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    Digital Pre-Distortion Techniques for RF Power Amplifiers John Wood

    27 January, 2010

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    It doesn’t matter what the raw linearity of the PA looks like, the DPD will take care of it!

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    Outline

    • Modern Communication s Signals and RFPAsSignals, Linearity, and Efficiency

    • Some Linearizer BasicsWhat’s nonlinearity?What are memory effects?What does a linearizer do?

    • Digital Pre-Distortion DPDSystem ArchitectureLinearization Results

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    Linearity Requirements

    • Wireless Communications Standards place stringent requirements on linearity performance of PAs

    -5 -4 -3 -2 -1 0 1 2 3 4 5-80

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    10CDMA2000 Signal with MASK

    Normalized Frequency (MHz)

    Nor

    mal

    ized

    Pow

    er (d

    B)

    -45dBc (30kHz)

    -55dBc (30kHz)

    ACLR1 – Adjacent Channel Power RatioACLR2 – Alternate Channel Power RatioSpectral Emission Mask –an absolute power limit

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    Crest Factor and Peak-to-Average Power Ratio

    • Crest Factor

    • Peak-to-Average Ratio

    • PAR usually expressed in dB as

    10*log10( PAR )

    CF = Peak Magnitude

    Sqrt( Average Power )

    PAR = CF2 = Peak PowerAverage Power

    0 50 100 150 200 250 300 350 400 450 5000

    0.5

    1

    1.5

    2

    2.5Sample Signal Envelope

    Mag

    nitu

    de

    Samples

    Average Magnitude

    Peak Magnitude

    WCDMA Signal

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    Amplifier PAR Effects• Peaks will be clipped even

    with ideal amplifier if input exceeds Pin,max

    • With enough clipping it appears as Gaussian noise to the receiver

    • Effects of clipping:In-band distortion

    – Degradation of BER– Higher EVM

    Out of Band Radiation – ACI problems – ACLR degradation

    Pout

    Pin

    OBO

    IBO

    Pin,max

    Pout,max

    G

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    Measuring PAR• Finding absolute max of a data signal is difficult!!• PAR easier to determine if statistically defined.

    • Create a probability density function of signal with histogram

    -4 -3 -2 -1 0 1 2 30

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800Histogram of Real (Inphase ) Data

    0 0.5 1 1.5 2 2.5 3 3.50

    200

    400

    600

    800

    1000

    1200

    1400Histogram of Magnitude Data

    I and Q parts of signal are Gaussian Magnitude considered Rayleigh

    WCDMA Signal Test Model 1: 64 DPCH ( SF = 128 ), No CFR

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    Cumulative Complementary Distribution Function

    CCDF• This is a statistical measure for digital signals

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    CCDF – Statistical Measure of PAR

    0 1 2 3 4 5 6 7 8 9 10

    0.01

    0.1

    1

    10

    100

    Peak Power (dB)

    CCDF - Normalized to AVG Pwr

    Pro

    b (%

    )

    0.01% PAR value means that the 99.99% of the signal has a magnitude lower than this PAR value (9dB in this case)

    From histogram of data CCDF can be derived

    CCDF shows the probability that a signal will exceed the peak power

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    What does this mean for the PA?

    • We want to operate the PA at highest efficiency

    • This point is at peak output power

    • We need to ensure the signal peak is no higher than P-1dB

    • For high PAR signals the average efficiency is extremely low

    Cripps, RFPA, Ch. 8, p. 225, Figure 8.3

    P-1dB

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    High-Efficiency PA Modes

    • Circuit architectures to maximize efficiency• Harmonically-loaded PAs

    Class E, F,…• Load modulation

    Doherty, LINC• Bias modulation

    Drain modulation, Envelope Tracking (ET), EER• Switching PAs

    Class D, S,…• High efficiency generally means very nonlinear⇒ Need for Linearization

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    Linearity and Efficiency

    • A Design CompromiseHighest efficiency is the most nonlinear regime of operation

    • Figure of Merit Highest efficiency at specified OBO, while still meeting ACLR, spectral mask specifications

    Linearizer or Pre-Distorter is essential

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    Outline

    • Modern Communication s Signals and RFPAsSignals, Linearity, and Efficiency

    • Some Linearizer BasicsWhat’s nonlinearity?What are memory effects?What does a linearizer do?

