Behavioral Modeling for Polar TransmittersJ. Stevenson Kenney

School of Electrical and Computer EngineeringGeorgia Institute of Technology

jskenney@ece .gatech.edu

I. Behavioral Modeling and Predistortion LinearizationBehavioral modeling of RF power amplifiers (PAs) has been studied for several decades, oftenwith the objective of determining inverse relations for use in correcting their distortion. Theearliest models were two-terminal "black boxes" that conveyed only input-output (unilateral)transfer function information. Such models were only of use for memoryless PAs whereby thegain compression (AM-AM distortion) and phase deviation (AM-PM distortion) could becorrected by suitable inverse functions using predistortion (pre-D) linearizers, as shown in Figure1. As adjacent channel power ratio (ACPR) and error vector magnitude (EVM) specifications forhigh data rate digital modulation formats placed more stringent requirements on linearizers, itbecame necessary to model PA memory effects. These more advanced models did account forRF frequency response, as well as long-term memory effects (i.e. thermal and bias relatedeffects) , but they were still just complicated transfer functions that necessarily included delayedversions of the input signal [1]. Using digital signal processing (DSP), such effects could becompensated for, often realized using high-speed FPGA-based look-up tables (LUTs) withadaptive feedback to update the table entries. A representative block diagram of an adaptivedigital pre-D system is shown in Figure 2. Figure 3 shows a memory compensating LUT with theassociated improvement in ACPR performance. It is clear that the complexity, both in hardwareand LUT updating algorithms, is increased dramatically over the memoryless case shown inFigure 1. While such architectures are within the cost (~$l 00) and power (~5W) budgets for basestation application, the use of such systems in mobile applications is often precluded.

Vi(t)~ f(·)

f = pre-D functionfi = LUT valuesg = gain functionx = input valuesXi = LUT indexes

Figure 1: Memoryless pre-D linearization using look-up tables.

In addition to cost and power consumption, another factor to consider for linearization of mobiletransmitters is the effect of load terminations. In base station applications that employed multiplegain stages and isolators on the PA output, the unilateral assumption was often justified.However, in mobile applications, it became necessary to compensate for load variations in somemanner. The advent of Agilent's P2D models was a large improvement in this respect [2]. Theability to simulate load impedance variations in simulation based on measured results allowedthe designer to compensate for such effects, at least within the realm of RF circuit design .

978-1-4244-4565-3/09 / $25.00 ©2009 IEEE

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Figure 3: Memory polynomial pre-D architecture and measured improvement of a 30W(PEP) LDMOS pes band PA.

However, P2D models do not provide much insight for the systems designer in developingarchitectures for pre-D linearizers. Nor do they provide much insight into what is causing thememory effects in the first place. Hence, the design of linearized PAs for mobile applicationsremains rather limited.

II. Digital Polar TransmittersIn parallel with the development of pre-D linearized PAs, polar transmitter architectures werebeing developed to improve PA efficiency for more demanding battery-powered mobileapplications. Digital polar transmitters have been developed that incorporate pre-D linearizationwith memory effect compensation to circumvent the effects of RF frequency response, as well asbias related effects [3]. Figure 4 shows a digital polar transmitter that uses memory effectcompensation and pre-D to achieve high efficiency in back-off, while maintaining adequateACPR performance.

Envelope Path

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Figure 4: Digital Polar Transmitter and measured ACPR suppression

For mobile applications adaptive feedback does provide some protection against slowly changingload variations, such as antenna loading. However, it does not account for instantaneous effects,such as harmonic reflection at high peak power levels. For this reason, we began investigatingfull three-port behavioral models that not only account for input-output nonlinearities andmemory effects, but also modulating terminal transfer functions and frequency response, as wellas harmonic termination effects related to memory effects in polar transmitter architectures. In[4], we reported that certain harmonic terminations reduced the phase rotation of the complexsidebands, which must be treated as a baseband memory effect. It was found through furtherresearch that reducing the 2nd harmonic level of the modulated RF carrier reduced such effectswhich often arise from mixing with the fundamental at the PA input. In this way, the modulation

transfer function may be treated as memoryless, and compensated accordingly using simple pre­D models and look-up tables, and thus greatly reducing complexity and DSP power consumption.Further studies that we have conducted indicate that push-pull PA architectures have similarharmonic suppression qualities so that memory effect reduction may be achieved without this useof stubs or other bulky components at the output of the PA. This effect has been found to beindependent of technology, proving effective on both GaAS HBT and GaAs HFET PAs .

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Pout [dB] Tone Spacil'9 [Hz]

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190

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10' 170

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(a) Single-ended GaAs HBT PA (b) Push-pull GaAs HBT PA

Figure 5: Harmonic termination effect in suppressing sideband rotation

III. Summary and Future WorkIn this paper, we have shown that behavioral modeling is an important tool for not onlypredicting PA distortion performance, but is also indispensable for correcting such signaldegradation in the transmit path. Digital pre-D has proven to be an effective means to suppressACPR in base station applications, but is too costly and complex for mobile applications. MobilePA architectures are increasing utilizing polar transmitter architectures to improve efficiency fordigitally modulated signals. We have shown that the combination of polar architecturescombined with digital pre-D allows high efficiency operation while still achieving adequatedistortion performance. Future work will include development of multiple-input/mulitiple output(MIMO) transmitters for use in mobile platforms.

AcknowledgmentsWe wish to thank RF Microdevices and Cree for donations of power amplifiers referenced in thispaper. We also wish to think Agilent Technologies and Texas Instruments for their donations andhelpful advice during the course of this work.

[1] H. Ku, M. D. McKinley, and 1. S. Kenney, "Quantifying Memory Effects in RF Power Amplifiers," IEEE Trans.Microwave Theory and Tech., Vol. 50, No. 12, pp. 2843-49, Dec. 2002"

[2] 1. Liu, L. P. Dunleavy, and H. Arslan, "Large Signal Behavioral Modeling of Nonlinear Amplifiers Based onLoadpull AM-AM and AM-PM Measurements," IEEE Transactions on Microwave Theory & Techniques, Vol.54, No.8, August 2006, pp. 3191-96.

[3] 1. H. Chen , P. Fedorencko, and 1. S. Kenney, "A Low Voltage W-CDMA Polar Transmitter with DigitalEnvelope Path Gain Comp ensation," IEEE Microwave and Wireless Lett., Vol. 16, No.7, pp. 428-30, July,2006.

[4] 1. S. Kenney and P. Fedorenko, "Identification of RF Power Amplifier Memory Effect Origins using Third­Order Intermodulation Distortion Amplitude and Phase Asymmetry," 2006 IEEE MTT-S Int. Microwave Symp.Dig., June 13-18, 2006, San Francisco, CA.