN pHEMT Power Amplifier Using non-Foster Matching / S. Lee, H. Park, J. Kim, Y. Kwon // Proc. 2015 IEEE MTT-S Int. Microw. Symp., Phoenix, AZ, USA, Мay 2015. IEEE, 2015. P. 1–4. doi: 10.1109/MWSYM.2015.7167127Lee S., Park H., Kim J., Kwon Y. A 6–18 GHz GaN pHEMT Power Amplifier Using non-Foster Matching. Proc. 2015 IEEE MTT-S Int. Microw. Symp., Phoenix, AZ, USA, Мay 2015. IEEE, 2015, pp. 1–4. doi: 10.1109/MWSYM.2015.7167127Akwuruoha C. N., Hu Z. 64 to 70 GHz Microstrip Non-Foster Circuit Class-J GaAs pHEMT Power Amplifier // Proc. 25th Telecommun. Forum, Belgrade, Serbia, Nov. 2017. IEEE, 2018. P. 1–4. doi: 10.1109/TELFOR.2017.8249391Akwuruoha C. N., Hu Z. 64 to 70 GHz Microstrip Non-Foster Circuit Class-J GaAs pHEMT Power Amplifier. Proc. 25th Telecommun. Forum, Belgrade, Serbia, Nov. 2017. IEEE, 2018, pp. 1–4. doi: 10.1109/TELFOR.2017.8249391Akwuruoha C. N., Hu Z. 55 to 59 GHz MMIC Non-Foster Circuit Enabled Class-J GaAs pHEMT Power Amplifier // Proc. 2018 Int. Conf. on Integr. Circuit Design and Technol., Otranto, Italy, Jun. 2018. IEEE, 2018. P. 149–152. doi: 10.1109/ICICDT.2018.8399778Akwuruoha C. N., Hu Z. 55 to 59 GHz MMIC Non-Foster Circuit Enabled Class-J GaAs pHEMT Power Amplifier. Proc. 2018 Int. Conf. on Integr. Circuit Design and Technol., Otranto, Italy, Jun. 2018. IEEE, 2018, pp. 149–152. doi: 10.1109/ICICDT.2018.8399778Chen Y., Mouthaan K. Wideband Varactorless LC VCO Using a Tunable Negative-Inductance Cell // IEEE Trans. on Circuits and Syst. I: Regular Papers. 2010. Vol. 57, no. 10. P. 2609–2617. doi: 10.1109/TCSI.2010.2046967Chen Y., Mouthaan K. Wideband Varactorless LC VCO Using a Tunable Negative-Inductance Cell. IEEE Trans. on Circuits and Syst. I: Regular Papers. 2010, vol. 57, no. 10, pp. 2609–2617. doi: 10.1109/TCSI.2010.2046967−189 dBc/Hz FOMT Wide Tuning Range Kaband VCO Using Tunable Negative Capacitance and Inductance Redistribution / Q. Wu, S. Elabd, T. K. Quach, A. Мattamana, S. R. Dooley, J. McCue, P. L. Orlando, G. L. Creech, A. W. Khalil // Proc. 2013 IEEE Radio Freq. Integr. Circuits Symp., Seattle, WA, USA, Jun. 2013. IEEE, 2013. P. 199–202. doi: 10.1109/RFIC.2013.6569560Wu Q., Elabd S., Quach T. K., Мattamana A., Dooley S. R., McCue J., Orlando P. L., Creech G. L., Khalil A. W. −189 dBc/Hz FOMT Wide Tuning Range Ka-band VCO Using Tunable Negative Capacitance and Inductance Redistribution. Proc. 2013 IEEE Radio Freq. Integr. Circuits Symp., Seattle, WA, USA, Jun. 2013. IEEE, 2013, pp. 199–202. doi: 10.1109/RFIC.2013.6569560A W-band Push-Push VCO Using Non-Foster Circuit for Enhanced Frequency Tuning Range / W. Lee, S. Lee, H. Park, K. Choi, W. Lee, Y. Kwon // Proc. 2016 URSI Asia-Pacific Radio Sci. Conf., Seoul, Korea, Aug. 2016. IEEE, 2016. P. 653–656.Lee W., Lee S., Park H., Choi K., Lee W., Kwon Y. A W-band Push-Push VCO Using Non-Foster Circuit for Enhanced Frequency Tuning Range. Proc. 2016 URSI Asia-Pacific Radio Sci. Conf., Seoul, Korea, Aug. 2016. IEEE, 2016, pp. 653–656.Ka-band VCO with Parasitic Capacitance Cancelling Technique / W. Lee, S.Lee, J. Choi, J. So, Y. Kwon // Electronics Let. 2017. Vol. 53, no. 1. P. 38–40. doi: 10.1049/el.2016.3799Lee W., Lee S., Choi J., So J., Kwon Y. Ka-band VCO with Parasitic Capacitance Cancelling Technique. Electronics Let. 2017, vol. 53, no. 1, pp. 38–40. doi: 10.1049/el.2016.3799Nguyen D.