    • Digital Pre-Distortion DPDSystem ArchitectureLinearization Results

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    Nonlinearity in a PA

    ( ) 21 21

    ( ) ( ) ( ) ( ) ... ( ) ( )N

    N nN n

    n

    y t f u t a u t a u t a u t a u t=

    = = + + =∑PA memoryless nonlinearity, modeled by a polynomial

    ( )1 0 1( ) cosu t A tω φ= +Apply a single-tone CW RF Signal

    u(t) y(t)

    ( ) ( ) ( )2 2 2 21 1 0 1 2 1 0 1 1 0 1( ) cos cos ... cosny t a A t a A t a A tω φ ω φ ω φ= + + + + + +yields

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    Trigonometric expansion…

    ( )1 1 0 1( ) cosy t a A tω φ= +

    ( )

    21

    2

    21

    2 0 1

    2

    cos 2 22

    Aa

    Aa tω φ

    +

    − +

    Writing out the response y(t)

    ( )31

    3 03 cos4Aa t 1ω φ+ +

    ( )31

    3 0cos 3 34Aa t 1ω φ+ +

    Linear gain

    DC Offset, or self-bias

    2nd Harmonic distortion

    3rd Harmonic distortion

    AM-AM &AM-PM

    … etc.

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    Measures of Distortion

    • Harmonic DistortionClearly the nonlinear polynomial function will give rise to harmonics of a single-tone input

    • AM-to-AM ConversionNonlinear changes in the output signal amplitude in response to input amplitude changes

    • AM-to-PM ConversionNonlinear changes in the output signal phase in response to input amplitude changes

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    Envelope Distortion• Envelope distortion can be estimated from a

    Two-Tone Power Series Analysis• The input signal is

    and

    • The 2-tone signal covers the complete dynamic range of the amplifier

    The Peak-to-Average Power Ratio is 3 dB

    • The amplifier output is a power series expansion

    1 2( ) cos( ) cos( )iu t u t u tω ω= +

    1 2 1 2,ω ω ω ω ωΔ = −

    2 3 4 51 2 3 4 5 ...i i i i iy a u a u a u a u a u= + + + + +

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    Two-tone output voltage

    Degree and Order• Each line is a ‘degree’

    power of v(t) in the polynomial expansion

    • The ‘order’ of the mixing frequency is the number of components

    3rd-order products are3ω1, 3ω2, 2ω1±ω2, 2ω2±ω1

    [ ][ ][ ][ ][ ]

    1 1 2

    222 1 2

    333 1 2

    444 1 2

    555 1 2

    ( ) cos( ) cos( )

    cos( ) cos( )

    cos( ) cos( )

    cos( ) cos( )

    cos( ) cos( )...

    y t a u t t

    a u t t

    a u t t

    a u t t

    a u t t

    ω ω

    ω ω

    ω ω

    ω ω

    ω ω

    = +

    + +

    + +

    + +

    + +

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    Two-tone Intermodulation Products

    • Odd-order mixing products are in the signal bandwidth

    Close to carrierIntermodulation (IM) products

    ω2ω12ω1-ω2 2ω2-ω1

    3ω1-2ω2 3ω2-2ω1

    Frequency

    Power dBm

    3rd-order IM

    5th-order IM

    AM/AM Cross-Mod

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    Additional Distortion Measures

    • In addition toHarmonic DistortionAM/AM and AM/PM conversion

    • Intermodulation DistortionNonlinear mixing between the various frequency components of the signal, ω1 and ω2, leading to new frequency components in the signal

