Estimation of Intermodulation Rejection Value as a Function of Frequency in Power Amplifier Using AM-AM and AM-PM Diagrams Based on Power Series Analysis

Affiliation(s)

Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran.

Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran.

ABSTRACT

A method to predict intermodulation (IM) products of two tone test based on Amplitude to amplitude (AM-AM) and amplitude to phase (AM-PM) diagrams of power amplifier is proposed in this paper. An RF power amplifier is mathe-matically modeled by a power series in order of 13. Coefficients of the transfer function are obtained by odd-order polynomial fitting of the transfer function of the power amplifier that is modeled by power series, with AM-AM and AM-PM diagrams. Because of considering AM-PM distortion, coefficients have become complex. By using this transfer function, analytical expressions of IM products are derived. Frequency effect of IM products are modeled in suggested method to estimate the effects of changing in input frequency on output. With the mean of this factor the model is able to predict IM products of wideband frequency input. Simulated results agree well with the predicted method in comparisons.

A method to predict intermodulation (IM) products of two tone test based on Amplitude to amplitude (AM-AM) and amplitude to phase (AM-PM) diagrams of power amplifier is proposed in this paper. An RF power amplifier is mathe-matically modeled by a power series in order of 13. Coefficients of the transfer function are obtained by odd-order polynomial fitting of the transfer function of the power amplifier that is modeled by power series, with AM-AM and AM-PM diagrams. Because of considering AM-PM distortion, coefficients have become complex. By using this transfer function, analytical expressions of IM products are derived. Frequency effect of IM products are modeled in suggested method to estimate the effects of changing in input frequency on output. With the mean of this factor the model is able to predict IM products of wideband frequency input. Simulated results agree well with the predicted method in comparisons.

KEYWORDS

Intermodulation Product; Two Tone Test; RF Power Amplifier; Power Series; AM-AM and AM-PM Diagrams

Intermodulation Product; Two Tone Test; RF Power Amplifier; Power Series; AM-AM and AM-PM Diagrams

Cite this paper

A. Kashi, M. Kamarei and M. Javadi, "Estimation of Intermodulation Rejection Value as a Function of Frequency in Power Amplifier Using AM-AM and AM-PM Diagrams Based on Power Series Analysis,"*Circuits and Systems*, Vol. 3 No. 3, 2012, pp. 282-287. doi: 10.4236/cs.2012.33039.

A. Kashi, M. Kamarei and M. Javadi, "Estimation of Intermodulation Rejection Value as a Function of Frequency in Power Amplifier Using AM-AM and AM-PM Diagrams Based on Power Series Analysis,"

References

[1] R. Raich, H. Qian and G. T. Zhou, “Orthogonal Polynomials for Power Amplifier Modeling and Predistorter Design,” IEEE Transactions on Vehicular Technology, Vol. 53, No. 5, 2004, pp. 1468-1479. doi:10.1109/TVT.2004.832415

[2] B. Larkin, “Multiple-Signal Intermodulation and Stability Consideration in the Use of Linear Repeaters,” Proceeding of 41st IEEE Vehicular Technology, St. Louis, 19-22 May 1991, pp. 747-752.

[3] Q. Wu, M. Testa and R. Larkin, “Linear RF Power Amplifier Design for CDMA Signal,” IEEE MIT-S Digest, Corvallis, June 1996, pp. 851-854.

[4] G. T. Zhou and J. S. Kenney, “Predicting Spectral Regrowth of Nonlinear Power Amplifiers,” IEEE Transactions on Communications, Vol. 50, No. 5, 2002, pp. 718-722. doi:10.1109/TCOMM.2002.1006553

[5] C. H. Tseng, “Estimation of Cubic Nonlinear Bandpass Channels in Orthogonal Frequency-Division Multiplexing Systems,” IEEE Transaction on Communications, Vol. 58, No. 5, 2010, pp. 1415-1425. doi:10.1109/TCOMM.2010.05.080573

