Measuring the Nonlinear and Dynamic Characteristics of Baseband Devices with an Overshoot at the Flat Top of Transient Response

Introduction. Bandwidth broadening and the growing complexity of the signal waveform result in the inadequacy of modern behavioral models used for simulating baseband devices (before and after the demodulator). To measure devices with an overshoot at the flat top of the transient response (TR), a nonlinear dynamic model in the form of a secondorder recursive filter can be used, whose characteristics are currently determined by the variational method. This article presents an alternative approach to measuring the characteristics of baseband devices with an overshoot at the flat top of TR. In this approach, the processing of results does not involve variational algorithms; instead, it qualifies as an indirect measurement of the characteristic functions of a second-order nonlinear recursive filter.
Aim. To consider an approach to determining the characteristics of nonlinear dynamical baseband devices with an overshoot at the flat top of the TR using non-iterative calculations based on the results of direct measurements.
Materials and methods. A device with an overshoot at the flat top on the TR is simulated by an equivalent electrical circuit, consisting of an in-series connected inductor and resistor with a parallel connected capacitor. The task is to determine the characteristics of each component: the voltage-current characteristic (VCC), the charge-voltage characteristic (CVC), and the magnetic flux-current characteristic (MFCC). The measurement object was a National Instruments PXI-5114 oscilloscope.
Results. The developed measurement technique has made it possible to accurately determine VCC, CVC, and MFCC for a device with an overshoot at the flat top without the need for iterative calculations (using indirect measurements). The error in the simulated TR using these measurements in relation to the actual values did not exceed 9 %, which is an acceptable result.
Conclusion. The proposed method for calculating characteristic functions without the need for iterations allows for the independent determination of the nonlinear characteristics of devices with an overshoot at the flat top of TR by setting the strobing point at various moments in time. The method is promising for further applications.

1. Al-kanan H., Li F., Tafuri F. F. Extended Saleh model for Behavioral Modeling of Envelope Tracking Power Amplifiers. IEEE 18th Wireless and Microwave Technology Conf. (WAMICON), Cocoa Beach, USA, 24−25 Apr. 2017. IEEE, 2017, pp. 14. doi: 10.1109/WAMICON.2017.7930244

2. Tafuri F. F., Larsen T. Extended Cann Model for Behavioral Modeling of Envelope Tracking Power Amplifiers. Intern. Symp. on Intelligent Signal Processing and Communication Systems, Naha, Japan, 12–15 Nov. 2013. IEEE, 2013, pp. 670–673. doi: 10.1109/ISPACS.2013.6704633

3. Gao X., Zhou Z. L., He M. J. SPICE Modeling of Wideband RF Front-End for Electromagnetic Coupling Analyses. IEEE 5th Intern. Symp. on Electromagnetic Compatibility (EMC-Beijing), Beijing, China, 28–31 Oct. 2017. IEEE, 2017, pp. 1–4. doi: 10.1109/EMC-B.2017.8260410

4. Sobhy M. I., Hosny E. A., Ng M. W. R., Bakkar E. A. Nonlinear System and Subsystem Modeling in the Domain. IEEE Trans. on Microwave Theory and Techniques. 1996, vol. 44, no. 12, pp. 2571–2579. doi: 10.1109/22.554605

5. Pedro J. C., Maas S. A. A Comparative Overview of Microwave and Wireless Power-Amplifier Behavioral Modeling Approaches. IEEE Trans. on Microwave Theory and Techniques. 2005, vol. 53, no. 4, pp. 1150–1163. doi: 10.1109/TMTT.2005.845723

6. Root D. E., Wood J., Tufillaro N., Schreurs D., Pekker A. Systematic Behavioral Modeling of Nonlinear Microwave/RF Circuits in the Time Domain Using Techniques from Nonlinear Dynamical Systems. Proc. of the IEEE Intern. Workshop on Behavioral Modeling and Simulation, Santa Rosa, USA, 08 Oct. 2002. IEEE, 2002, pp. 71–74. doi: 10.1109/BMAS.2002.1291060

