Embrace Circuit Nonlinearity to get Transmitter 'Linearity' and Energy Efficiency

Earl McCuneRF Communications Consulting

Santa Clara, California

IEEE MTT-S Distinguished Microwave Lecture

Microwave Theory & Techniques Society (MTT-S)

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11

DML Presentation Outline

Carefully examine the PA problemA ‘backwards’ design approachPerformance CharacterizationMeasurementsConclusions

12

PA Design: Getting more Difficult

Design power level follows PEP, not PrmsPrms sets communication rangeHigher PAPR increases PEP

Distortion tolerance goes down as signal order increases

Bandwidth is tough to achieve, particularly in mobile devicesLow supply voltage and high PEP combination Low RL at the transistor to generate the needed

powerHigh impedance ratio from the OMN reduces BW

Aggregated bands – a major headache

13

Standards Progression

Signals are evolving in the direction of higher PAPRExample signals here are

scaled for equal rms power

Envelope voltage probability density is shown

There is also increasing probability of zero-magnitude activity

Linearity requirements are increased if the zero-magnitude curvature is not positive 0%

1%2%3%

0 1 2 3 4 5

0%1%2%3%

0 1 2 3

0%1%2%3%

0 1 2 3

0%2%4%6%

0 1 2 3

0%

50%

100%

0 1 2 3

GSM, GPRS

EDGE

UMTS

HSPA

OFDM

Bluetooth 1.0, ZigBee

14

PAPR Progression

PAPR increases as the signal type progressesSystem impacts

Constant range (fixed rms output power): PA cost increases with PEPSame PA size : range decreases from decreasing rms output power

UMTS

LTEHSPA

WiMAX

15

Signal Order

The order of the signal (M) influences EVM specifications, thus PA linearity

DefinitionM = the number of signal states available to any symbol

= 2b b = number of bits per symbol

Car

rier

Freq

uenc

y

Upper subcarriersLower subcarriers

Frequency

f

……f1 fN/2f-N/2 f-1

b = 2M = 4

b = 6M = 64 b = 52*2 = 104

M = 2104 ; ~ 1031

16

Bandwidth Efficiency: Shannon

A measure of how many bits per second are communicated through a given bandwidth

Shannon (1948) showed that in a noise limited brickwall channel of bandwidth B, error-free communication (not error-free transmission!) is possible as long as the data rate R is less than a capacity value C

• PS is rms signal power• PN is rms noise power within (brickwall) bandwidth B

This is an upper bound on signal bandwidth efficiencyCoding is required, though nothing is said about the associated complexity (or its

costs)

BWRB

bps/Hz

2log 1 S

N

PC BP

bps

17

Power vs. Bandwidth Efficiency

• SNR is the only variable we have to increase the available bandwidth efficiency

• Shannon’s limit plot on a linear scale makes the relationship explicit

• To get high bandwidth efficiency, Shannon shows that high relative power is required

012345678910

0 1 2 3 4

Power Ratio

Bandwidth Efficiency C/B (bps/Hz)

0

200

400

600

800

1000

1200

0 2 4 6 8 10

Power Ratio

Bandwidth Efficiency C/B (bps/Hz)

2 1C

S B

N

PP

18

Bandwidth Efficiency: QAM

Data rate RBits per symbol = log2MTime per symbol = TS

Occupied bandwidth BNyquist filtered, at BW60

Bandwidth efficiency

2log

S

MRT

2

2

loglog

1 1S

BW

S

MT MR

BT

1

S

BT

19

Bandwidth Efficiency: OFDM

Data rate RBits per symbol = Nlog2MsubTime per symbol = TS+cp

Occupied bandwidth BUnfiltered, at BW20(not an equal comparison)

Bandwidth efficiency

2log

1sub

S

N MRcp T

2

2

log1 log

1

sub

S subBW

S

N Mcp T MRNB cpT

S

NB N fT

20

Signal Comparison

OFDM PAPR is double (in dB) that of QAMSignificant PA cost impact

OFDM signal order greatly exceeds that of QAMLess tolerant of distortionMore linearity needed in the PA