-A., Seo C. A Novel Varactorless Tuning Technique for Clapp VCO Design Using Tunable Negative Capacitor to Increase Frequency-Tuning Range // IEEE Access. 2021. Vol. 9. P. 99562–99570. doi: 10.1109/ACCESS.2021.3096187Nguyen D.-A., Seo C. A Novel Varactorless Tuning Technique for Clapp VCO Design Using Tunable Negative Capacitor to Increase Frequency-Tuning Range. IEEE Access. 2021, vol. 9, pp. 99562–99570. doi: 10.1109/ACCESS.2021.3096187A Frequency Independent Phase Inverting All-Pass Network Suitable for a Design of Ultra-Wideband 180° Phase Shifters / D. Kholodnyak, V. Turgaliev, A. Rusakov, K. Zemlyakov, I. Vendik // Proc 2011 41st European Microwave Conf., Мanchester, UK, Oct. 2011. IEEE, 2011. P. 643–646. doi: 10.23919/EuMC.2011.6101987Kholodnyak D., Turgaliev V., Rusakov A., Zemlyakov K., Vendik I. A Frequency Independent Phase Inverting All-Pass Network Suitable for a Design of Ultra-Wideband 180° Phase Shifters. Proc 2011 41st European Microwave Conf., Мanchester, UK, Oct. 2011. IEEE, 2011, pp. 643–646. doi: 10.23919/EuMC.2011.6101987Buyantuev B., Kholodnyak D. Design of Immittance Inverters and Phase Inverters with Non-Foster Elements // Proc. 22nd Int. Conf. on Microwaves, Radar and Wireless Communications, Poznan, Poland, Мay 2018. IEEE, 2018. P. 29–32. doi: 10.23919/MIKON.2018.8405203Buyantuev B., Kholodnyak D. Design of Immittance Inverters and Phase Inverters with Non-Foster Elements. Proc. 22nd Int. Conf. on Microwaves, Radar and Wireless Communications, Poznan, Poland, Мay 2018. IEEE, 2018, pp. 29–32. doi: 10.23919/MIKON.2018.8405203Wide-band Active Tunable Phase Shifter Using Improved Non-Foster Circuit / S. Al Mokdad, R. Lababidi, M. Le Roy, S. Sadek, A. Perennec, D. Le Jeune // Proc 2018 25th IEEE Int. Conf. on Electronics, Circuits and Syst., Bordeaux, France, Dec. 2018. IEEE, 2019. P. 449–452. doi: 10.1109/ICECS.2018.8618011Al Mokdad S., Lababidi R., Le Roy M., Sadek S., Perennec A., Le Jeune D. Wide-band Active Tunable Phase Shifter Using Improved Non-Foster Circuit. Proc 2018 25th IEEE Int. Conf. on Electronics, Circuits and Syst., Bordeaux, France, Dec. 2018. IEEE, 2019, pp. 449–452. doi: 10.1109/ICECS.2018.8618011Kholodnyak D. V., Turgaliev V. M. Towards a Design of the Ultra-Wideband Microwave Devices Using the Non-Foster Negative Reactances // Proc. 7th German Microwave Conf., Ilmenau, Germany, Мar. 2012. IEEE, 2012. P. 1–4.Kholodnyak D. V., Turgaliev V. M. Towards a Design of the Ultra-Wideband Microwave Devices Using the Non-Foster Negative Reactances. Proc. 7th German Microwave Conf, Ilmenau, Germany, Мar. 2012. IEEE, 2012, pp. 1–4.Shi T., Tang M.-C., Ziolkowski R. W. The Design of a Compact, Wide Bandwidth, Non-Foster-Based Substrate Integrated Waveguide Filter // Proc. 2018 IEEE Asia-Pacific Conf. on Antennas and Propag., Auckland, New Zealand, Aug. 2018. IEEE, 2018. P. 54–56. doi: 10.1109/APCAP.2018.8538271Shi T., Tang M.-C., Ziolkowski R. W. The Design of a Compact, Wide Bandwidth, Non-Foster-Based Substrate Integrated Waveguide Filter. Proc. 2018 IEEE Asia-Pacific Conf. on Antennas and Propag., Auckland, New Zealand, Aug. 2018. IEEE, 2018, pp. 54–56. doi: 10.1109/APCAP.2018.8538271Physically Oriented Design of Negative Capacitors Based on Linvill’s Floating Impedance Converter / В. Buiantuev, N. Kalmykov, D. Kholodnyak, A. Brizić, L. Vincelj, S. Hrabar // IEEE Trans. on Microwave Theory & Techniques. 