Large-signal PHEMT and HBT modeling for power amplifier ...pasymposium.ucsd.edu/papers2002/CJWei2002PAWorkshop.pdf · Large-signal PHEMT and HBT modeling for power amplifier applications

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


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)


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



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


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


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


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)


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

Documents

Large-signal PHEMT and HBT modeling for power amplifier ...pasymposium.ucsd.edu/papers2002/CJWei2002PAWorkshop.pdf · Large-signal PHEMT and HBT modeling for power amplifier applications