    • Cross Modulation DistortionNonlinear mixing between the various frequency components of the signal, ω1 and ω2, resulting in products at existing frequency components of the signal

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    Error Vector Measure

    Assume a simple cubic model:

    Even though the AM-AM compression is the same, a3 is different

    31 3o i iv a v a v= +

    S. C. Cripps, Advanced Techniques in RFPA Design, Figs 3.4 & 3.5

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    Modulated AM-AM & AM-PM

    AM-to-AM AM-to-PM

    Gain and Phase Deviation dependences on input power, as a function of time captured using a modulated signal, showing the variations in instantaneous values. DUT is a 400 W Doherty amplifier; red = measured, blue = modeled

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    Memory Effects

    • The output at time tn is dependent not only on the input at time tn, but also on the input at previous times

    • The number of time samples that need to be considered is the memory depth, M

    • Practical systems have a finite memory depth:fading memory

    PA

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    Vg Vd

    Input Matching Network

    OutputMatchingNetwork

    Drain BiasGate Bias

    RF Source

    Sources of memory in RF PAShort Term Memory

    Cg, Cd, τ

    Long Term Memory

    Thermal,Traps

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    Short Term Memory Effects

    • These are memory effects that occur on the timescale of the signal

    For RF PAs this can mean at the carrier timescale or the envelope timescale

    • RF frequency responseBand-pass or low-pass nature of the matching networks

    • AM-PM Phase changes resulting from large-signal drive

    • TransistorDevice capacitancesTransit times

    ( )( )Q V tt

    ∂∂} (or more strictly, effects)

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    Long Term Memory Effects

    • Take place on a timescale that is much longer than the signal timescale

    • Thermal Thermal time constants in semiconductor devices can range from 10s to 100s of microseconds, to ~ 1 second

    • Trapping MechanismsTime constants from microseconds to secondsMore prevalent in III-V semiconductors (HCI in MOS?)

    • Bias CircuitsRF filters, capacitors, and chokes on bias lines introduce storage timesRelationship to VBW

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    Nonlinear Memory Mechanisms

    f1 f2 f1 f2f1 f2DC

    IM3IM2

    vgs

    Long Term Memory

    Filters out DC and IM2

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    A Simple Pre-distorter

    • Let the amplifier Gain be described by a polynomial

    • Linear gain requires

    • If we can find another function, G, and pass the signal through first so that:

    • We get Linear Gain• We do not get more power• We get sharper saturation

    ( )2 31 2 3( ) ... F ( )o i i i NL iv t a v a v a v v t= + + + =

    ( )( ) 1( ) F G ( ) ( )o i iv t v t a v t= =

    1( ) ( )oL iv t a v t=Power out

    Power In

    Actual Gain, F

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    The Pre-distorter Function

    The secret is finding the pre-distorter function G• The pre-distorter function is an inverse of the nonlinear

    contributions from the amplifier

    IM products:distortion

    f0f0

    PA

    IM productsin anti-phase

    f0f0

    PA

    f0

    Note increased input signal bandwidth

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    The Pre-Distorter…

    • …increases the peak-to-average power ratio of the signal that is input to the PA

    Gain expansion characteristic of the PD

    • …increases the bandwidth of the signal that is input to the PA

    Distortion components are added to the signal to cancel out the distortion of the PA

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    Outline

    • Modern Communication s Signals and RFPAsSignals, Linearity, and Efficiency

    • Some Linearizer BasicsWhat’s nonlinearity?What are memory effects?What does a linearizer do?

