distributed and transient electro-thermal modeling and its

1MISES Non-Linear RF Lab

Distributed and TransientElectro-thermal Modeling and Its

Impact on RF Predistortion

Patrick Roblin*Wenhua Dai

*The Ohio State University


Outline

• Introduction

• Electrical modeling

• Part I: Image method thermal modeling anddistributed thermal model

• Part II: Transient thermal response and memoryeffects in RF predistorter

• Part III: Experimental results on memory effects


Introduction•High power devices suffer from self-heat during operation, whichaffects its electrical performances.

•Most of the power device models use simple low pass RC circuit tomodel the self-heating The non-uniformly distributed temperatureacross the power device requires a model to capture the temperaturedistribution.

•Dynamic self-heating due to the low frequency modulation envelopcauses thermal memory effects.

•Memory effects are categorized into thermal and electrical memoryeffects. Via simulation we can identify their separate contributions.

•Temperature rise in a multilayer material involves fast and slowtime constants. A multiple RC time-constant model is required tocapture the complete device electro-thermal dynamic.


Thermal Rth Measurement

20 fingers6.34C/W

144 fingers1.44 C/W

Rth is obtained through steady state temperature measurement- calculated using an average device temperature- exhibits a nonlinear scaling with the device size


Thermal Time Constant Measurement

−+

−+=2

21

1 expexp)(ττ

tA

tAItI DCdsds

Thermal time constant can beobtained through pulse IVmeasurement: the Drain currentdecrease/increase due to theheating

- Measured rise time maybeaffected by Cgs, Ls, and the powersupply.

- Two competing temperaturedependences (Vth, mobility) maycancel each other, resulting in areduced thermal dependence.Time (s)

I D(A

)

6x10-60


Large Signal Electro-Thermal Model

Electrical part

Thermal part

G

S

D

Tsub

Tdev

•Nonlinear large signal electrical model

•IV characterization from both iso-thermaland pulse measurement

•S-parameter characterization from iso-thermal measurement

•Parasitics from cold FET measurement

•Simple RC circuit to model thetemperature response


0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Extrinsic Vds in Volts

Dra

in C

urre

nt in

Am

psVgs from 4 to 6.5 in steps of 0.25 V

2829 30 31 32 34 35 36 38 39 41 42

29

30 32 34 36 38 41 43 46 49 52 55

29

31 34 37 41 45 49 53 57 62 67 73

29

32 37 42 47 52 58 64 70 77 84 91

29

33 39 46 53 60 68 75 83 91 100 109

29

3342 50 59 68 77 87 96 106 115 125

29

34

44 54 65 76 87 97 108 119 130 141

29

34

46 58 71 83 96 108 120 132 145 157

29

34

47 62 76 90 104 118 131 145 158 172

29

33

48 65 81 97 112 127 142 157 172 187

29

34

48 6786

103120

136 152 168 184

Electro-Thermal IV for LDMOSFETTemperature

in C


Model Verification UsingScattering Parameters

S21/15

S11 S22

S12*60 1

2

3

4

5

6

S11

S12

×80ej3π/4

S21

S22

× ej3π/4

OSUFET B-spline model (2 bias points) AET analytic model


Model Verification Through Loapull

Loadpull test bench


Model Verification using the HarmonicResponse of an Amplifier

1 W amplifier


Part I: Lateral Thermal Model

• 3D steady state temperature calculation

• Experimental Results

• ADS implementation

• Results


Image Method for Steady StateTemperature Field

P0

P01 P02

P010 P012 P020 P021

0

Z1

Z2

Z

YP0

P01

P012

P02

P010

air

Layer 1

Layer 2

Layer 3

adiabatic

Green function: ''4

)',( dydxk

qdT s

rrr

∆=

π

B.C. : ( ) ( )+− === 11 ZZTZZT

Image sources are formed so that B.C be satisfied

Based on: Rinaldi, N, “Generalized image method with application to the thermal modeling ofpower devices and circuits” IEEE Trans. on Electron Devices, Vol. 49, No. 4, p. 679, 2002.


Non-Linear Scaling of Average Rth

16

4

1

# of cells

1.0748 µm

2.7912µm

6.173 µm

Rth oC/WGate Width

2.8 oC/W measured in our testbed for 12 µm devices.

The device models cannot rely on linear scaling rule for Rth becauseof the lateral heat flow.


