1

Distributed and Multi-Time-Constant Electro-thermal Modeling and Its Impact on RF Predistortion

Wenhua Dai, The Ohio State UniversityPatrick Roblin, The Ohio State University

Michel Frei, Agere Systems

2

Outline

• Introduction

• Electrical modeling

• Image method in thermal modeling

• Distributed thermal model

• Multi-time-constant thermal model

• Thermal memory effects in RF predistorter

• Conclusion

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Introduction•High power devices self-heat during operation, which affects its electrical performances.

•Most of the power device models use simple low pass RC circuit to model the self-heating

•The non-uniformly distributed temperature across the power device requires a model to capture the temperature distribution

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

•Memory effects are categorized into thermal and electrical memory effects. They are usually bonded together and it is difficult toquantify each of them separately.

•Temperature rise in a multilayer material involves fast and slowtime constants. Simple RC model can’t capture them.

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Thermal Rth Measurement

20 fingers6.34C/W

144 fingers1.44 C/W

Rth is obtained through steady state temperature measurement- the average value- nonlinear scaling to the device size

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Thermal Time Constant Measurement

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟⎟⎠

⎞⎜⎜⎝

⎛ −+=

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11 expexp)(

ττtAtAItI DCdsds

Thermal time constant is obtained through pulse IV measurement, Drain current decrease/increase due to the heating

- Measured rise time maybe affected by Cgs, Ls, and power supplier

- Two competing thermal effects (Vth, mobility) may cancel each other, resulting less thermal effects

Time (s)

I D(A

)

6x10-60

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Large Signal Electro-Thermal Model

Electrical part

Thermal part

G

S

D

Tsub

Tdev

•Nonlinear large signal electrical model

•IV characterization from both iso-thermal and pulse measurement

•S-parameter characterization from iso-thermal measurement

•Parasitics from cold FET measurement

•Simple RC circuit to model the temperature response

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Model Verification Through Loapull

Loadpull test bench

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Model Verification Through Amplifier

1 W amplifier

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Part I: Lateral Thermal Model

• 3D steady state temperature calculation

• Experimental Results

• ADS implementation

• Results

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Image Method for Steady State Temperature 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

Δ=

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 of power devices and circuits”

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Proposed Distributed Thermal Model

Mutual heat flow is modeled by mutual thermal resistance

Extraction from Rth matrix calculation through image method

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

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Distributed Electro-Thermal Model Reduction

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 matrix implemented in ADS

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Transient Simulation on 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

in C

urre

nt (A

)

Red – one-finger approximationMagenta – distributed 16 fingersBlue – distributed 8 fingers

5 10 15 20 25 30 350 40

30

40

50

60

70

80

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Time (msec)

Dev

ice

Tem

pera

ture

(C)

Center

Edge

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

•Temperature distribution is seen in distributed model

•Non-distributed model reports the averages temperature across the fingers

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

Drain current

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Part II: Transient Thermal Modeling and Memory effects

• Approximate transient response with image method

• Multistage RC model for ADS implementation

• Impact of transient thermal model on a RF amplifier with a predistorter

• Results for multisine excitation

• Results for IS95 CDMA excitation

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Image Method for Approximated Transient Temperature Rise in Multilayer Structure

∫ ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−⎟⎠⎞

⎜⎝⎛ −

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−⎟⎠⎞

⎜⎝⎛ −

=−L

uz

s duu

yYfu

yYfu

xXfu

xXfekqtzyxT

2

012122

2

4),,,(

π

( ) )(erf xxf =DtL =

Time dependent Green function of a rectangular heat source:

YY1 Y2

X1X2

X

Z

Approximation 1: when D1=D2, boundary condition is independent of time, so that image method can be usedApproximation 2: thermal conductivity of layer 2 is large enough

Layer 1

Layer 2 Boundary conditions:

( ) ( )+− === 11 ZZTZZT

Z1

For all t

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Transient Temperature Rise

Shift in time

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

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Proposed Multi-time-constant Thermal Model