    • Digital Pre-Distortion DPDSystem ArchitectureLinearization Results

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    Digital Pre-distortion in BTS Transmitter

    • Signal is sampled at PA output• Down-converted to IF or zero-IF• Digitization using fast ADC• ‘Predistorter’ converts to I & Q, compares with input I & Q

    signals, and generates output signal which is converted to analog signal, and up-converted to RF

    • Signal pre-conditioning in the digital domain

    ADC

    DAC PADigital Signal

    I

    QPre-

    emphasisPre-

    Distorter

    To Antenna

    Up-Conversion

    Down-Conversion

    Digital Domain

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    Typical Digital Pre-Distortion System

    Baseband I & Q signals are combined – can be several carriersCrest Factor Reduction to limit Peak-to-Average Power RatioPre-distortion FunctionDSP also accomplishes time alignment, update of DPD parametersFast ADC/DAC, high dynamic range (16 bit, >200 MSPS typical)RF up/down-conversion

    Down-Conversion

    RF in

    RF out0

    90

    ADC

    DAC

    Pre-Distorter

    Time-align &

    De-interleave

    Up-Conversion:IQ Modulator

    DSP domain RF domain

    DAC

    Digital Up-

    converter

    Crest Factor

    Reduction

    PatternGenerator

    I

    Q

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    Digital Up-Converter• The purpose of the DUC is to take the sampled data

    signals and up-convert to the sample rate of the digital signal processing system

    • In the digital domain, the up-conversion is performed by re-sampling or interpolation:

    The digital signal is padded with zeros to reach the correct sample rateThe signal is then interpolated between the zerosA digital filter is applied to retrieve the correct frequency and phase response

    • Example: WCDMA native sampling rate is 3.84 MspsIf the digital IF (DSP clock rate) is 61.44 MHzWCDMA signal needs to be oversampled by 16X

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    Crest Factor Reduction

    • The gain expansion characteristic of the pre-distorter means that the signal input to the PA is of high peak-to-average power ratio

    • CFR can reduce this PAPR to manageable levels, and can avoid the PA operating in saturation

    Power out

    Power In

    Actual Gain, F

    Essential for DPD Applications

    Average power

    Peak power

    PAPR into PA

    Peak power required for DPD

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    CFR Principle

    • The signal peaks above a threshold level are detected• The magnitude of the peak is reduced to below some target

    value• Filtering is required to re-shape the signal spectrum

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    Resampling prior to DPD

    • The bandwidth of the signal after DPD (b) is much wider than the original input signal (a)

    • To reconstruct this DPD signal in the analog domain, it must be sampled at a higher rate than the input

    • Under-sampling will lead to aliasing (c)

    • This cannot be removed by over-sampling at the output of the DPD

    • Over-sample at DPD input

    Figure from Zhu et al, IEEE Trans MTT 56(7) pp1524-34 (2008)

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    DPD Linearizer Action

    Pre-distorter (PD) • takes the input signal• Compares with feedback signal sampled at output of PA• Adjusts the PD function to minimize the difference

    Gain, phase parameters of AM-AM and AM-PMCoefficients in polynomial series function

    • Memory effects require comparison over several time samples

    PD PA

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    1

    0 1[ ] [ ] [ ]

    Q P pa qp in in

    q pV n V n q V n qα −

    = == − −∑∑

    Regular polynomial, with added dimensions for delays

    Pre-Distortion Block

    Memory Polynomial Pre-Distorter

    z-1

    z-1

    z-1

    Vin

    PA

    Polynomial degree P

    Polynomialdegree P

    Polynomialdegree P

    1

    2

    Q

    Va

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    Linearizer Myths & Misunderstandings

    Linearizers• do not increase the output power available• do not increase gain• do not improve the noise floor• have a harder saturation characteristic

    In saturation this can create more distortion & noise• work best at low signal levels• do not necessarily accommodate memory effects• have a finite linearizing bandwidth• consume additional power, reducing system

    efficiency

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    Two Carrier GSM Performance