7. Root D. E., Verspecht J., Sharrit D., Wood J., Cognata A. Broad-band Poly-Harmonic Distortion (PHD) Behavioral Models from Fast Automated Simulations and Large-Signal Vectorial Network Measurements. IEEE Trans. on Microwave Theory and Techniques. 2005, vol. 53, no. 11, pp. 3656–3664. doi: 10.1109/TMTT.2005.855728

8. Adonyev O., Izhutkin V. Development of Broadband Transceiver Module for S-band Antenna Array using mathematical model of X-parameters: Transmission Path. Intern. Youth Conf. on Radio Electronics, Moscow, Russia, 12–14 March 2020. IEEE, 2020, pp. 1–6. doi: 10.1109/REEPE49198.2020.9059184

9. Amini A. R., Boumaiza S. Time-invariant Behavioral Modeling For Harmonic Balance Simulation Based On Waveform Shape Maps. IEEE MTT-S Intern. Conf. on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), Ottawa, Canada, 11–14 Aug. 2015. IEEE, 2015, pp. 1–3. doi: 10.1109/NEMO.2015.7415098

10. Li B., Hu X., Kan N., Peng B., Wang W., Ghannouchi F. M. Multistate Digital Predistortion of Nonlinear Effect in PD-NOMA System. IEEE Microwave and Wireless Technology Let. 2024, vol. 34, no. 1, pp. 103–106. doi: 10.1109/LMWT.2023.3333885

11. Labutin S. A. Correction of Nonlinear Inertial Distortions of Pulse Signals in Measuring Transducers, Communication Equipment. Ser.: Radio Measuring Equipment. 1989, iss. 1, pp. 9–15. (In Russ.)

12. Labutin S. A. Estimation and Correction of Dynamic Signal Distortions Based on Nonlinear Models of Measuring Instruments. Measuring Equipment. Metrology. 1986, no. 12, pp. 22–29. (In Russ.)

13. Lanne A. A. Synthesis of Nonlinear Systems. Non-Recursive Systems, Deterministic Case, Electronic Modeling. 1980, no. 1, pp. 60–68. (In Russ.)

14. Nazarov M. A., Semenov E. V. Minimalistic System of Characteristics of Non-linear Baseband Pulse Devices and Its Measurement. J. of the Russian Universities. Radioelectronics. 2023, vol. 26, no. 4, pp. 123–132. (In Russ.) doi: 10.32603/1993-8985-2023-26-4-123-132

15. Semyonov E. V. Simple Behavioral Model of Baseband Pulse Devices in the Form of a Second-Order Nonlinear Recursive Filter. IEEE Trans. on Circuits and Systems II: Express Briefs. 2021, vol. 68, no. 6, pp. 2192–2196. doi: 10.1109/TCSII.2020.3048819

16. Nazarov M. A. Semyonov E. V. Simple Behavioral Model of a Recording Device Using a Second-Order Non-Linear Recursive Filter. Proc. TUSUR. 2022, vol. 25, no. 4, pp. 110–114. (In Russ.) doi: 10.21293/1818-0442-2022-25-4-110-114

17. Singleton H. E. Theory of Nonlinear Transducers. MIT. Research Lab. of electronics. Tech. rep. Available at: https://dspace.mit.edu/bitstream/handle/1721.1/4896/RLETR-160-04722817.pdf (accessed 30.04.2023).

18. PXI-5114 Specification. Available at: https://www.ni.com/docs/en-US/bundle/pxi-5114-specs/page/specs.html (accessed 01.11.2022).

19. Waveform Generator Siglent SDG7000A. Available at: https://www.siglenteu.com/waveformgenerators/sdg7000a-arbitrary-waveform-generator/ (accessed 28.08.2024).

20. Semyonov E. V. Analysis of the Structure of Nonlinear Distortions at Baseband Pulse Impacts Using Behavioral Nonlinear Models of Electrical Circuits. J. of the Russian Universities. Radioelectronics. 2022, vol. 25, no. 2, pp. 29–39. (In Russ.) doi: 10.32603/1993-8985-2022-25-2-29-39