Distributed and Multi-TimeConstant Electro-thermal Modeling
and Its Impact on RF Predistortion
Wenhua Dai, The Ohio State University
Patrick Roblin, The Ohio State University
Michel Frei, Agere Systems
1
Outline
• Introduction
• Electrical modeling
• Image method in thermal modeling
• Distributed thermal model
• Multi-time-constant thermal model
• Thermal memory effects in RF predistorter
• Conclusion
2
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 to
quantify each of them separately.
•Temperature rise in a multilayer material involves fast and slow
time constants. Simple RC model can’t capture them.
3
Thermal Rth Measurement
20 fingers
6.34C/W
144 fingers
1.44 C/W
Rth is obtained through steady state temperature measurement
- the average value
- nonlinear scaling to the device size
4
Thermal Time Constant Measurement
⎛ −t ⎞
⎛ −t ⎞
I ds (t ) = I ds DC + A1 exp⎜⎜ ⎟⎟ + A2 exp⎜⎜ ⎟⎟
⎝ τ1 ⎠
⎝ τ2 ⎠
Thermal time constant is obtained
through pulse IV measurement,
Drain current decrease/increase due
to the heating
ID (A)
- 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
0
Time (s)
6x10-6
5
Large Signal Electro-Thermal Model
D
G
•Nonlinear large signal electrical model
•IV characterization from both iso-thermal
and pulse measurement
Electrical part
Thermal part
S
Tsub
•S-parameter characterization from isothermal measurement
•Parasitics from cold FET measurement
•Simple RC circuit to model the
temperature response
Tdev
6
Model Verification Through Loapull
Loadpull test bench
7
Model Verification Through Amplifier
1 W amplifier
8
Part I: Lateral Thermal Model
• 3D steady state temperature calculation
• Experimental Results
• ADS implementation
• Results
9
Image Method for Steady State
Temperature Field
P010
Green function:
air
0
P0
Z1
P01
Z2
P012
dT (r, r ' ) =
qs
dx' dy '
4π kΔr
adiabatic
Y
Layer 1
Layer 2
(
) (
T Z = Z1− = T Z = Z1+
B.C. :
)
Image sources are formed so that B.C be satisfied
Layer 3
P0
Z
P01
P02
P010
P02
P012
P020
Based on Rinaldi, N, “Generalized image method with application to
10
the thermal modeling of power devices and circuits”
P021
Proposed Distributed Thermal Model
Mutual heat flow is modeled
by mutual thermal resistance
Extraction from Rth matrix
calculation through image
method
P=1W
8 fingers
Heat Area=1.45mm x 1.27mm
Rth=1.67 C/W
11
Distributed Electro-Thermal Model
Reduction
Fingers are symmetrical to the center
Number of fingers is reduced by half
Each finger has its size doubled
Rth matrix folded, each Cth is doubled
⎡ R1,1 + R1,n
⎢
2
⎢
M
⎢R + R
n/2 , n
⎢ n/2,1
⎢⎣
2
Thermal Y matrix
implemented in ADS
12
R1,n/2 + R1,n/2+1 ⎤
⎥
2
⎥
O
M
Rn/2,n/2 + Rn/2,n/2+1 ⎥
⎥
L
⎥⎦
2
L
Device Temperature(C)
Transient Simulation on Distributed
Model
3 models: non-distributed,
distributed,
distributed half
Device Temperature
80
Center
70
60
50
Red – one-finger approximation
Magenta – distributed 16 fingers
Blue – distributed 8 fingers
Edge
40
30
20
0
5
10
15
20
25
30
35
40
Time (msec)
Drain current
Drain Current (A)
2.5
•Temperature distribution is seen in
distributed model
•Non-distributed model reports the
averages temperature across the fingers
2.0
1.5
•Overall electrical behavior is consistent,
indicating the non-distributed model has
enough accuracy
1.0
0.5
0.0
0
5
10
15
20
25
Time (msec)
30
35
40
13
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
14
Image Method for Approximated Transient
Temperature Rise in Multilayer Structure
Time dependent Green function of a rectangular heat source:
qs
T ( x, y , z , t ) =
4k π
X
X2
Y1 Y2
Layer 1
Z1
Layer 2
Z
0
−
e
z2
u2
⎡ ⎛ X2 − x ⎞
⎛ Y1 − y ⎞⎤
⎛ X 1 − x ⎞⎤ ⎡ ⎛ Y2 − y ⎞
⎢ f ⎜ u ⎟ − f ⎜ u ⎟⎥ ⎢ f ⎜ u ⎟ − f ⎜ u ⎟⎥ du