    A

    *3 RMMINH

    Ref 55.7 dBm

    **

    *

    *

    CLRWR

    2 RMMAXH

    3DB

    RBW 30 kHzVBW 30 kHz

    Offset 46.7 dB↑POS 55.721

    LVL

    1 RM

    SWT 5 sAtt 15 dB*

    NOR

    *

    Center 1.8425 GHz Span 5 MHz500 kHz/

    -40

    -30

    -20

    -10

    0

    10

    20

    30

    40

    50

    Standard: NONE

    Tx Channels

    Ch1 43.49 dBm(Ref)

    Ch2 43.48 dBm

    Total 46.50 dBm

    Adjacent Channel

    Lower -40.71 dB Upper -41.46 dB Alternate Channel

    Lower -60.28 dB Upper -71.00 dB 2nd Alternate Channel

    Lower -63.49 dB Upper -65.39 dB

    1

    Marker 1 [T1 ] -2.91 dB 1.842830500 GHz

    ↑POS 55.721 dBm

    A

    *3 RMMINH

    Ref 56.2 dBm

    **

    *2 RMMAXH

    3DB

    RBW 30 kHzVBW 30 kHz

    Offset 46.7 dBPOS 56.176 d

    LVL

    SWT 2 sAtt 15 dB*

    NOR

    *

    Center 1.8425 GHz Span 5 MHz500 kHz/

    *1 RMAVG

    -40

    -30

    -20

    -10

    0

    10

    20

    30

    40

    50

    Standard: NONE

    Tx Channels

    Ch1 43.91 dBm(Ref)

    Ch2 43.96 dBm

    Total 46.95 dBm

    Adjacent Channel

    Lower -70.11 dB Upper -70.65 dB Alternate Channel

    Lower -73.40 dB Upper -74.78 dB 2nd Alternate Channel

    Lower -74.55 dB Upper -77.04 dB

    SWP 20 of 20

    1

    Marker 1 [T1 ] -2.68 dB 1.842830500 GHz

    POS 56.176 dBm

    DPD Results are achieved using TI GC5322 Evaluation ModuleIntermodulation products are below -70dBc up to 46.9dBm of output power42% final stage efficiency and 36% two-stage power added efficiency

    Before DPD After DPD

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    *

    *

    Center 1.84244 GHz Span 15.2 MHz1.52 MHz/

    *

    -80

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    Standard: NONE

    Tx Channels

    Ch1 -2.36 dBm(Ref)

    Ch2 -2.46 dBm

    Total 0.60 dBm

    Lower Upper dB dB Adjacent -29.36 -28.28 Alternate -46.96 -47.17 2nd Alt -50.44 -50.44 3rd Alt -56.71 -56.32 4th Alt -61.18 -61.21 5th Alt -70.41 -70.86 6th Alt -80.71 -81.52 7th Alt -81.29 -81.75 8th Alt -80.84 -82.88 9th Alt -81.16 -82.56 10th Alt -82.31 -83.09 11th Alt -83.39 -83.75

    SWP 20 of 20

    1

    RF PA before DPD

    240 W Doherty PA2C-GSM Signal at 1800 MHz

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    RF PA after DPD

    *

    *

    Center 1.84244 GHz Span 15.2 MHz1.52 MHz/

    *

    -80

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    Standard: NONE

    Tx Channels

    Ch1 -2.11 dBm(Ref)

    Ch2 -2.08 dBm

    Total 0.91 dBm

    Lower Upper dB dB Adjacent -70.73 -69.91 Alternate -81.18 -81.33 2nd Alt -79.73 -82.81 3rd Alt -76.54 -78.03 4th Alt -73.46 -73.18 5th Alt -75.14 -74.35 6th Alt -80.57 -80.42 7th Alt -80.72 -82.05 8th Alt -81.35 -82.52 9th Alt -81.94 -84.67 10th Alt -83.91 -84.95 11th Alt -85.99 -85.19

    SWP 20 of 20

    1

    240 W Doherty PA2C-GSM Signal at 1800 MHz

    Class 1 linearization at Pout = 47 dBm average

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    RF PA before DPD

    3

    N

    Center 957.44 MHz Span 18 MHz1.8 MHz/

    *

    -90

    -80

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    Standard: NONE

    Tx Channels

    Ch1 -5.44 dBm(Ref)