[6] M. E. Gadringer, C. Schuberth and G. Magerl “Behavioral Modeling of the Frequency Translation Process in Direct Conversion Transmitters,” International Journal of RF and Microwave Computer-Aided Engineering, Vol. 20, No. 3, 2010, pp. 347-359. doi:10.1002/mmce.20439

[7] S. J. Yi, S. Nam, S. H. Oh and J. H. Han, “Prediction of a CDMA Output Spectrum Based on Intermodulation Products of Two-Tone Test,” IEEE Transaction on Microwave Theory and Techniques, Vol. 49, No. 5, 2001, pp. 767-946. doi:10.1109/22.920152

[8] A. H. Coskun and S. Demir, “A Mathematical Characterization and Analysis of a Feedforward Circuit for CDMA Applications,” IEEE Transaction on Microwave Theory and Techniques, Vol. 51, No. 3, 2003, pp. 767777. doi:10.1109/TMTT.2003.808582

[9] C. Liu, H. Xiao, Q. Wu and F. Lit, “Linear RF Power Amplifier Design for Wireless Signals: A Spectrum Analysis Approach,” International Conference on Acoustics, Speech, and Signal Processing, Vol. 4, 2003, pp. 568-571.

[10] A. M. A. Hemmatyar and F. Farzaneh, “Predicting of InterModulation Rejection Values for the First and Second Adjacent Channels in Feed-Forward Linearised Microwave Amplifiers Using Closed-Form Expressions,” IET Microwaves Antennas & Propagation, Vol. 1, No. 3, 2007, pp. 782-789. doi:10.1049/iet-map:20060342

[11] M. L. Ku, S. H. Lu, L. C. Wang and S. H. Yan, “Nonlinear Effect of Receiver Amplifier for 60 GHz Radio Communication,” IEEE International Conference on Vehicular Technology, 5-8 September 2011, pp. 1-5. doi:10.1109/VETECF.2011.6093112

[12] K. G. Gard, H. M. Gutierrez and M. B. Steer, “Characterization of Spectral Regrowth in Microwave Amplifiers Based on the Nonlinear Transformation of a Complex Gaussian Process,” IEEE Transaction on Microwave Theory and Techniques, Vol. 47, No. 7, 1999, pp. 1059-1069. doi:10.1109/22.775437

[13] G. T. Zhou, “Analysis of Spectral Regrowth of Weakly Nonlinear Power Amplifiers,” IEEE Communication Letters, Vol. 4, No. 11, 2000, pp. 357-359.

[14] C. Liu, H. Xiao, Q. Wu and F. Li, “Linear RF Power Amplifier Design for TDMA Signals: A Spectrum Analysis Approach,” Proceedings of International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, Vol. 4, May 2001, pp. 2665-2668. doi:10.1109/ICASSP.2001.940550

[15] M. M. Rahmati, A. Abdipour, A. Mohammadi and G. Moradi, “An Analytic Approach for CDMA Output of Feed forward Power Amplifier,” Analog Integrated Circuit and Signal Processing, Vol. 66, No. 3, 2011, pp. 349-361.

[16] E. Cottais, Y. Wang and S. Toutain, “Spectral Regrowth at the Output of a Memoryless Power Amplifier with Multicarrier Signals,” IEEE Transactions on Communications, Vol. 56, No. 7, 2008, pp. 1111-1118. doi:10.1109/TCOMM.2008.050149

[17] J. P. Aikio and T. Rahkonen, “A Comprehensive Analysis of AM-AM and AM-PM Conversion in an LDMOS RF Power Amplifier,” IEEE Transactions on Microwave Theory and Techniques, Vol. 57, No. 2, 2009, pp. 262-270. doi:10.1109/TMTT.2008.2011161

[18] S. Meza, M. O’Droma, Y. Lei and A. Goacher, “Some New Memorylessbehavioral Models of Wireless Transmitter Solid State Power Amplifiers,” IEEE Automation, Quality and Testing, Robotics, Vol. 1, 2008, pp. 96-98. doi:10.1109/AQTR.2008.4588714

[19] M. Masood, J. Staudinger, J. Wood, M. Bokatius and J. S. Kenney, “Linearity Considerations for a High Power Doherty Amplifier,” IEEE International Conference on Power Amplifier for Wireless and Radio Applications, Atlanta, 15-18 January 2012, pp. 77-80. doi:10.1109/PAWR.2012.6174912

[20] L. W. Couch, “Digital and Analog Communication Systems,” Prentice-Hall Inc., Upper Saddle River, 1996.