OFDM bandwidth efficiency matches that of QAM

What are we paying for ?? (LTE = long-term employment )

1

1E+10

1E+20

1E+30

1E+40

1E+50

1E+60

1E+70

1E+80

1E+90

1E+100

1E+110

1E+120

1E+130

1E+140

0 2 4 6 8 10

Signal Order M

Bandwidth Efficiency  (bps/Hz)

M‐QAMOFDM (48x M‐QAM)

1

3

5

7

9

11

13

15

0 2 4 6 8 10

PAPR

  (dB

)

Bandwidth Efficiency  (bps/Hz)

OFDM

M‐QAM

21

PA Energy Efficiency

Maximum energy efficiency occurs at the onset of clippingCircuit linearity happens at much lower energy efficiencyAt high energy efficiency, the conventional transistor model no

longer applies

Amplifier Characteristics - 7th order

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.5 1.0 1.5 2.0

Input (normalized to P1dB)

Nor

mal

ized

Out

put

linearcompressedEfficiency

output clipping

Linearized

"Linear"

OBO(Output backoff)

1 dB

PAPR

3 dB

6 dB9 dB

12 dB

22

“Backwards” Approach

Normally we start with a linear design, then work hard to improve its energy efficiency

Instead, let’s start with a very energy efficient design, then work hard to make sure it generates signals accuratelyMaximally energy efficient circuit: a switch

23

Circuit Operation and Model

Intended operation at the endpoints of the load lineIncreased drive neededFar into output compression

Transistor does not regulate load current

0.0

0.5

1.0

1.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

VDS (V)

ID (A

)

RL

ControlInput

IL

ActiveDevice

VS

RSW

SL

L SW

VIR R

24

Practical Model Values

FET performance aligns well with the switch model In general, need to add an AM offset voltage (VAMO)

Origin offset is observed from HBT devicesRelated to VCE,SAT?

RF Input

Power Supply

Load Resistance

(RL)

ON Resistance(RSW)

Offset Voltage(VAMO)

+–

+

+

0.33 0.0 V

0.65 0.12 V

3.2 0.14 V

Measured model parameters:HFET HBT (High Power) HBT (Low Power)

HFET HBT (High Power)

VAMO

RSW

25

PA Operating Modes

Linear is only sensitive to RF input powerC-mode is only sensitive to power supplyP-mode is sensitive to both power supply and RF input power

But only at very low power supply values

HBT PA Operating Modes

-40

-30

-20

-10

0

10

20

30

40

-60 -50 -40 -30 -20 -10 0

Input RF Power (dBm)

PA O

utpu

t Pow

er (d

Bm

)

3.5V = Vcc31.75V0.87V0.5V0.4V0.3V0.2V

C-Mode

P-Mode

Traditional Linear

Linear C-Mode P-Mode

0 Vcc Vcc

G 0 GVccPout

PinPout

Operating mode is defined by which input parameters the RF output is sensitive to

26

‘Gain’ when Nonlinear 1

The concept of amplifier gain is intuitive when everything is linear

Slope gain – the slope of the amplifier transfer function (waveform integrity)

Ratiometric gain – the ratio of output signal to input signal

These results diverge in compressed operation

xaxy 1)(

1)()( axydxdxgd

11)( axxaxgr

27

‘Gain’ when Nonlinear 2

Slope Gain

Relates to waveform distortion

Goes to zero when the output is clipping

Ratiometric Gain

Relates to amplifier added power: the usual RF gain definition

Output power is never zero, and can be less than Pin

Output RF Power increases into waveform clipping

Amplifier Characteristics - 7th order

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Input (normalized to P1dB)

Norm

aliz

ed O

utpu

t

linear compressed normalized gain IO Ratio

in

out2

in

2out

in

out

inoutinoutR

VVlog20

RV

RV

log10

pplog10

)plog(10)plog(10P-PG

Slope

28

Linearity Control

By satisfying two design conditions, linearity control is transferred away from the RF transistor

These design conditions must remain valid at all output envelope values

Signal linearity becomes a ‘video’ problem, relegated to the dynamic power supply