2022. Vol. 70, no. 1. P. 139–154. doi: 10.1109/TMTT.2021.3131544Buiantuev В., Kalmykov N., Kholodnyak D., Brizić A., Vincelj L., Hrabar S. Physically Oriented Design of Negative Capacitors Based on Linvill’s Floating Impedance Converter. IEEE Trans. on Microwave Theory & Techniques. 2022, vol. 70, no. 1, pp. 139–154. doi: 10.1109/TMTT.2021.3131544Kalmykov N., Kholodnyak D. Non-Foster Elements Pave the Way to Design Novel Wideband and Tunable Bandpass Filters // Proc. of 2022 Asia-Pacific Microwave Conf. (APMC 2022), Yokohama, Japan, November 2022. IEEE, 2023. P. 830–832. doi: 10.23919/APMC55665.2022.9999939Kalmykov N., Kholodnyak D. Non-Foster Elements Pave the Way to Design Novel Wideband and Tunable Bandpass Filters. Proc. of 2022 Asia-Pacific Microwave Conf. (APMC 2022), Yokohama, Japan, November 2022. IEEE, 2023, pp. 830–832. doi: 10.23919/APMC55665.2022.9999939Use of Non-Foster Elements based on Compensated Passive Structure in Tunable Bandpass Filter / B. Okorn, D. Nožina, D. Žanic, S. Hrabar // 2023 Int. Symp. ELMAR, Zadar, Croatia, September 2023. IEEE, 2023. P. 117–122. doi: 10.1109/ELMAR59410.2023.10253914Okorn B., Nožina D., Žanic D., Hrabar S. Use of Non-Foster Elements based on Compensated Passive Structure in Tunable Bandpass Filter. 2023 Int. Symp. ELMAR, Zadar, Croatia, September 2023. IEEE, 2023, pp. 117–122. doi: 10.1109/ELMAR59410.2023.10253914Kolev S., Delacressonniere B., Gautier J. L. Using a Negative Capacitance to Increase the Tuning Range of a Varactor Diode in MMIC Technology // IEEE Trans. Microwave Theory & Tech. 2001. Vol. 49, no. 12. P. 2425–2430. doi: 10.1109/22.971631Kolev S., Delacressonniere B., Gautier J. L. Using a Negative Capacitance to Increase the Tuning Range of a Varactor Diode in MMIC Technology. IEEE Trans. Microwave Theory & Tech. 2001, vol. 49, no. 12, pp. 2425–2430. doi: 10.1109/22.971631Leontyev A., Kalmykov N., Kholodnyak D. Varactor Diode Tunability Enhancement by Means of a Non-Foster Negative Capacitor on Linvill’s NIC // Proc. of 2023 IEEE Int. Symp. on Radio-Frequency Integration Technology (RFIT 2023). Cairns, Australia, August 2023. IEEE, 2023. P. 70–72. doi: 10.1109/RFIT58767.2023.10243351Leontyev A., Kalmykov N., Kholodnyak D. Varactor Diode Tunability Enhancement by Means of a Non-Foster Negative Capacitor on Linvill’s NIC. Proc. of 2023 IEEE Int. Symp. on Radio-Frequency Integration Technology (RFIT 2023), Cairns, Australia, August 2023. IEEE, 2023, pp. 70–72. doi: 10.1109/RFIT58767.2023.10243351Linvill J. G. Transistor Negative-Impedance Converters // Proc. IRE. 1953. Vol. 41, no. 6. P. 725– 729. doi: 10.1109/JRPROC.1953.274251Linvill J. G. Transistor Negative-Impedance Converters. Proc. IRE. 1953, vol. 41, no. 6, pp. 725– 729. doi: 10.1109/JRPROC.1953.274251Active Tunable Inductor Using Non-Foster Element / E. Vorobev, V. Turgaliev, D. Kholodnyak, N. Ivanov // Proc. IEEE Conf. of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus). St. Petersburg, Russia, Apr 2017. IEEE, 2017. P. 346–349. doi: 10.1109/EIConRus.2017.7910562Vorobev E., Turgaliev V., Kholodnyak D., Ivanov N. Active Tunable Inductor Using Non-Foster Element. Proc. IEEE Conf. of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), St. Petersburg, Russia, Apr 2017. IEEE, 2017, pp. 346–349. doi: 10.1109/EIConRus.2017.7910562Saadat S., Aghasi H., Afshari E. Low-Power Negative Inductance Integrated Circuits for GHz Applications // IEEE Microw. and