[21] T. S. Rappaport, “Wireless Communication Principle and Practice,” Prentice-Hall Inc., Upper Saddle River, 1996.

[22] M. C. Jeruchim, P. Balabon and K. S. Shanmugan, “Simulation of Communication Systems,” Kluwer Academic Publishers, Springer, New York, 2002.

[23] A. Chatterjee, S. Devarakond and S. Sen, “Phase Distortion to Amplitude Conversion-Based Low-Cost Measurement of AM-AM and AM-PM Effects in RF Power Amplifiers,” IEEE Transaction on Very Large Scale Integration (VLSI) Systems, Vol. PP, Issue 99, 2011, pp. 1-13. doi:10.1109/TVLSI.2011.2160376

[1] R. Raich, H. Qian and G. T. Zhou, “Orthogonal Polynomials for Power Amplifier Modeling and Predistorter Design,” IEEE Transactions on Vehicular Technology, Vol. 53, No. 5, 2004, pp. 1468-1479. doi:10.1109/TVT.2004.832415

[2] B. Larkin, “Multiple-Signal Intermodulation and Stability Consideration in the Use of Linear Repeaters,” Proceeding of 41st IEEE Vehicular Technology, St. Louis, 19-22 May 1991, pp. 747-752.

[3] Q. Wu, M. Testa and R. Larkin, “Linear RF Power Amplifier Design for CDMA Signal,” IEEE MIT-S Digest, Corvallis, June 1996, pp. 851-854.

[4] G. T. Zhou and J. S. Kenney, “Predicting Spectral Regrowth of Nonlinear Power Amplifiers,” IEEE Transactions on Communications, Vol. 50, No. 5, 2002, pp. 718-722. doi:10.1109/TCOMM.2002.1006553

[5] C. H. Tseng, “Estimation of Cubic Nonlinear Bandpass Channels in Orthogonal Frequency-Division Multiplexing Systems,” IEEE Transaction on Communications, Vol. 58, No. 5, 2010, pp. 1415-1425. doi:10.1109/TCOMM.2010.05.080573

[6] M. E. Gadringer, C. Schuberth and G. Magerl “Behavioral Modeling of the Frequency Translation Process in Direct Conversion Transmitters,” International Journal of RF and Microwave Computer-Aided Engineering, Vol. 20, No. 3, 2010, pp. 347-359. doi:10.1002/mmce.20439

[7] S. J. Yi, S. Nam, S. H. Oh and J. H. Han, “Prediction of a CDMA Output Spectrum Based on Intermodulation Products of Two-Tone Test,” IEEE Transaction on Microwave Theory and Techniques, Vol. 49, No. 5, 2001, pp. 767-946. doi:10.1109/22.920152

[8] A. H. Coskun and S. Demir, “A Mathematical Characterization and Analysis of a Feedforward Circuit for CDMA Applications,” IEEE Transaction on Microwave Theory and Techniques, Vol. 51, No. 3, 2003, pp. 767777. doi:10.1109/TMTT.2003.808582

[9] C. Liu, H. Xiao, Q. Wu and F. Lit, “Linear RF Power Amplifier Design for Wireless Signals: A Spectrum Analysis Approach,” International Conference on Acoustics, Speech, and Signal Processing, Vol. 4, 2003, pp. 568-571.