CCAMOL

CC

LONCE,L

AMOCC

ONCE,L

AMOCCL

VV ; RV

RR ; R

VV

RRVVI

SIGNALQL III

Controlled Current Source Switch

RF Input

Power Supply

Load Resistance

(RL) RF Input

Power Supply

Load Resistance

(RL)

ON Resistance(RCE,ON)

Offset Voltage(VAMO)

+ –

New Design ConditionsLsignalout RIV

LLout RIV

29

SSR: Stage Series Resistance

V/I ratio should be proportional to load resistance (and be constant) if the transistor is switching

If plot is linear, transistor is regulating its current (CCS)

Raptor D2 Resistance vs. Drain Voltages

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

VDD2

PA D

2 R

esis

tanc

e(oh

m)

3.4

32.4

1.4

10.5

0.20.1

0.05

0.001V2=V3

VFINAL

VDRIVER

Final stage resistance vs. VFINAL

Fina

l sta

ge re

sist

ance

()

DDreg

VI

R

1

This device is showing both CCS and switch characteristics

S

S

IVSSR

Ohm’s Law:

30

Power Control

Transmitter power control over an extremely wide rangeNeeded for CDMA systems

Using both C-mode and P-modeEnvelope dynamic range is in addition to this rms power rangeFor this UMTS design, signal + envelope dynamic range exceeds 110 dB

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

-70 -60 -50 -40 -30 -20 -10 0 10 20 30

Powe r Co mman d (dBm)

Pout

mea

s. (d

Bm

)

Power control is calibrated from +28 to -60 dBm: an 88 dB dynamic range +28 dBm PA output -50 dBm PA output

31

Output Backoff Elimination

Peak envelope power is unchanged for an envelope-varying signal: PEP = PSAT

This holds true for all signals, including WCDMA

Minimum possible transistor size

GMSK (2.5W rms) and EDGE (1.2W rms) : identical peak powers

32

Circuit Stability

In either the ON or OFF state, the differential gain is essentially zeros-parameters no longer hold

Oscillation cannot be supported when differential gain is < 1Operated properly (deep into output compression) this circuit

approach is unconditionally stable

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

VGS (V)

gm (A

/V)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

FET

Cur

rent

(A)

gm

ID

33

Temperature Stability

Using the proposed design criteria

Thermal stability is inherentNo compensation is used

EDGE Power Spectral Density Overlay (1842.8MHz)

Temperature Sweep: 29C → 70C → 29C20 watts rms power output

S AMOL

L SW

S

L

V VIR R

V R

FET used (LDMOS)

Negligible wrt RL

34

836 MHz GPRS/EGPRS PA TEMP rise+34.1 dBm peak (+34.1/+30.9 GMSK/EDGE)

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8# ACTIVE TX SLOTS

CA

SE T

EMP

RIS

E (C

)

8

1817

1615

1211

10

2329

GPRS/EGPRS classes

4 RX # RX = # TX 4 RX # RX = # TX

GPRS

EGPRS

Very Low Temperature Rise

Overall thermal rise is quite low in all cases< +20C for 8 GPRS slots @2.5W each, +11C for class-12 (4TX)+11C for 8 EDGE slots @1.2W each, +5C for class-12 (4 TX)

EDGE Thermal Rise is lower than for GMSKArtifact of no-backoff operation, no quiescent current, and EDGE PAR

BlackRed

Half-duplex classFull-duplex class

35

Manufacturing Stability

Assume 0.1 nominal Switch ON resistanceLet ON resistance vary from 50% to 200% of nominal

Output power changes only about 0.5dB

PA Error vs. Switch Resistance

-5-4.5

-4-3.5

-3-2.5

-2-1.5

-1-0.5

0

0.01 0.1 1

Switch Transistor Resistance (ohms)

PA O

utpu

t Pow

er E

rror

(dB)

36

Operation Stability: Ageing

1000 hours accelerated ageing testClass-12 GPRS TX, +85C operational

Drift is not measurable within instrument varianceSimilar stability seen for spectral specifications