Distributed Thermal Model

Mutual heat flow is modeledby mutual thermal resistance

Extraction from Rth matrixcalculation through imagemethod

P=1W8 fingersHeat Area=1.45mm x 1.27mmRth=1.67 C/W


Distributed Electro-Thermal ModelReduction

Fingers are symmetrical to the centerNumber of fingers is reduced by halfEach finger has its size doubledRth matrix folded, each Cth is doubled

++

++

+

+

22

22

1n/2n/2,n/2n/2,n,n/21,n/2

1n/2,1n/2,1n,11,1

RRRR

RRRR

L

MOM

L

Thermal Y matriximplemented in ADS


Transient Simulation with Distributed Model

5 10 15 20 25 30 350 40

0.5

1.0

1.5

2.0

0.0

2.5

Time (msec)

Dra

inC

urre

nt(A

)

Red (line) – one-finger approximationMagenta (o) – distributed 16 fingersBlue (x)– distributed 8 fingers

5 10 15 20 25 30 350 40

30

40

50

60

70

20

80

Time (msec)

Dev

ice

Tem

pera

ture

(C)

Center

Edge

•Temperature distribution is seen indistributed model

•Non-distributed model reports theaverages temperature across the fingers

•Overall electrical behavior is consistent,indicating the non-distributed model hasenough accuracy

Drain current

Device Temperature 3 models: non-distributed,distributed,distributed half


Results for Part I: Lateral DistributedThermal model

• A recently reported image method can facilitate the thermal modeling ofmultilayer devices to account for lateral distributed thermal effects inlarge multifinger devices.

• Model was implemented in a circuit simulator using a distributed lateralthermal model using a single RC time constant for each finger.

• Temperature distribution can be reproduced. This is useful in applicationswhere accurate temperature information is required.

• However the overall electrical behavior can be modeled with enoughaccuracy by a non-distributed model reproducing the averagetemperature.

• An important application of distributed model is however to predict thenon-linear scaling of Rth with device area.


Part II: Transient Thermal Modeling andMemory effects

• Approximate transient response with image method

• Multistage RC model for ADS implementation

• Impact of transient thermal model on a RF amplifierwith a predistorter

• Results for multisine excitation on 1W and 60W PAs

• Results for IS95 CDMA excitation


Image Method for Approximated TransientTemperature Rise in Multilayer Structure

∫

−−

−

−−

−=

−Lu

z

s duu

yYf

u

yYf

u

xXf

u

xXfe

k

qtzyxT

2

0

12122

2

4),,,(

π

( ) )(erf xxf =DtL =

Time dependent Green function of a rectangular heat source:

Y

X

Z

Y1 Y2

X1X2

Approximation 1: when D1=D2, boundary condition isindependent oftime, so that image method can be usedApproximation 2: thermal conductivity of layer 2 is largeenough

Layer 1

Layer 2Boundary conditions:

( ) ( )+− === 11 ZZTZZT

Z1

For all t


Transient Temperature Rise

Shift in time

FEM provides ‘true’ temperature response, long computation timeImage method provides approximated solution


Multi-time-constant Thermal Model

Slow and fast transient temperaturerise can be modeled

Rth includes junction, Si chip, flange,and copper block

Extraction from transient temperaturemeasurement/calculation


Thermal Parameter Extraction

8.890.51

5.39e-10.35

1.24e-42.18

9.38e-61.97

1.29e-61.165-stage

2.390.83

7.38e-52.98

2.45e-62.363-stage

1.60e-56.171-stage

Cth (F)Rth (Ohm)

Extracts Rth and Cth by curve fitting in log scaleConstraint total Rth constant


Amplifier

Transistor model

Input matching

Thermal network

Output matching


Two-tone Simulation

Temperature at f2-f1

2KHzf =∆ 2MHzf =∆

Temperature at f2-f1 IMD3

•Low modulation frequency generates bigger temperature variation•Temperature variations are too small to affect the electrical behavior (IMD3)•Class A amplifier less sensitive


Thermal Step Response for Devices ofVarious Sizes

10−8

10−6

10−4

10−2

100

102

0

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Nor

mal

ized

Tem

pera

ture

Ris

e

1W LDMOS, Z1=300um, Rth=5.5C/W, Area=2.3e5 um2



The thermal RC timeconstant increases with thedevice area or with thinnerSilicon layer.