[10] A. M. A. Hemmatyar and F. Farzaneh, “Predicting of InterModulation Rejection Values for the First and Second Adjacent Channels in Feed-Forward Linearised Microwave Amplifiers Using Closed-Form Expressions,” IET Microwaves Antennas & Propagation, Vol. 1, No. 3, 2007, pp. 782-789. doi:10.1049/iet-map:20060342

[11] M. L. Ku, S. H. Lu, L. C. Wang and S. H. Yan, “Nonlinear Effect of Receiver Amplifier for 60 GHz Radio Communication,” IEEE International Conference on Vehicular Technology, 5-8 September 2011, pp. 1-5. doi:10.1109/VETECF.2011.6093112

[12] K. G. Gard, H. M. Gutierrez and M. B. Steer, “Characterization of Spectral Regrowth in Microwave Amplifiers Based on the Nonlinear Transformation of a Complex Gaussian Process,” IEEE Transaction on Microwave Theory and Techniques, Vol. 47, No. 7, 1999, pp. 1059-1069. doi:10.1109/22.775437

[13] G. T. Zhou, “Analysis of Spectral Regrowth of Weakly Nonlinear Power Amplifiers,” IEEE Communication Letters, Vol. 4, No. 11, 2000, pp. 357-359.

[14] C. Liu, H. Xiao, Q. Wu and F. Li, “Linear RF Power Amplifier Design for TDMA Signals: A Spectrum Analysis Approach,” Proceedings of International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, Vol. 4, May 2001, pp. 2665-2668. doi:10.1109/ICASSP.2001.940550

[15] M. M. Rahmati, A. Abdipour, A. Mohammadi and G. Moradi, “An Analytic Approach for CDMA Output of Feed forward Power Amplifier,” Analog Integrated Circuit and Signal Processing, Vol. 66, No. 3, 2011, pp. 349-361.

[16] E. Cottais, Y. Wang and S. Toutain, “Spectral Regrowth at the Output of a Memoryless Power Amplifier with Multicarrier Signals,” IEEE Transactions on Communications, Vol. 56, No. 7, 2008, pp. 1111-1118. doi:10.1109/TCOMM.2008.050149

[17] J. P. Aikio and T. Rahkonen, “A Comprehensive Analysis of AM-AM and AM-PM Conversion in an LDMOS RF Power Amplifier,” IEEE Transactions on Microwave Theory and Techniques, Vol. 57, No. 2, 2009, pp. 262-270. doi:10.1109/TMTT.2008.2011161

[18] S. Meza, M. O’Droma, Y. Lei and A. Goacher, “Some New Memorylessbehavioral Models of Wireless Transmitter Solid State Power Amplifiers,” IEEE Automation, Quality and Testing, Robotics, Vol. 1, 2008, pp. 96-98. doi:10.1109/AQTR.2008.4588714

[19] M. Masood, J. Staudinger, J. Wood, M. Bokatius and J. S. Kenney, “Linearity Considerations for a High Power Doherty Amplifier,” IEEE International Conference on Power Amplifier for Wireless and Radio Applications, Atlanta, 15-18 January 2012, pp. 77-80. doi:10.1109/PAWR.2012.6174912

[20] L. W. Couch, “Digital and Analog Communication Systems,” Prentice-Hall Inc., Upper Saddle River, 1996.

[21] T. S. Rappaport, “Wireless Communication Principle and Practice,” Prentice-Hall Inc., Upper Saddle River, 1996.

[22] M. C. Jeruchim, P. Balabon and K. S. Shanmugan, “Simulation of Communication Systems,” Kluwer Academic Publishers, Springer, New York, 2002.

[23] A. Chatterjee, S. Devarakond and S. Sen, “Phase Distortion to Amplitude Conversion-Based Low-Cost Measurement of AM-AM and AM-PM Effects in RF Power Amplifiers,” IEEE Transaction on Very Large Scale Integration (VLSI) Systems, Vol. PP, Issue 99, 2011, pp. 1-13. doi:10.1109/TVLSI.2011.2160376