0

5

10

15

20

25

30

0 100 200 300 400 500 600 700 800 900 1000

EDG

E R

MS

Pow

er (d

Bm

)

Trial Number

EDGE Power Consistency

PLEV = 8

PLEV = 13

PLEV = 19

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500 600 700 800 900 1000

EDG

E R

MS

EVM

(%)

Trial Number

EDGE EVM Consistency

PLEV = 8

PLEV = 13

PLEV = 19

37

Definitions

Lineartransfer function of the circuit, such Vout/Vin, has the

largest power series expansion coefficient being the linear (first-order) one

Doubler: second order coefficient dominatesTripler: third order coefficient dominatesand so on…A 2-port process

Polara 3-port processone input signal controls a polar parameter

(magnitude or phase) of the circuit output signal

38

Is this Linear, or Polar?

In our approach to start from a maximum efficiency circuit, we have come to implement a polar systemThis is a natural result, not an initial objective‘PA’ is a 3-port multiplier, not a 2-port amplifier

Switch open-close timing maps directly to signal phaseChanges in switch timing map directly to phase modulation

Optimizing an envelope tracking design for improved energy efficiency results in this polar operation

ttta cosRF

taAM

P cosM t t

39

ConclusionsDesigning for energy efficiency first, then for

linearity, does workBest output power for a transistor sizeLinearity (output signal accuracy) can be excellent

Design procedures are very different from conventional linear designDefinitions of Gain need to be expandeds-parameters do not applyNew design conditions

Innate circuit stabilities also resultFaster design, lower manufacturing cost

40

ReferencesS. C. Cripps, RF Power Amplifiers for Wireless Communication, 2ed, Artech House (Boston/London), 2006.E McCune, “High-Efficiency Multi-mode, Multi-band Terminal Power Amplifiers”, IEEE Microwave Magazine, vol. 6, No.

1, March 2005, pp. 44-55E. McCune, “Advanced Architectures for High-Efficiency Multi-mode, Multi-band Terminal Power Amplifiers,”

Proceedings of the IEEE Radio and Wireless Conference (RAWCON), Atlanta, October 2004F. E. Terman, Radio Engineers Handbook, McGraw-Hill (New York), 1943C. Buoli, A. Abbiatti, D. Riccardi, “Microwave Power Amplifier with ‘Envelope Controlled’ Drain Power Supply,” Proc. of

the 25th European Microwave Conference, Sept 1995, pp. 31-35G. Hanington, P. Chen, P. M. Asbeck, and L. E. Larson, “High efficiency power amplifier using dynamic power-supply

voltage for CDMA applications,” IEEE Trans. Microwave Theory and Techniques, vol. 47, no. 8, pp. 1471–1476, Aug. 1999

L. R. Kahn, “Single sideband transmission by envelope elimination and restoration,” Proc. IRE, vol. 40, no. 7, pp. 803-806, July 1952.

F. H. Raab, “Intermodulation distortion in Kahn-technique transmitters,” IEEE Trans. Microwave Theory Tech., vol. 44, Dec. 1996, pp. 2273–2278

E. McCune, “Polar Modulation and Power Amplifiers,” Workshop WSC at the 2009 International Microwave Symposium, Boston, June 7-11, 2009

A. van Roermund, H. Casier, M. Steyaert (Eds.), Analog Circuit Design: Smart Data Converters, Filters on Chip, Multimode Transmitters, Springer, 2010, (Ch.13) “Multimode Transmitters: Easier with Strong Nonlinearity,” E. McCune

F. H. Raab, P. Asbeck, S. Cripps, P. B. Kenington, Z. B. Popovic, N. Pothecary, J. F. Sevic, and N. O. Sokal, "Power amplifiers and transmitters for RF and microwave," IEEE Trans. Microwave Theory and Techniques, vol. 50, no. 3, pp. 814-826, March 2002

W. Sander, S. Schell, B. Sander, “Polar Modulator for Multi-mode Cell Phones,” Proceedings of the 2003 Custom Integrated Circuits Conference (CICC), San Jose, Sept. 2003