    Ch2 -5.55 dBm

    Ch3 -5.63 dBm

    Ch4 -5.79 dBm

    T t l 0 42 dB

    Lower Upper dB dB Adjacent -32.33 -32.21 Alternate -33.63 -35.00 2nd Alt -40.21 -39.68 3rd Alt -45.76 -44.98 4th Alt -51.58 -52.42 5th Alt -61.89 -60.63 6th Alt -59.40 -59.14 7th Alt -59.02 -59.72 8th Alt -62.78 -63.66 9th Alt -66.51 -65.69

    SWP 20 of 20

    1↑POS 5.843 dBm

    Pout = 100 W average

    ~500 W Doherty PA4C-GSM Signal at 940 MHz

  • TMFreescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2010.

    RF PA after DPD

    Center 940.44 MHz Span 18 MHz1.8 MHz/

    *

    -90

    -80

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    Standard: NONE

    Tx Channels

    Ch1 -5.65 dBm(Ref)

    Ch2 -5.69 dBm

    Ch3 5 70 dB

    Lower Upper dB dB Adjacent -61.68 -61.47 Alternate -65.43 -67.18 2nd Alt -70.29 -69.88 3rd Alt -69.79 -68.37 4th Alt -75.97 -75.71

    SWP 20 of 20

    1POS 6.368 dBm

    ~500 W Doherty PA4C-GSM Signal at 940 MHz

    Class 2 linearization at Pout = 50 dBm average

  • TMFreescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2010.

    9260 Doherty + IC9080 Driver 4C-GSM -- DUC Gain modified (1/15/09)

    -80

    -75

    -70

    -65

    -60

    -55

    -50

    36 38 40 42 44 46 48 50 52 54

    Output Power(dBm)

    IM P

    rodu

    cts

    (dB

    c)

    20

    25

    30

    35

    40

    45

    50

    Effic

    ienc

    y (%

    )

    ADJ_LADJ_UALT1_LALT1_UALT2_LALT2_UALT3_LALT3_UWide_LWide_UEfficiencyPAE

    Class 2 spec.

    DPD of 500 W Doherty PA under Drive-up

    940 MHz, 4C-GSM

  • TMFreescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2010.

    Backup

  • TMFreescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2010.

    GSM/EDGE Transmit Mask

    Sign

    al A

    mpl

    itude

    , dB

    c

    GSM/EDGE has stringent requirements

    Digital Pre-Distortion Techniques for RF Power Amplifiers OutlineLinearity RequirementsCrest Factor and Peak-to-Average Power RatioAmplifier PAR EffectsMeasuring PARCumulative Complementary Distribution FunctionCCDF – Statistical Measure of PARWhat does this mean for the PA?High-Efficiency PA ModesLinearity and EfficiencyOutline Nonlinearity in a PATrigonometric expansion…Measures of DistortionEnvelope DistortionTwo-tone output voltageTwo-tone Intermodulation ProductsAdditional Distortion MeasuresError Vector MeasureModulated AM-AM & AM-PMMemory EffectsSources of memory in RF PAShort Term Memory EffectsLong Term Memory EffectsNonlinear Memory MechanismsA Simple Pre-distorterThe Pre-distorter FunctionThe Pre-Distorter…OutlineDigital Pre-distortion in BTS TransmitterTypical Digital Pre-Distortion SystemDigital Up-ConverterCrest Factor ReductionCFR PrincipleResampling prior to DPDDPD Linearizer ActionMemory Polynomial Pre-DistorterLinearizer Myths & MisunderstandingsTwo Carrier GSM PerformanceRF PA before DPDRF PA after DPDRF PA before DPDRF PA after DPDDPD of 500 W Doherty PA under Drive-upBackupGSM/EDGE Transmit Mask

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