Impact of Thermal Memory Effectson RF-Predistortion

f0 = 880MHz

RF predistorter is expected to be more sensitiveto low frequency temperature variation

9-tonesignal


Background and Motivation

• Memory effects (frequency dependence of non-linearities) inRF PAs (power amplier) degrade the performance of a PAlinearization [1]

• The linearization degradation for signals with bandwidth above1MHz is linked to fast electrical memory effects rather thanslow thermal memory effects [2]

[1] J. S. Kenney, W. Woo, L. Ding, R. Raich, H. Ku, and G.T. Zhou,``The Impact of Memory Effectson Predistortion Linearization of RF Power Amplifiers,'' Proc. of the 8th Int. Symp. onMicrowave and Optical Techn.

[2] W. Dai and P. Roblin,``Distributed and Multi-Time-Constant Electro-Thermal Modeling and itsimpact on ACPR in RF predistortion'' ARFTG 62 Conference, Denver, Co., pp. 89-98, Dec.2003.

From recent studies :


PA(DUT)PA linear

LO

Vectorial

Linearization parameters

/ DSP

Interface

DACsFPGA

ADCs

RF source

RFoutput

IQ modulator

Predistortion

FPGA Digital Testbed for RF Predistortion

�

DUT : Power Amplifier

Digital Testbed

�

Before linearization After linearization


RF-Predistorter in ADS9-tone source signalNewman’s Phase (1965)f0=880MHzPAR=2.6


ACPR versus Multisine Bandwidth

Strong memoryeffects at lowfrequencies

Above 1MHz,electrical memoryeffects dominates

Pout=P1dB-6=22dBm

RC3 and RC5 convergesRC1 deviates

Distributed model gives thesame ACPR as RC1 does


Spectral Regrowth for a 1MHzBandwidth Multisine}

In band

Upperadj

Loweradj

} }

Center freq: 880MHz9 tonesTone-spacing: 0.1MHz

Small differencesbetween thermal models

tones9adjbandofpowertotal

tones9inbandofpowertotal=ACPR

Pout Lacpr Uacprno pred 24.08 -31.14 -31.12with pred 21.88 -66.59 -66.47


Spectral Regrowth for a 1KHzBandwidth Multisine

Center freq: 880MHz9 tonesTone-spacing: 0.1KHz

Pout Lacpr Uacprno pred 24.08 -31.25 -31.32RC1 pred 21.88 -63.27 -63.46RC5 pred 21.88 -64.17 -66.39

Noticeable differences up to3dB between thermal models

tones9adjbandofpowertotal

tones9inbandofpowertotal=ACPR


IS95 CDMA simulation

24.024.024.024.128.1Pout (dBm)

-40.2

-44.2

Direct

-59.4-59.4-59.4-58.9HACPR (dBc)

-61.6-61.6-61.6-61.3LACPR (dBc)

RC5RC3RC1RC0

Env simulation of IS95 CDMA signalBandwidth: 1.2288MHzTime: 0 – 0.833msFreq resolution: 2.4KHzFrequency span: 5MHzInput PAR: 7.39

Improved thermal model has a negligibleeffect for a class A with IS95

Power level: P1dB-4dB=24dBm

** ACPR defined as power ratio of 30KHzadjband to 1.2288MHz inband


Conditions for Strong ThermalMemory Effects

•ACPR needs to be strongly sensitive to fluctuationsof the temperature

Note: ACPR is more sensitive to Delta T when using apredistorter (by a factor 10)

Note: sensitivity is 0.43dB/C (small)

•Amplifier needs to exhibit a large fluctuation(variance) of the temperature

Note: temperature fluctuation increases with input RF powerand Rth


Temperature Variation

Temperature variations are small for CDMA source in the class A amp consideredhere.

Pout=29dBmPout=24dBm

RC5 and RC3 have converged,But RC1 is not accurate.

