A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA

A comparative analysis of behavioral models for RF power amplifiers

Preface. About the Authors. Acknowledgments. 1 Power Amplifier Fundamentals. 1.1 Introduction. 1.2 Definition of Power Amplifier Parameters. 1.3 Distortion Parameters. 1.4 Power Match Condition. 1.5 Class of Operation. 1.6 Overview of Semiconductors for PAs. 1.7 Devices for PA. 1.8 Appendix: Demonstration of Useful Relationships. 1.9 References. 2 Power Amplifier Design. 2.1 Introduction. 2.2 Design Flow. 2.3 Simplified Approaches. 2.4 The Tuned Load Amplifier. 2.5 Sample Design of a Tuned Load PA. 2.6 References. 3 Nonlinear Analysis for Power Amplifiers. 3.1 Introduction. 3.2 Linear vs. Nonlinear Circuits. 3.3 Time Domain Integration. 3.4 Example. 3.5 Solution by Series Expansion. 3.6 The Volterra Series. 3.7 The Fourier Series. 3.8 The Harmonic Balance. 3.9 Envelope Analysis. 3.10 Spectral Balance. 3.11 Large Signal Stability Issue. 3.12 References. 4 Load Pull. 4.1 Introduction. 4.2 Passive Source/Load Pull Measurement Systems. 4.3 Active Source/Load Pull Measurement Systems. 4.4 Measurement Test-sets. 4.5 Advanced Load Pull Measurements. 4.6 Source/Load Pull Characterization. 4.7 Determination of Optimum Load Condition. 4.8 Appendix: Construction of Simplified Load Pull Contours through Linear Simulations. 4.9 References. 5 High Efficiency PA Design Theory. 5.1 Introduction. 5.2 Power Balance in a PA. 5.3 Ideal Approaches. 5.4 High Frequency Harmonic Tuning Approaches. 5.5 High Frequency Third Harmonic Tuned (Class F). 5.6 High Frequency Second Harmonic Tuned. 5.7 High Frequency Second and Third Harmonic Tuned. 5.8 Design by Harmonic Tuning. 5.9 Final Remarks. 5.10 References. 6 Switched Amplifiers. 6.1 Introduction. 6.2 The Ideal Class E Amplifier. 6.3 Class E Behavioural Analysis. 6.4 Low Frequency Class E Amplifier Design. 6.5 Class E Amplifier Design with 50# Duty-cycle. 6.6 Examples of High Frequency Class E Amplifiers. 6.7 Class E vs. Harmonic Tuned. 6.8 Class E Final Remarks. 6.9 Appendix: Demonstration of Useful Relationships. 6.10 References. 7 High Frequency Class F Power Amplifiers. 7.1 Introduction. 7.2 Class F Description Based on Voltage Wave-shaping. 7.3 High Frequency Class F Amplifiers. 7.4 Bias Level Selection. 7.5 Class F Output Matching Network Design. 7.6 Class F Design Examples. 7.7 References. 8 High Frequency Harmonic Tuned Power Amplifiers. 8.1 Introduction. 8.2 Theory of Harmonic Tuned PA Design. 8.3 Input Device Nonlinear Phenomena: Theoretical Analysis. 8.4 Input Device Nonlinear Phenomena: Experimental Results. 8.5 Output Device Nonlinear Phenomena. 8.6 Design of a Second HT Power Amplifier. 8.7 Design of a Second and Third HT Power Amplifier. 8.8 Example of 2nd HT GaN PA. 8.9 Final Remarks. 8.10 References. 9 High Linearity in Efficient Power Amplifiers. 9.1 Introduction. 9.2 Systems Classification. 9.3 Linearity Issue. 9.4 Bias Point Influence on IMD. 9.5 Harmonic Loading Effects on IMD. 9.6 Appendix: Volterra Analysis Example. 9.7 References. 10 Power Combining. 10.1 Introduction. 10.2 Device Scaling Properties. 10.3 Power Budget. 10.4 Power Combiner Classification. 10.5 The T-junction Power Divider. 10.6 Wilkinson Combiner. 10.7 The Quadrature (90 ) Hybrid. 10.8 The 180 Hybrid (Ring Coupler or Rat-race). 10.9 Bus-bar Combiner. 10.10 Other Planar Combiners. 10.11 Corporate Combiners. 10.12 Resonating Planar Combiners. 10.13 Graceful Degradation. 10.14 Matching Properties of Combined PAs. 10.15 Unbalance Issue in Hybrid Combiners. 10.16 Appendix: Basic Properties of Three-port Networks. 10.17 References. 11 The Doherty Power Amplifier. 11.1 Introduction. 11.2 Doherty's Idea. 11.3 The Classical Doherty Configuration. 11.4 The 'AB-C' Doherty Amplifier Analysis. 11.5 Power Splitter Sizing. 11.6 Evaluation of the Gain in a Doherty Amplifier. 11.7 Design Example. 11.8 Advanced Solutions. 11.9 References. Index.