Wireless Compon. Let. 2015. Vol. 25, no. 2. P. 118–120. doi: 10.1109/LMWC.2014.2382631Saadat S., Aghasi H., Afshari E. Low-Power Negative Inductance Integrated Circuits for GHz Applications. IEEE Microw. and Wireless Compon. Let. 2015, vol. 25, no. 2, pp. 118–120. doi: 10.1109/LMWC.2014.2382631White C.R., May J.W., Colburn J.S A Variable Negative-Inductance Integrated Circuit at UHF Frequencies // IEEE Microw. and Wireless Compon. Let. 2012. Vol. 22, no. 1. P. 35–37. doi: 10.1109/LMWC.2011.2175718White C. R., May J. W., Colburn J. S. A Variable Negative-Inductance Integrated Circuit at UHF Frequencies // IEEE Microw. and Wireless Compon. Let. 2012, vol. 22, no. 1, pp. 35–37. doi: 10.1109/LMWC.2011.2175718Covington J. M. C., Smith K. L, Shehan J. W Measurement of a CMOS Negative Inductor for Wide-band Non-Foster Metamaterials // Proc IEEE SOUTH EASTCON 2014. Lexington, USA. 13–16 Mar. 2014. IEEE, 2014. P. 1–4. doi: 10.1109/SECON.2014.6950694Covington J. M. C., Smith K. L, Shehan J. W Measurement of a CMOS Negative Inductor for Wide-band Non-Foster Metamaterials. Proc IEEE SOUTHEASTCON 2014, Lexington, USA. 13–16 Mar. 2014. IEEE, 2014, pp. 1–4. doi: 10.1109/SECON.2014.6950694Paillot J.-M., Cordeau D A Wideband Varactor-Tuned BICMOS Negative Inductance Design // Proc 2014 Int. Conf. on Appl. and Theor. Electricity (ICATE). Craiova, Romania, Mar. 2014. IEEE, 2014. P. 1–4. doi: 10.1109/ICATE.2014.6972591Paillot J.-M., Cordeau D A Wideband Varactor-Tuned BICMOS Negative Inductance Design. Proc 2014 Int. Conf. on Appl. and Theor. Electricity (ICATE), Craiova, Romania, Mar. 2014. IEEE, 2014, pp. 1–4. doi: 10.1109/ICATE.2014.6972591Zhenxing X., Meiling L., Zhu Q. Realizing Wideband Negative Inductor Using Current Feedback Amplifier // Microw. and Opt. Technol. Let. 2016. Vol. 58, no. 7. P. 1723–1728. doi: 10.1002/mop.29896Zhenxing X., Meiling L., Zhu Q. Realizing Wideband Negative Inductor Using Current Feedback Amplifier. Microw. and Opt. Technol. Let. 2016, vol. 58, no. 7, pp. 1723–1728. doi: 10.1002/mop.29896Hong J.-S., Lancaster M. J. Microstrip Filters for RF–Microwave Applications. N.Y.: John Wiley & Sons, Inc., 2001. 457 p.Hong J.-S., Lancaster M. J. Microstrip Filters for RF–Microwave Applications. N.Y., John Wiley & Sons, Inc., 2001, 457 p.Full Conditions for the Stability Analysis of Negative Impedance Converters / J. L. Jimenez-Мartin, V. Gonzalez-Posadas, A. Parra-Cerrada, A. Blanco-Campo, E. Ugarte-Munoz, D. Segovia-Vargas // Proc. 6th Eur. Conf. Antennas Propag. Prague, Czech Republic, Мar. 2012. IEEE, 2012. P. 135–138. doi: 10.1109/EuCAP.2012.6206680Jimenez-Мartin J. L., Gonzalez-Posadas V., Parra-Cerrada A., Blanco-Campo A., Ugarte-Munoz E., Segovia-Vargas D. Full Conditions for the Stability Analysis of Negative Impedance Converters. Proc. 6th Eur. Conf. Antennas Propag., Prague, Czech Republic, Мar. 2012. IEEE, 2012, pp. 135–138. doi: 10.1109/EuCAP.2012.6206680Tang Q., Xin H. Stability Analysis of Non-Foster Circuit Using Normalized Determinant Function // IEEE Trans. Microw. Theory Techn. 2017. Vol. 65, no. 9. P. 3269–3277. doi: 10.1109/TMTT.2017.2687425Tang Q., Xin H. Stability Analysis of Non-Foster Circuit Using Normalized Determinant Function. IEEE Trans. Microw. Theory Techn. 2017, vol. 65, no. 9, pp. 3269–3277. doi: 10.1109/TMTT.2017.2687425

The authors declare that there are no conflicts of interest present.