Perturbation Based Modelling of Differential Amplifier Circuit

Authors: Rahul Bansal, Sudipta Majumdar

Abstract:

This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316710

References:

[1] A. Townley, P. Swirhun, D. Titz, A. Bisognin, F. Gianesello, R. Pilard, A. M. Niknejad, ”A 94-GHz 4TX174RX Phased-Array FMCW Radar Transceiver With Antenna-in-Package,” IEEE Journal of Solid-State Circuits, vol. 52, no. 5, pp. 1245-1259 (2017).
[2] B. Yousefzadeh, S. H. Shalmany, K. A. Makinwa, ”A BJT-based temperature-to-digital converter with ±60mK (3σ) inaccuracy from −55oC to +125oC in 0.16−μm CMOS”, IEEE Journal of Solid-State Circuits, vol. 52, no. 4, pp. 1044-1052, 2017.
[3] B. Sadhu, Y. Tousi, J. Hallin, S. Sahl, S. K. Reynolds, O. Renstrom and G. Weibull, ”A 28-GHz 32-Element TRX Phased-Array IC With Concurrent Dual-Polarized Operation and Orthogonal Phase and Gain Control for 5G Communications”, IEEE Journal of Solid-State Circuits, vol. 52, no. 12, pp. 3373-3391, 2017.
[4] M. Wang, Y. Liu, Z. Li, X. Wang, M. M. Sarfraz, Y. Xiao and H. Zhang, ”A 6-bit 38 GHz SiGe BiCMOS phase shifter for 5G phased array communications”, IEICE Electronics Express, vol. 14, no. 13, pp. 1-10, 2017.
[5] A. Ushida and L. O. Chua, ”Frequency-domain analysis of nonlinear circuits driven by multi-tone signals”, IEEE Transactions on circuits and systems, vol. 31, no. 9, pp. 766-779, 1984.
[6] T. J. Aprille and T. N. Trick, ”Steady-state analysis of nonlinear circuits with periodic inputs”, Proceedings of the IEEE, vol. 60, no. 1, pp. 108-114, 1972.
[7] K. Mayaram, D. C. Lee, S. Moinian, D. A. Rich and J. Roychowdhury, ”Computer-aided circuit analysis tools for RFIC simulation: algorithms, features, and limitations”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 47, no. 4, pp. 274-286, 2000.
[8] S. M. Lee, N. Kim, D. Kong and D. Seo, ”A DAC With an Impedance Attenuator and Distortion Analysis Using Volterra Series”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 25, no. 10, pp. 2929-2938, 2017.
[9] R. N. Braithwaite, ”Digital Predistortion of an RF Power Amplifier Using a Reduced Volterra Series Model With a Memory Polynomial Estimator”, IEEE Transactions on Microwave Theory and Techniques, vol. 65, no. 10, pp. 3613-3623 2017.
[10] B. Song, S. He, J. Peng and Y. Zhao, ”Dynamic deviation memory polynomial model for digital predistortion”, Electronics Letters, vol. 53, no. 9, pp. 606-607, 2017.
[11] X. Wu, F. Grassi, P. Manfredi and D. V. Ginste, Perturbative Analysis of Differential-to-Common Mode Conversion in Asymmetric Nonuniform Interconnects”, IEEE Transactions on Electromagnetic Compatibility, vol. 60, no. 1, pp. 7-15, 2018.
[12] S. Afifi and R. Dusseaux, ”Scattering From 2-D Perfect Electromagnetic Conductor Rough Surface: Analysis With the Small Perturbation Method and the Small-Slope Approximation”, IEEE Transactions on Antennas and Propagation, vol. 66, no. 1, pp. 340-346, 2018.
[13] S. Mishra and R. D. S. Yadava, ”A Method for Chaotic Self-Modulation in Nonlinear Colpitts Oscillator and its Potential Applications”, Circuits, Systems, and Signal Processing, pp. 1-21, 2017.
[14] W. Q. Liu, X. M. Wang and Z. L. Deng, ”Robust centralized and weighted measurement fusion Kalman predictors with multiplicative noises, uncertain noise variances, and missing measurements” Circuits, Systems, and Signal Processing, pp. 1-40, 2017.
[15] M. V. Thuan and D. C. Huong, ”New Results on Exponential Stability and Passivity Analysis of Delayed Switched Systems with Nonlinear Perturbations”, Circuits, Systems, and Signal Processing, pp. 1-24, 2017.
[16] A. Buonomo and A. L. Schiavo, ”Predicting nonlinear distortion in multistage amplifiers and gm-C filters”, Analog Integrated Circuits and Signal Processing, vol. 77, no. 3, pp. 483-493, 2013.
[17] H. Wang, M. Qi and B. Wang, ”PPV modeling of memristor-based oscillators and application to ONN pattern recognition”, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 6, pp. 610-614 2017.
[18] W. Wang, S. K. Nguang, S. Zhong and F. Liu, ”New delay-dependent stability criteria for uncertain neutral system with time-varying delays and nonlinear perturbations”, Circuits, Systems, and Signal Processing, vol. 33, no. 9, pp. 2719-2740, 2014.
[19] S. Lakshmanan, J. H. Park and H. Y. Jung, ”Robust delay-dependent stability criteria for dynamic systems with nonlinear perturbations and leakage delay”, Circuits, systems, and signal processing, vol. 32, no. 4, pp. 1637-1657, 2013.
[20] A. Rathee and H. Parthasarathy, ”Perturbation-based stochastic modeling of nonlinear circuits”. Circuits, Systems, and Signal Processing, vol. 32, no. 1, pp. 123-141, 2013.
[21] A. Rathee and H. Parthasarathy, ”Perturbation-Based Fourier Series Analysis of Transistor Amplifier”, Circuits, Systems, and Signal Processing, vol. 31, no. 1, pp. 313-328, 2012.