distributed and transient electro-thermal modeling and its
TRANSCRIPT
1MISES Non-Linear RF Lab
Distributed and TransientElectro-thermal Modeling and Its
Impact on RF Predistortion
Patrick Roblin*Wenhua Dai
*The Ohio State University
2MISES Non-Linear RF Lab
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
3MISES Non-Linear RF Lab
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.
4MISES Non-Linear RF Lab
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
5MISES Non-Linear RF Lab
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
6MISES Non-Linear RF Lab
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
7MISES Non-Linear RF Lab
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
8MISES Non-Linear RF Lab
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
9MISES Non-Linear RF Lab
Model Verification Through Loapull
Loadpull test bench
10MISES Non-Linear RF Lab
Model Verification using the HarmonicResponse of an Amplifier
1 W amplifier
11MISES Non-Linear RF Lab
Part I: Lateral Thermal Model
• 3D steady state temperature calculation
• Experimental Results
• ADS implementation
• Results
12MISES Non-Linear RF Lab
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.
13MISES Non-Linear RF Lab
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.
14MISES Non-Linear RF Lab
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
15MISES Non-Linear RF Lab
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
16MISES Non-Linear RF Lab
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
17MISES Non-Linear RF Lab
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.
18MISES Non-Linear RF Lab
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
19MISES Non-Linear RF Lab
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
20MISES Non-Linear RF Lab
Transient Temperature Rise
Shift in time
FEM provides ‘true’ temperature response, long computation timeImage method provides approximated solution
21MISES Non-Linear RF Lab
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
22MISES Non-Linear RF Lab
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
23MISES Non-Linear RF Lab
Amplifier
Transistor model
Input matching
Thermal network
Output matching
24MISES Non-Linear RF Lab
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
25MISES Non-Linear RF Lab
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
30W LDMOS, Z1=300um, Rth=0.48C/W, Area=6.9e6 um2
60W LDMOS, Z1=50um, Rth=1.1C/W, Area=1.1e6 um2
The thermal RC timeconstant increases with thedevice area or with thinnerSilicon layer.
26MISES Non-Linear RF Lab
Impact of Thermal Memory Effectson RF-Predistortion
f0 = 880MHz
RF predistorter is expected to be more sensitiveto low frequency temperature variation
9-tonesignal
27MISES Non-Linear RF Lab
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 :
28MISES Non-Linear RF Lab
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
29MISES Non-Linear RF Lab
RF-Predistorter in ADS9-tone source signalNewman’s Phase (1965)f0=880MHzPAR=2.6
30MISES Non-Linear RF Lab
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
31MISES Non-Linear RF Lab
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
32MISES Non-Linear RF Lab
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
33MISES Non-Linear RF Lab
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
34MISES Non-Linear RF Lab
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
35MISES Non-Linear RF Lab
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
36MISES Non-Linear RF Lab
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
37MISES Non-Linear RF Lab
Class AB 60W Amplifier
4-port S-parameters are used to control the IF terminationwhich affects the electrical memory effects are reduced
38MISES Non-Linear RF Lab
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)
39MISES Non-Linear RF Lab
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.
40MISES Non-Linear RF Lab
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
41MISES Non-Linear RF Lab
• 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
42MISES Non-Linear RF Lab
)()(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:
43MISES Non-Linear RF Lab
•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
44MISES Non-Linear RF Lab
•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
45MISES Non-Linear RF Lab
•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
46MISES Non-Linear RF Lab
• 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