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Large-signal PHEMT and HBT modeling for power amplifier applications
Ce-Jun WeiSkyworks Inc.
Sept. 9 2002
Agenda
• Introduction• Phemt modeling issues• Empirical model vs table-based model; Charge model vs ‘no-charge’ model• Class-inverse-F operation of power PHEMTs• Models of III-V-based HBTs
• Modofied GP model• VBIC model• Modified VBIC model• Thermal coupling model
• Small-signal and large-signal HBT model verification• HBT modeling application to power amplifier
Challenges of modeling for power amplifier designs
• PHEMT/HBTs feature higher efficiency, high frequency and good linearity and are being widely used in power amplifiers for wireless communications
• Commercial models are difficult to predict consistent small-signal and large-signal power performance including linearity.
The requirements for a good model are:• Must be capable of reproducing three-terminal dc IV curves over wide range and
possible IV collapses• Must be capable of fitting measured S-parameters over a wide bias range• Must accurately predict power, efficiency and linearity • Must be able to predict load-pull behavior• Must be scaleable to large-size used in power amplifiers• Good convergence
PHEMT modeling issue: Self-heating
• Positive RF Gds but Negative DC Gdso at Higher Power Dissipation Region
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Vds (V)
Id A
)
PHEMT modeling issue: I-V dispersion
• - DC-IV Does Not Mean Equal to RF-IV• -RF IVs That Fit RF Gm and RF Gds Differ From Each Other
0.0
0.1
0.2
0.3
0.4
0.0 2.0 4.0 6.0Vds (V)
Id A
)
0.0
0.1
0.2
0.3
0.4
0 2 4 6Vds (V)
Igm
(A
)
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0 2 4 6Vds (V)Ig
ds
(A
)
DC IV RF IV That Fits RF Gm RF IV That Fits RF Gds
PHEMT modeling issue: Charge Conservation?
• 2d-charge Qg Can Be Integrated From Extracted (Based on Measurement Data)Cgs(vgs,vgd) and Cgd(vgs,vgd) and Should Be Path-independent
Charge Conservation or Path Independence Rule Requires:Qg= ƒ(Cgs dvgs + Cgd dVgd )
∂ Cgs/ ∂ Vgd= ∂ Cgd/ ∂ Vgs
For Small Size Devices and No Significant Dispersion, Path Independence Does Hold. In general, it does not hold, because of improper equivalent circuit
PHEMT modeling issue: consistence and others
• A derived small-signal model from the large-signal model must be consistent with small-signal models over a wide range of biases
• 2D QV Functions in Large-signal Model Introduce Additional Trans-capacitances that do not exist in small-signal models
• Be continuous up to at least third derivatives of IV and QV curves
• Accurate gate current model including leakage and breakdown
Qgd(Vgs,Vgd)
Qgs(Vgs,Vgd)
Empirical model verses Table-based model
• Both models use simple �-shaped intrinsic equivalent circuit• Both models use IV and QV characteristics and assume path-independence• Both models use simple linear or nonlinear RC-type circuit on drain side to
account for low-frequency dispersion• Empirical models have advantages of approximate mapping onto device
physical structure, large-dynamic range independent of measurement range. Their disadvantage is accuracy.
• Table-based models have advantages of least-parameter-extraction, technology-independence, accuracy but the disadvantages are: slower convergence, limited validity in its measurement range in extraction.
Dispersion model of PHEMTs
• Instead of Using RC Branch in Drain Port, Alpha Model Uses a Feed-back and Feed-forward Circuit to Modify the RF Gds and RF Gm.
• Self-heating Effects Are Modeled by a Sub-thermal-circuit and a Coefficient of Id Modification
Qgd
Qgs CdsVgs
Vrf Rrf
Crf
= Id (1-exp(-ct Vth))Id(Vgt,Vds)
VCVS
VCVS
S
Cfb Vrf
� Id
Rg Lg Rd Ld
Ls Rs
Vgt
CthIth=Vds Id Rth
Vth Thermal Sub-circuit
Self-heatingInduced Current
Feedback
Gm=+GmoCfb
Gds=+GdsoCbk
Feed-forward
‘No-Charge’ model• Use Capacitive Current
Sources to Replace Charge Sources
• Create a Virtual Node (Voltages dv_dt) That Are Proportional to Time-derivative of Vgs or Vgd. The Capacitance Current, C(Vs)*dV_dt , Is the Nonlinear Function ofVgs,vgd and dV_dt
igd
igsids
Cgd dVgd/dt
Cgs dVgs/dt
+-
V
CSVS (1/C)
C dv/dt
Charge model verses ‘Non-charge’ model
• No extra trans-capacitances are involved• Complete and one-by-one-correspondence consistence with small-
signal models over all bias-points measured• Care must be taken to avoid average component of capacitive
currents. Use CR broke circuit for each current • Charge model is still better in convergence.• Both models can be table-based or empirical.