0.25 C1.25 CRC5

0.01 C1.5 CRC1

high frequency∆Tlow frequency∆T


Sensitivity of ACPR to Temperaturewith Predistorter

Sensitivity of ACPR

-67

-66.5

-66

-65.5

-65

-64.5

-64

-63.5

-63

-62.5

-62

30 35 40 45 50 55

Tdev (C)

AC

PR

(dB

c)

LACPR

HACPR0.36dB/C

0.42dB/C0.43dB/C

0.34dB/C

Measure ACPR vs.Tsub in RC0 model

Predistorter optimized at this temperature

Sensitivity is non-negligible


Class AB 60W Amplifier

4-port S-parameters are used to control the IF terminationwhich affects the electrical memory effects are reduced


ACPR Degradation for 60W PA

Up to 17 dB degradation of ACPR at low and high bandwidth

17 dB

LSB USB

AC

PR

Bandwidth (Hz) Bandwidth (Hz)


Results for Part II: Transient Thermal Modeling andMemory Effects in LDMOSFETs

• Transient thermal response can be obtained form FEM simulation or using anapproximate image method extended to predict the 3D transient thermal responseof a multi-layer LDMOSFET device.

• The comparison of 1, 3 and 5 stage RC thermal time constant models in circuitsimulations shows that the 3 and 5 stage RC models have essentially converged,and provide better accuracy in reporting both fast and slow temperaturefluctuations. Larger devices exhibit larger thermal delay.

• Thermal memory effects are found to be dominant over electrical memory effectswith bandwith below 100 and 10 kHz in 1W and 60W devices respectively.These thermal fluctuations can be easily handled using adaptive techniques.

• Electrical memory effects were found to dominate over thermal memory effectswith bandwidth over 1 MHz

• Dynamic thermal memory effects were demonstrated to have a negligible impacton the linearization of a class A and AB amplifers for wide bandwith sources.

• Fast electrical memory effects are the primary mechanism degrading thelinearization performance at wide bandwidth.


Part III: Experimental Results on Memory EffectsSetup used for the PA Characterization

Large signal network analyser

��

LSNAClock reference

I & Q

��

��

The vectorial source generator used(ESG 4438C) is synchronized with the LSNA10 MHz reference clock


• Class AB LD-MOSFET PA operating at 895 MHz

Amplifier Under Test

Gain: 13 dB, P1dB: 27.5dBm, PAE =34%,

13 dB Gain

3rd Order5th Order


)()(a

)(

1*

12

23

m

mm

a

bY

ωωωωω

+−

=−

()mω−ω( ωm)+2ω(

ω+ ω

ω

2bb22b

b2ω)( )m

m

1 ω)(a )1 mω+ω(a

RFRFPA

VDC

)()(a

)2(

12

1*

23

m

mm

a

bY

ωωωωω+

+=+

Extraction ofYm3-&Ym3+ using a 2-tone Signal

• Thea1 & b2 waves are measured with the LSNA

• Generalized Volterra coefficientsYm3- andYm3+ for IMD3:


•Comparison of amplitude ofYm3- andYm3+ versus the modulationfrequency�m for different power levels (-4 ~ 6 dBm).•The amplitude difference at 3 MHz tone spacing is up to 40%

Comparison of Amplitude ofYm3- andYm3+

-4 dBm

6 dBm 6 dBm

|Ym3-|

Modulation Frequency �m Modulation Frequency �m

|Ym3+|

-4 dBm


•Comparison of phase ofYm3- andYm3+ versus the modulationfrequency�m for different power levels (-4 ~ 6 dBm).•60� angle difference at 3MHz tone spacing: memory effects

Comparison of the Phase ofYm3- andYm3+

-4 dBm

6 dBm

-4 dBm

6 dBm

60�

Modulation Frequency �m

�Ym3- �Ym3+

Modulation Frequency �m


•The difference in amplitude and phase betweenYm3- andYm3+

is mostly significant above 0.3 MHz•Referred to as adifferential memory effect

Difference ofYm3- andYm3+

-4 dBm

6 dBm

-4 dBm

6 dBm

00 �

�(Ym3+- Ym3-)|Ym3+- Ym3-|

Modulation Frequency �mModulation Frequency �m


• Below 0.3 MHz the difference in phase and amplitudeof Ym3- andYm3+ is small in the PA under test

• Above 0.3 MHz the difference in phase and amplitudeincreases rapidly with tone spacing

• This indicates the presence of a strong differentialmemory effect between the LSB & USB for widebandwidth signals

• There is however no experimental evidence for a strongdifferential memory effect induced by self-heating.

Results from Part III on Non-LinearMeasurements

distributed and transient electro-thermal modeling and its

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