⎠⎦
⎝
⎠⎦ ⎣ ⎝
⎠
⎝
⎠
⎣ ⎝
f (x ) = erf ( x)
Y
X1
∫
2L
L = Dt
Boundary conditions:
(
) (
T Z = Z1− = T Z = Z1+
)
For all t
Approximation 1: when D1=D2, boundary condition is
independent of time, so that image method can be used
Approximation 2: thermal conductivity of layer 2 is large
enough
15
Transient Temperature Rise
Shift in time
FEM provides ‘true’ temperature response, long computation time
Image method provides approximated solution
16
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
17
Thermal Parameter Extraction
Rth (Ohm) Cth (F)
1-stage
6.17
1.60e-5
3-stage
2.36
2.45e-6
2.98
7.38e-5
0.83
2.39
1.16
1.29e-6
1.97
9.38e-6
2.18
1.24e-4
0.35
5.39e-1
0.51
8.89
5-stage
Extracts Rth and Cth by curve fitting in log scale
Constraint total Rth constant
18
Amplifier
Transistor model
Output matching
Input matching
Thermal network
19
Two-tone Simulation
Temperature at f2-f1
Δf = 2KHz
Temperature at f2-f1
IMD3
Δf = 2MHz
•Low modulation frequency generates bigger temperature variation
•Temperature variations are too small to affect the electrical behavior (IMD3)
•Class A amplifier less sensitive
20
RF-Predistortion Circuit
9-tone
signal
f0 = 880MHz
RF predistorter is expected to be more sensitive
to low frequency temperature variation
21
RF-Predistorter in ADS
9-tone source signal
Newman’s Phase (1965)
f0=880MHz
PAR=2.6
22
ACPR versus Multisine Bandwidth
Pout=P1dB-6=22dBm
Above 1MHz,
electrical memory
effects dominates
Strong memory
effects at low
frequencies
Distributed model gives the
same ACPR as RC1 does
RC3 and RC5 converges
RC1 deviates
23
Spectral Regrowth for a 1MHz
Bandwidth Multisine
}
Center freq: 880MHz
9 tones
Tone-spacing: 0.1MHz
In band
}
Lower
adj
}
Upper
adj
Pout
no pred 24.08
with pred 21.88
Lacpr
-31.14
-66.59
Uacpr
-31.12
-66.47
Small differences
between thermal models
ACPR =
total power of inband 9 tones
total power of adjband 9 tones
24
Spectral Regrowth for a 1KHz
Bandwidth Multisine
Center freq: 880MHz
9 tones
Tone-spacing: 0.1KHz
Pout
no pred 24.08
RC1 pred 21.88
RC5 pred 21.88
Lacpr
-31.25
-63.27
-64.17
Uacpr
-31.32
-63.46
-66.39
Noticeable differences up to
3dB between thermal models
ACPR =
total power of inband 9 tones
total power of adjband 9 tones
25
IS95 CDMA simulation
Power level: P1dB-4dB=24dBm
Direct
RC0
RC1
RC3
RC5
LACPR (dBc)
-44.2
-61.3
-61.6
-61.6
-61.6
HACPR (dBc)
-40.2
-58.9
-59.4
-59.4
-59.4
28.1
24.1
24.0
24.0
24.0
Pout (dBm)
** ACPR defined as power ratio of 30KHz
adjband to 1.2288MHz inband
Env simulation of IS95 CDMA signal
Bandwidth: 1.2288MHz
Time: 0 – 0.833ms
Freq resolution: 2.4KHz
Frequency span: 5MHz
Input PAR: 7.39
Improved thermal model has a negligible
effect for a class A with IS95
26
Conditions for Strong Thermal
Memory Effects
•ACPR needs to be strongly sensitive to fluctuations
of the temperature
Note: 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
27
Temperature Variation
Pout=24dBm
Pout=29dBm
low frequency ΔT
RC5 and RC3 have converged,
But RC1 is not accurate.
high frequency ΔT
RC1
1.5 C
0.01 C
RC5
1.25 C
0.25 C
Temperature variations are small for CDMA source in the class A amp studied
Other amplifiers need to be analyzed
28
Sensitivity of ACPR to Temperature
with Predistorter
Sensitivity of ACPR
Measure ACPR vs.
Tsub in RC0 model
-62
-62.5
-63
0.43dB/C
ACPR (dBc)
-63.5
0.42dB/C
-64
LACPR
-64.5
HACPR
0.36dB/C
-65
0.34dB/C
-65.5
-66
-66.5
-67
30
35
40
45
50
55
Tdev (C)
Predistorter optimized at this temperature
29
Sensitivity is nonnegligible
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
30
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.
31
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.
32