Application: 2-tone Load-pull Simulation
m1
indep(PAE_contours_p) (0.000 to 6.000)
PAE_contours_p
m1
indep(Pdel_contours_p) (0.000 to 57.000)
Pdel_contours_p
m2
-83.437 -100.154
Minimum 5th-OrderIMD, dBc
Minimum 3rd-OrderIMD, dBcm1
indep(m1)=6PAE_contours_p=0.728 / 141.714level=3.252045, number=1impedance = Z0 * (0.176 + j0.338)
• The Results Are Verified by Comparing the Measured at Several PointsThirdOlevel=-impeda
indep(ThirdOrdIMD_contours_p) (0.000 to 31.000)
ThirdOrdIMD_contours_p
m3
indep(FifthOrdIMD_contours_p) (0.000 to 27.000)
FifthOrdIMD_contours_p
Gain TMD & FMDGain Unchanged
but TMD Improved by
8 dB
Application: Waveform at Inverse-F and Class-F Operation
-2
0
2
4
6
8
10
12
0 200 400 600 800 1000 1200
Time (ps)
Vd
s (
V)
-100
-50
0
50
100
150
200
250
300
Id (
mA
)
-50
0
50
100
150
200
250
0 200 400 600 800 1000
Phase (rad) at 0.938GHz
Vd
s (V
)
012345678
Id (m
A)
Class Inverse-F (PAE 80%) Class F (PAE 69%)2nd: open; 3rd: short 2nd: short; 3rd: open
Vds = 3.2 V Vg = -0.88 V (Inverse F), Vg = -1.1 V (Class-F), Total Wg = 2 mmSymbol: Measured Line: Modeled
Application: load-line of ideal Inverse-F and Class-F Operation
High PAE Requirement: - Id � 0 when Vd swings, Vd minimized , when Id swings
- fast transit for Id*Vd � 0 (broken line)
Class F: visit more time on resistive loss area than clss inverse-F
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10
Vds (V)
Ids
(A)
Class IF
Class F
Bias point
HBT modeling
• Most hand-set PA’s are using HBTs• The advantages over PHEMTs: unipolar DC supply,
uniformity and high yield, linearity. Caution must be taken on thermal management
• Commercial and non-conmercial models- Commercial models: GP, � VBIC, Mextram, Hicum- Non-commercial models: � Modified-GP, � Modified-VBIC or others
VBIC model and features
• �Self-heating• � Separation of the
transfer current and base current
• External BE diode• Parasitic PNP• Early effect on Tf• Quasi-saturation• � Comprehensive
Temperature-dependent parameters
Modified GP model and features• �major Self-heating effects including nonlinear terms• � Separation of the transfer current and base current• � Comprehensive Temperature-dependent parameters• � Additional terminal for thermal coupling simulation
E
dTj
C
B
C1R1SRC1
CSRC2
CSRC1
RbCdbeCjbe
CdbcCjbcDbc
Re
Rcx
Cjbc1
RbiDbei
Dbce
Icc-Iee
Dbep
Tf and Cbc characteristics that commercial models can not fit
0.00E+00
1.00E+10
2.00E+10
3.00E+10
4.00E+10
5.00E+10
6.00E+10
0 0.01 0.02 0.03 0.04
Collector current (A)
Cu
roff
fre
qu
en
cy (
Hz)
Vcb
1.0E-14
1.0E-13
1.0E-12
1.0E-110 0.05 0.1 0.15
Collector current (A)
Ba
se
-co
llec
tor
ca
pa
cit
an
ce
(F
)measured
Ft as function of Vcb & IcVcb=-0.8, & -0.5 to 4 V step 0.5 V
Cbc as finction of Vbc & IcVbc=0.5 to 3.5 V step 0.5 V
Modified VBIC model and features• �Self-heating• � accurate Tf model to
account for ft drop at higher current (Kirk Effect)
• � Vbc & Ic dependent Cbc due to mobile-charge modulation and Kirk Effect
• � Implemented with SDD in ADS
Tj
ELE RE Rth
VCVS
1PF
VAR1EqnVar
Idvbcdt
C
MOD_VBIC
RCI
RCX
LC
LBRBRBI
B
_VAR2EqnVar
Ic-Vc and Vb-Vc curves at constant Ib modeled vs measured
Ae=56um^2 Ic-Vc Vb-Vc
1 2 3 40 5
0.00
0.01
0.02
0.03
0.04
-0.01
0.05
Vc
IC.i
Ic_m
eas.
iIc
_mea
s2.i
Ic_m
eas3
.iIc
_mea
s4.i
Ic_m
eas5
.iIc
_mea
s6.i
Ic_m
eas7
.iIc
_mea
s8.i
Ic_m
eas9
.iIc
_mea
s10.
i
Symbol:Modeled, Solid line:Measured
1 2 3 40 5
0.025
0.030
0.035
0.040
0.020
0.045
VDS
I_Ic
.i, A
VCva
r("d
atas
etN
ame.
