Power Amplifier Linearization Techniques: An Overview

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1 Power Amplifier Linearization Techniques: An Overview Workshop on RF Circuits for 2.5G and 3G Wireless Systems February 4, 2001 Joel L. Dawson Ph.D. Candidate, Stanford University

2 List of Topics Motivation for using linearization Linearization as a theoretical problem Survey of commonly employed techniques

3 Linearity vs. Power Efficiency Power efficiency Battery lifetime Thermal management Linearity Sophisticated Modulation Techniques Spectral efficiency

4 PA Tradeoffs Power Efficiency => Switching PA s (class D, E, F) Linearity => Class A, AB, B, C.

5 Can nonlinear system theory help? Theory of time-invariant (or, stationary ) nonlinear systems is well-developed. Volterra series, Weiner systems, Hammerstein systems... Problem: Intensely formal, and usually lacks the conceptual clarity that leads to design insight.

6 Example: 3 rd order nonlinearity in a two-tone experiment The input tones: 2α cosω1t + 2β cosω2t α α β β jω t j t j t j t e 1 ω1 ω2 2, e, e, ω e Output sinusoids at: 3ω 1, 3ω 2, 2ω 1 -ω 2, 2ω 2 -ω 1, 2ω 1 +ω 2, 2ω 2 +ω 1 H 3 (s 1,s 2,s 3 ) An output product: α 2 j( 2ω ω )t 1 2 βh ( jω, jω, jω ) e

sinusoids at: 3ω 1, 3ω 2, 2ω 1 -ω 2, 2ω 2 -ω 1, 2ω 1 +ω 2, 2ω 2 +ω 1 H 3 (s

7 So where does the theory leave us? Odd order nonlinearities cause distortion products that are in-band. Outrageous behavior in the lab may imply that the device under test is not time-invariant.

8 Design implications: An important measure of the strength of a given linearization method is its robustness to poor characterization of the PA. Design, if possible, to force PA to behave as a benign nonlinear system (e.g., look for ways to preserve time-invariance).

9 Technique I: Power Backoff 2 Basic principle: V = = o ( x) a0 a1x a2x n= For small inputs, this term is dominant. 0 a n x n I BIAS RFC C B R L i S I BIAS >> i S Low efficiency

10 Power Backoff, cont. Output power (db) First-order output Higher-order IM term Input Power (db)

11 Corrective distortion: predistortion and/or postdistortion x F 1 ( ) H ( ) F 2 ( ) (Power amplifier) Most general problem: choose F 1 and F 2 such that F 2 (H(F 1 (x))) is a linear function of the input variable x.

12 Technique II: Predistortion Baseband Data F A ( ) PA LO Baseband Data F D ( ) PA LO

13 Key design issues for a predistorter: In analog case, how to realize the predistortion function. Initial calibration or training. Sensitive to drift.

14 Technique III: Adaptive Predistortion x(t) Predistorter PA - Σ e sym (t) e sys (t) e sym (t) System Estimator - Σ e sys (t) e sys (t)

15 Adaptive Predistortion: advantages Does not suffer the bandwidth limitation incurred by continuous-feedback techniques. Solves the problem of drift sensitivity.

16 Adaptive Predistortion: design issues New, discrete-time feedback stability problem associated with model estimation. Depends on having a good power amplifier model. Complexity: incurs power overhead of a DSP chip.

17 Technique IV: Feedforward Linearization Gain = A 0 V in PA delay #2 Σ V out 1/A 0 Perfectly linear delay #1 - Σ A 0

18 Feedforward: stable, but... Matching delay lines, amplifier gains not trivial. Susceptible to drift and aging. Low-loss delay lines, summations critical.

19 Technique V: Envelope Elimination and Restoration Envelope Detector V in Limiter PA Switching PA

20 EER design issues Phase matching between the two signal paths critical. Polar feedback a possibility. Restoring the envelope in a power-efficient way is very challenging.

21 Technique VI: LINC LInear amplification with Nonlinear Components PA 1 Signal Separator Switching PA s Σ PA 2 a ( 0 t)cos[ ω ct + φ( t)] = 0.5V 0 sin[ ωct + φ( t) + θ ( t)] 0.5V sin[ ωct + φ( t) + θ ( t)] θ ( t) = sin a( t 1 ) V 0 Constant-amplitude terms

22 LINC design issues Signal separation complicated, but possible. Good power combining with low loss and high isolation is the key barrier.

23 Technique VII: Cartesian Feedback I Q - Σ - Σ H(s) H(s) sinωt cosωt PA sinωt cosωt

24 Major design consideration in CFB sinωt systems: phase alignment PA cosωt sin(ωt+φ) L eff = H(s)cosφ + [H(s)sinφ]2 1+H(s)cosφ cos(ωt+φ)

25 CFB Strengths and Weaknesses W: Bandwidth limitation W: Stability concerns S: Low-complexity S: Highly resistant to drift and aging SS: Robust to poor characterization of PA

26 Summary Power Backoff: simplicity; low power efficiency. Predistortion: conceptually clear; requires good PA model. Adaptive Predistortion: No drift problem; introduces complexity. Feedforward: No stability worries; matching and drift concerns. EER: Possibly high-efficiency; adds another power amp problem. LINC: Conceptually appealing; fundamental implementation issues. CFB: simplicity, robust to poor PA model; stability concerns.

27 Copies of these slides... Available at the conclusion of ISSCC 2001.

The front end of the receiver performs the frequency translation, channel selection and amplification of the signal.

The front end of the receiver performs the frequency translation, channel selection and amplification of the signal. Many receivers must be capable of handling a very wide range of signal powers at the input while still producing the correct output. This must be done in the presence of noise and interference which occasionally