Analysis of the Structure of Nonlinear Distortions at Baseband Pulse Impacts Using Behavioral Nonlinear Models of Electrical Circuits

Introduction. Measuring harmonic distortions of a baseband pulse signal constitutes a problem due to the continuous nature of their spectrum. In order to obtain nonlinear distortions of a signal, a comparison should be conducted either of the object’s responses to two different test signals or those of the real object and its linearized model. However, such an approach does not distinguish between various physical factors that cause nonlinear distortions. This, as a result, complicates the optimization of devices.
Aim. To develop an approach capable of determining the contribution of various sources to the nonlinear distortion of baseband pulse signals.
Materials and methods. The method under consideration involves a synthesis of a nonlinear behavioral model for an object and a comparison of the model’s output signals when linearizing some (or all) of the characteristic functions in this model. This allows distinguishing the contribution of inertialess, capacitive nonlinearity and nonlinearity associated with signal recirculation in feedbacks. An example of a three-stage baseband pulse amplifier (with step functions as test signals) is provided, for which a behavioral model was synthesized in the form of a second-order nonlinear recursive filter.
Results. The aggregate signal of nonlinear distortions obtained using the presented method was found to be similar to that obtained by subtracting the responses to two different test signals. Further, the distortions caused by static amplitude nonlinearity, capacitive reactivity nonlinearity and energy recirculation between different reactive storages were distinguished. The nonlinearity of the amplitude characteristic exhibits its effect at the end of the transient process, the nonlinearity with the capacitive nature – at the beginning of the transient process, and the nonlinearity of energy recirculation – in the middle part of the transient process. It is shown that even parts of the nonlinear distortions at step impact, caused by individual physical nonlinearity factors, exceed the harmonic distortions of a RF-pulse signal.
Conclusion. The considered method is particularly useful when designing wideband devices with feedbacks, since the nonlinearity of energy recirculation takes effect long after the visual end of the transient process.

1. Brockbank R. A., Wass C. A. A. Non-Linear Distortion in Transmission Systems. J. of the Institution of Electrical Engineers. Part III: Radio and Communication Engineering. 1945, vol. 92, no. 17, pp. 45–56. doi: 10.1049/ji-3-2.1945.0011

2. Komuro T., Sobukawa S., Sakayori H., Kono M., Kobayashi H. Total Harmonic Distortion Measurement System of Electronic Devices Up to 100 MHz with Remarkable Sensitivity. IEEE Trans. On Instrumentation and Measurement. 2007, vol. 56, no. 6, pp. 2360–2368. doi: 10.1109/TIM.2007.904548

3. Figueiredo R., Carvalho N. B., Piacibello A., Camarchia V. Nonlinear Dynamic RF System Characterization: Envelope Intermodulation Distortion Profiles – A Noise Power Ratio-Based Approach. IEEE Trans. on Microwave Theory and Techniques. 2021, vol. 69, no. 9, pp. 4256–4271. doi: 10.1109/TMTT.2021.3092398

4. Farsi S., Draxler P., Gheidi H., Nauwelaers B. K. J. C., Asbeck P., Schreurs D. Characterization of Intermodulation and Memory Effects Using Offset Multisine Excitation. IEEE Trans. on Microwave Theory and Techniques. 2014, vol. 62, no. 3, pp. 645–657. doi: 10.1109/TMTT.2014.2302745

5. Lavrador P. M., Pedro J. C. Evaluation of Signal-To-Noise and Distortion Ratio Degradation in Nonlinear Systems. IEEE Trans. on Microwave Theory and Techniques. 2004, vol. 52, no. 3, pp. 813–822. doi: 10.1109/TMTT.2004.823543

6. Martins J. P., Carvalho N. B., Pedro J. C. Intermodulation Distortion of Third-Order Nonlinear Systems with Memory under Multisine Excitations. IEEE Trans. on Microwave Theory and Techniques. 2007, vol. 55, no. 6, pp. 1264–1271. doi: 10.1109/TMTT.2007.896794

7. Semyonov E. V., Semyonov A. V. Using the Difference Between Convolutions of Test Signals and Responses of an Object to Study the Nonlinearity of the Conversion of Ultra-Wideband Signals. J. of Communications Technology and Electronics. 2007, vol. 52, no. 4, pp. 480–485. (In Russ.)

8. Semyonov E., Loschilov A. Measurements of the Nonlinearity of the Ultra Wideband Signals Transformation. Ultra Wideband Communications: Novel Trends – System, Architecture And Implementation; ed. by M. Matin. Rijeka, Croatia, InTech, 2011, pp. 3–16. doi: 10.5772/16867

9. Ivanov I. F., Trofimov V. S. On a Unified Method for Measuring the Nonlinearity of Pulsed Devices. Radiotekhnika [Radio engineering]. 1963, vol. 18, no. 2, pp. 52–60. (In Russ.)

10. Arnstein D. S., Vuong X. T., Cotner C. B., Daryanani H. M. The IM Microscope: a New Approach to Nonlinear Analysis of Signals in Satellite Communications Systems. COMSAT Technical Review. 1992, vol. 22, no. 1, pp. 93–123. Available at: https://www.comsatlegacy.com/COMSAT%20Technical%20Review/CTR%20Spring%201992,%20INT-VI%20and%20Sig%20Process,%20V.22-1,.PDF (accessed 07.12.2021)

11. Haining W., Jiangang L., Jiqin W., Chenxin Z. Calculating Passive Intermodulation Products with IM Microscope Method. J. of Air Force Engineering University: Natural Science Edition. 2005, vol. 6, no. 3, pp. 47–49. Available at: http://kjgcdx.ijournal.cn/ch/reader/create_pdf.aspx?file_no=20050314 (accessed 07.12.2021)

12. 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

13. Pedro J. C., Carvalho N. B., Lavrador P. M. Modeling Nonlinear Behavior of Band-Pass Memoryless And Dynamic Systems. IEEE MTT-S Intern. Microwave Symp. Digest. Philadelphia, USA, 8–13 Jun. 2003, vol. 3, pp. 2133–2136. doi: 10.1109/MWSYM.2003.1210584

14. 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

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