.IT-3
0")
var(
"dat
aset
Nam
e..IT
-20"
)va
r("d
atas
etN
ame.
.IT-1
0")
data
setN
ame.
.IT0
data
setN
ame.
.IT10
data
setN
ame.
.IT20
data
setN
ame.
.IT30
data
setN
ame.
.IT40
data
setN
ame.
.IT50
data
setN
ame.
.IT60
data
setN
ame.
.IT70
Modified VBIC fits ft at higher current
Ft as function of Vcb & Ic Vcb=0V Solid line: Modified VBIC Broken line: VBIC model
0.00E+00
1.00E+10
2.00E+10
3.00E+10
4.00E+10
5.00E+10
6.00E+10
7.00E+10
0.0 10.0 20.0 30.0 40.0
Ic (mA) at Vcb=0 V
cuto
ff f
req
uen
cy (
Hz)
ft-modelft_measft-vbic
IV collapse modeled vs measured
Ae=960 um2 Ib=0.4mA to 4.4 mA step 0.4mA
simulated measured
1 2 3 40 5
0
100
200
300
400
-100
500
VDS
IDS
.i, m
A
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5
Vc (V)
Ic-m
eas
(A)
Power performance Modeled vs Measured
m1Pin=-19.000Gain=18.283
-15 -10 -5 0 5-20 10
0
5
10
15
20
-5
25
10
20
30
40
50
0
60
Pin
Gai
n
m1
PA
E
Pou
tva
r("P
swee
p..G
ain"
)va
r("P
Sw
eep.
.Pou
t") P
sweep..E
fficiency
V27 H1503-901 720um^2 Vc=3.2V Ic=7.54mA
Harmonics performance Modeled vs Measured
V27 H1503-901 60um^2 Vc=3.5V Ic=7mA
-30 -25 -20 -15 -10-35 -5
-60
-40
-20
0
-80
20
Pin
f1f2f3L
oadP
ull_
VB
IC..f
1L
oadP
ull_
VB
IC..f
2L
oadP
ull_
VB
IC..f
3
Pin_meas
dat
ase
tNa
me.
.PO
ut_
mea
sva
r("d
atas
etN
am
e..2
F1"
)va
r("d
atas
etN
am
e..3
F1"
)
Vc=3.5 V Vb=1.357 V
Ic=6.98 mA Rbext=600ohm
Source: f1: 0.78�26.7
F2: 0.6 �6.8
F3: 0.17 �168
Load: f1 0.32 �26.7
F2: 0.77 �-88.4
F3: 0.67 �-137.5
Symbol:measured, solid line:new model, broken lin:VBIC
IM3 & IM5 performance Modeled vs Measured
V27 H1503-901 60um^2 Vc=3.5V Ic=7mA
Vc=3.5 V Vb=1.357 V
Ic=6.98 mA Rbext=600ohm
Source: f1: 0.78�26.7
F2: 0.6 �6.8
F3: 0.17 �168
Load: f1 0.32 �26.7
F2: 0.77 �-88.4
F3: 0.67 �-137.5-30 -25 -20 -15 -10-35 -5
-60
-40
-20
0
-80
20
Pin
Pou
tIM
3HIM
3LIM
5HIM
5Ltw
oton
e_M
TF
Q..
IM3H
twot
one_
MT
FQ
..IM
3Ltw
oton
e_M
TF
Q..
IM5H
twot
one_
MT
FQ
..IM
5Ltw
oton
e_M
TF
Q..
Pou
tM
AX
PA
E..
IM3H
MA
XP
AE
..IM
3LM
AX
PA
E..
IM5H
MA
XP
AE
..IM
5LM
AX
PA
E..
