Perturbation Based Modelling of Differential Amplifier Circuit

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.

Authors:

• Rahul Bansal
• Sudipta Majumdar

Keywords:

• Differential amplifier
• perturbation method
• Taylor series.

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.