Slow and fast transient temperature rise can be modeled

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

Extraction from transient temperature measurement/calculation

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Thermal Parameter ExtractionRth (Ohm) Cth (F)

1-stage 6.17 1.60e-53-stage 2.36 2.45e-6

2.98 7.38e-50.83 2.39

5-stage 1.16 1.29e-61.97 9.38e-62.18 1.24e-40.35 5.39e-10.51 8.89

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

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AmplifierTransistor model

Input matching

Thermal network

Output matching

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Two-tone SimulationTemperature at f2-f1

2KHzf =Δ 2MHzf =Δ

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

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RF-Predistortion Circuit

f0 = 880MHz

9-tone signal

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

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

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ACPR versus Multisine Bandwidth

Strong memory effects at low frequencies

Pout=P1dB-6=22dBm

Above 1MHz, electrical memory effects dominates

RC3 and RC5 convergesRC1 deviates

Distributed model gives the same ACPR as RC1 does

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Spectral Regrowth for a 1MHz Bandwidth Multisine}

In band

Upperadj

Loweradj

} }

Center freq: 880MHz9 tonesTone-spacing: 0.1MHz

Small differences between thermal models

tones9adjband ofpower total tones9inbandofpower total

=ACPR

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

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Spectral Regrowth for a 1KHz Bandwidth 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 to 3dB between thermal models

tones9adjband ofpower total tones9inbandofpower total

=ACPR

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IS95 CDMA simulationDirect RC0 RC1 RC3 RC5

LACPR (dBc) -44.2

-40.2

Pout (dBm) 28.1 24.1 24.0 24.0 24.0

-61.3 -61.6 -61.6 -61.6

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

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

Improved thermal model has a negligible effect for a class A with IS95

Power level: P1dB-4dB=24dBm

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

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Conditions for Strong Thermal Memory Effects

•ACPR needs to be strongly sensitive to fluctuations of the temperatureNote: ACPR is more sensitive to Delta T when using a predistorter (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 power and Rth

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Temperature Variation

Temperature variations are small for CDMA source in the class A amp studiedOther amplifiers need to be analyzed

Pout=29dBmPout=24dBm

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

low frequency ΔT high frequency ΔTRC1 1.5 C 0.01 C

RC5 1.25 C 0.25 C

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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)

ACPR

(dB

c)

LACPRHACPR0.36dB/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

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Conclusion

• An electro-thermal model for LDMOSFETs was extracted from RF and DC thermal measurement and implemented in ADS and used to design power amplifiers

• Various thermal models were then compared to establish the impact of the thermal memory effects on the predistortion linearization

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Results for Part I: Lateral Distributed Thermal model

• A recently reported image method for multilayer devices was implemented to study lateral distributed thermal effects in large multifinger devices.

• Model was implemented in ADS using a distributed lateral thermal model using a single RC time constant for each finger.

• Temperature distribution was reproduced. This is useful in applications where accurate temperature information is required.

• The overall electrical behavior can be modeled with enough accuracy by a non-distributed model reproducing the average temperature.

• Another application of distributed model is to predict the non-linear scaling of Rth with device area.

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Results for Part II: Transient Thermal Modeling for Memory Effect in LDMOSFETs

• An approximate image method was developed to predict the 3D transient thermal response of a multi-layer LDMOSFET device.

• Results obtained with the new model compares well with numerical results from transient FEM simulations.

• 1, 3 and 5 stage RC thermal models are compared. Simulations show that RC3 and RC5 converged, and have better accuracy in reporting fast and low temperature fluctuations.

• Thermal memory effects were found to be dominant over electrical memory effects with bandwith below 100KHz

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

• Thermal memory effects were demonstrated to have a negligible impact on the linearization of a class A amplifer for a IS95 CDMA source.

• The negligible impact of thermal memory effects on predistortion was verified to originate from the small temperature fluctuations (because of low Rth) and the low sensitivity of the LDMOSFET to these fluctuations.