1. Distributed and Multi-Time-Constant 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

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

3. 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.

4. 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

5. Thermal Time Constant Measurement
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
ID (A)
6x10-6
Time (s)

6. Large Signal Electro-Thermal Model
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
Electrical part S
Thermal part
Tsub
Tdev

7. Model Verification Through Loapull
Loadpull test bench

8. Model Verification Through Amplifier
1 W amplifier

9. Part I: Lateral Thermal Model
3D steady state temperature calculation
Experimental Results
ADS implementation
Results

10. Image Method for Steady State Temperature Field
Green function:
air
adiabatic P0 Y
B.C. :
Layer 1 Z1
P01
Layer 2
Image sources are formed so that B.C be satisfied Z2
P012
Layer 3 P0
P01
P02
P010
P012
P020
P021 Z
P02
Based on Rinaldi, N, “Generalized image method with application to the thermal modeling of power devices and circuits”

11. 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

12. 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
Thermal Y matrix implemented in ADS

13. Transient Simulation on Distributed Model
Device Temperature
3 models: non-distributed,
distributed,
distributed half 5 10 15 20 25 30 35 40 50 60 70 80
Time (msec)
Device Temperature(C)
Center
Edge
Red – one-finger approximation
Magenta – distributed 16 fingers
Blue – distributed 8 fingers
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

14. 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

15. Image Method for Approximated Transient Temperature Rise in Multilayer Structure
Time dependent Green function of a rectangular heat source: X X2 X1 Y Y1 Y2
Layer 1 Z1
Boundary conditions:
Layer 2
For all t Z
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

16. Transient Temperature Rise
Shift in time
FEM provides ‘true’ temperature response, long computation time
Image method provides approximated solution

17. 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

18. 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
5-stage
1.16
1.29e-6
1.97
9.38e-6
2.18
1.24e-4
0.35
5.39e-1
0.51
8.89
Extracts Rth and Cth by curve fitting in log scale
Constraint total Rth constant

19. Amplifier Transistor model Output matching Input matching
Thermal network

20. Two-tone Simulation Temperature at f2-f1 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

21. RF-Predistortion Circuit
9-tone
signal
f0 = 880MHz
RF predistorter is expected to be more sensitive to low frequency temperature variation

22. RF-Predistorter in ADS
9-tone source signal
Newman’s Phase (1965)
f0=880MHz
PAR=2.6

23. 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

24. Spectral Regrowth for a 1MHz Bandwidth Multisine
In band
Upper
adj
Lower
Center freq: 880MHz
9 tones
Tone-spacing: 0.1MHz
Pout Lacpr Uacpr
no pred
with pred
Small differences between thermal models

25. Spectral Regrowth for a 1KHz Bandwidth Multisine
Center freq: 880MHz
9 tones
Tone-spacing: 0.1KHz
Pout Lacpr Uacpr
no pred
RC1 pred
RC5 pred
Noticeable differences up to 3dB between thermal models

26. IS95 CDMA simulation Power level: P1dB-4dB=24dBm
Direct
RC0
RC1
RC3
RC5
LACPR (dBc)
-44.2
-61.3
-61.6
HACPR (dBc)
-40.2
-58.9
-59.4
Pout (dBm)
28.1
24.1
24.0
** ACPR defined as power ratio of 30KHz adjband to MHz inband
Env simulation of IS95 CDMA signal
Bandwidth: MHz
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

27. 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

28. Temperature Variation
Pout=24dBm
Pout=29dBm
low frequency T
high frequency T
RC1
1.5 C
0.01 C
RC5
1.25 C
0.25 C
RC5 and RC3 have converged,
But RC1 is not accurate.
Temperature variations are small for CDMA source in the class A amp studied
Other amplifiers need to be analyzed

29. Sensitivity of ACPR to Temperature with Predistorter
0.36dB/C
0.42dB/C
0.43dB/C
0.34dB/C
Measure ACPR vs. Tsub in RC0 model
Sensitivity is non-negligible
Predistorter optimized at this temperature

30. 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

31. 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.

32. 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.