Po1
Symbol:measured, solid line:new model, broken lin:VBIC
Linearity improves for punch-through structure
28.841 30.157 31.473 32.789 34.105 35.421 36.736 38.052 39.368 40.684 above
Punch-throughPunchPunch--throughthrough
Pout load-pull, Modeled vs Measured
V27 H1503-901 720um^2 Vc=3.2V Ic=37mA Pin=0dBm Gamm(2)=0.52<-117
Pout_step=1
Range8 : >max-1
Range9 �: max-2
Range10 �: max-3
Range11 �: max-5
Range12 �: max-7
Range13 ◇:max-10
Range13 � :max-15
Max=21.4
indep(Pdel_contours_p) (0.000 to 41.000)
Pd
el_
con
tou
rs_
p
(0.000 to 126.000)
ran
ge
8ra
ng
e9
rang
e1
0ra
nge
11
rang
e1
2ra
nge
13
rang
e1
4
21.78
Maximum PowerDelivered, dBm
PAE load-pull, Modeled vs Measured
V27 H1503-901 720um^2 Vc=3.2V Ic=37mA Pin=0dBm Gamm(2)=0.52<-117
PAE_step=5
range1 : >max-6
range2 � : max-15
range3 � : max-25
range4 � : max-35
range5 � : max-45
range6◇:max-55
Max=61.6indep(PAE_contours_p) (0.000 to 49.000)
PA
E_c
onto
urs_
p
(0.000 to 126.000)
rang
e1ra
nge2
rang
e3ra
nge4
rang
e5ra
nge6
rang
e7
61.67
Maximum Power-AddedEfficiency, %
IM3 load-pull, Modeled vs Measured
V27 H1503-901 720um^2 Vc=3.2V Ic=37mAPin=0dBm Gamm(2)=0.52<-117
m3indep(m3)=4ThirdOrdIMD_contours_p=0.679 / 13level=-6.539738, number=2impedance = Z0 * (0.223 + j0.395)
indep(ThirdOrdIMD_contours_p) (0.000 to 29.000)
Th
ird
Ord
IMD
_co
nto
urs
_p
m3
(0.000 to 108.000)
rang
e1
rang
e2
rang
e3
rang
e5
rang
e6
rang
e4
5.1
IM3_modeled_step=2
range1 : -18� -16
range2: � -16� -14
range3 � : -14� -12
Range4 +: -12� -10
Range5 x: -10� -8
Ranger6 �:>-8
PAE load-pull for 2nd harmonic, Modeled vs Measured
V27 H1503-901 720um^2 Vc=3.2V Ic=37mAPin=3dBm Gamm(1)=0.558<111
PAE_modeled_step=2.5
range1 : max-3� max
range2 � : max-6 � max-3
range3 � : max-10� max-6
range4 � : max-15� max-10
range5 � : max-20� max-15
ranger6◇:<max-20
Max=56.7
60.99
Maximum Cal.PAE, %
indep(PAE_contours_p) (0.000 to 24.000)
PA
E_c
onto
urs_
p
(0.000 to 126.000)
rang
e1ra
nge2
rang
e3ra
nge4
rang
e5ra
nge6
rang
e7
No obvious difference of class F and inverse-F!
Pout load-pull for 2nd harmonic, Modeled vs Measured
V27 H1503-901 720um^2 Vc=3.2V Ic=37mAPin=3dBm Gamm(1)=0.558<111
For Pout inverse-F is better than class F!
Pout_modeled_step=0.5
Range8 : 19.9� 20.9
range9 � : 18.9� 19.9
range10 � : 17.9� 18.9
range11 � : 15.9� 17.9
range12: 13.9� 15.9
range13: 10.9� 13.9
ranger13: <10.9
indep(Pdel_contours_p) (0.000 to 23.000)
Pde
l_co
ntou
rs_p
(0.000 to 126.000)
rang
e8ra
nge9
rang
e10
rang
e11
rang
e12
rang
e13
rang
e14
21.90
Maximum Cal. Pout, dBm
IM3 load-pull for 2nd harmonic, Modeled vs Measured
V27 H1503-901 720um^2 Vc=3.2V Ic=37mAPin=3dBm Gamm(1)=0.558<111
For IM3 inverse-F is also better than class F!
m1indep(m1)=3ThirdOrdIMD_contours_p=0.736 / 19.224level=-10.834816, number=1impedance = Z0 * (3.019 + j3.197)
indep(ThirdOrdIMD_contours_p) (0.000 to 27.000)
Th
ird
Ord
IMD
_co
nto
urs
_p
m1
(0.000 to 126.000)
ran
ge1
ran
ge2
ran
ge3
ran
ge5
ran
ge6
ran
ge4
-11.685
Minimum 3rd-OrderIMD, dBc
IM3_modeled_step=0.5
range1 : -13� -12.5
range2 � : -12.5� -12
range3 � : -12� -11
Range4 +: -11� -10
Range5 x: -10� -8
ranger6:>-8
Conclusion
• The problems with conventional large-signal PHEMT models are addressed that include: dispersion, ‘non-charge-conservation’ originated from use of simple equivalent circuit, etc
• Dispersion and ‘no-charge’ models are presented that overcome the difficulties• The issues in HBT modeling in terms of mobile charge-modulation and Kirk
effects are addressed and modified MP and VBIC models are presented• The models are verified with comprehensive load-pull results• Class inverse-F with 2nd harmonic tuned at high impedance is recommended for
PHEMT PA design due to its higher PAE over class-F and is likely useful due to its better linearity for HBT power amplifiers.
Acknowledgement
• Dr. Gene Tkachenko, Dr. Ding Dai for his support• Significant contribution by Dr. G. Tkachenko, A. Klimashow, J, Gering
and D. Bartle