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High Efficiency RF and Microwave Solid State Power Amplifiers

This paper proposes a new behavioral model to treat memory effects in nonlinear power amplifiers (PAs) Phenomena such as asymmetries in lower and upper intermodulation terms, and variation of AM/AM and AM/PM, depending on signal history, are often observed in high-power PAs To treat these phenomena, this paper presents a model based on the previously developed memory polynomial model The contribution made in this paper is to augment the memory polynomial model to include a sparse delay tap structure that reduces the parameter space required for accurate model identification A figure-of-merit, called the memory effect ratio, is defined to quantify the relative level of distortion due to memory effects, as compared to the memoryless portion Another figure-of-merit is defined as the memory effect modeling ratio, which quantifies the degree to which the PA memory effects have been accounted for in the model This new technique is validated using a variety of RF PAs, including an 880-MHz and a 21-GHz high-power laterally diffused metal-oxide semiconductor PA and various signals such as two-tone, eight-tone, and IS-95B signals

Behavioral modeling of nonlinear RF power amplifiers considering memory effects

The polynomial model is commonly used in power amplifier (PA) modeling and predistorter design. However, the conventional polynomial model exhibits numerical instabilities when higher order terms are included. In this paper, we introduce a novel set of orthogonal polynomials, which can be used for PA as well as predistorter modeling. Theoretically, the conventional and orthogonal polynomial models are "equivalent" and, thus, should behave similarly. In practice, however, the two approaches can perform quite differently in the presence of finite precision processing. Simulation results show that the orthogonal polynomials can alleviate the numerical instability problem associated with the conventional polynomials and generally yield better PA modeling accuracy as well as predistortion linearization performance.

Orthogonal polynomials for power amplifier modeling and predistorter design

In this paper, we propose an efficient open-loop digital predistorter (DPD) derived from the dynamic deviation reduction-based Volterra series that allows compensation for both nonlinear distortion and memory effects induced by RF power amplifiers in wireless transmitters. In this approach, the parameters of the predistorter can be directly extracted from an offline system identification process. This eliminates the usual requirement for a closed-loop real-time parameter adaptation, which dramatically reduces the implementation complexity of the system. It is shown that a further reduction in system complexity can be achieved by applying under-sampling theory in the model extraction and utilizing parameter interpolation in the DPD implementation. Experimental results show that by utilizing this technique with only a small number of parameters, nonlinear distortion induced by the PA can be significantly reduced, as evaluated by both adjacent channel power ratio reduction and normalized root mean square error improvement. A comparison with a memoryless polynomial function based predistorter and an analysis of the impact of decresting are also presented.

Open-Loop Digital Predistorter for RF Power Amplifiers Using Dynamic Deviation Reduction-Based Volterra Series

RF power amplifier modes Doherty and Chireix - themes and variations topics in PA non-linearity envelope feedback predistortion feedforward microwave-power amplifier design.

Steve C. Cripps

Papers

Advanced Techniques in RF Power Amplifier Design