A scalable GaN HEMT large-signal model for high-efficiency RF power amplifier design

Abstract

This paper presents a large-signal empirical model for GaN HEMT devices using an improved Angelov drain current formulation with self-heating effect and a modified non-linear capacitance model. The established model for small gate-width GaN HEMTs is validated by on-wafer load-pull measurements up to 14 GHz. Moreover, a scalable large-signal model is presented by adding scalable parameters to drain-source current and non-linear capacitance equations. The scalable model of a 1.25 mm GaN HEMT has been employed to design a class-AB power amplifier for validation purposes. The results show that good agreement has been achieved between the simulated and measured results with 37.2 dBm saturation output power (P sat) and 58% maximum power-added-efficiency at 3 GHz.

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A scalable GaN HEMT large-signal model
for high-efficiency RF power amplifier
design
Yuehang Xua, Wenli Fub, Changsi Wanga, Chunjiang Renc, Haiyan
Luc, Weibin Zhengd, Xuming Yud, Bo Yana & Ruimin Xua
a Fundamental Science on EHF Laboratory, University of Electronic
Science and Technology of China (UESTC), Chengdu 611731, P.R.
China
b National Key Laboratory of Science and Technology on Space
Microwave, China Academy of Space Technology (Xi’an), Xi’an
710100, China
c Science and Technology on Monolithic Integrated Circuits and
Modules Laboratory, Nanjing 210016, P.R. China
d Nanjing Electronic Devices Institute, Nanjing 210016, P.R. China
Published online: 03 Sep 2014.
To cite this article: Yuehang Xu, Wenli Fu, Changsi Wang, Chunjiang Ren, Haiyan Lu, Weibin
Zheng, Xuming Yu, Bo Yan & Ruimin Xu (2014): A scalable GaN HEMT large-signal model for high-
efficiency RF power amplifier design, Journal of Electromagnetic Waves and Applications, DOI:
10.1080/09205071.2014.947440
To link to this article: http://dx.doi.org/10.1080/09205071.2014.947440
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A scalable GaN HEMT large-signal model for high-efficiency RF
power amplifier design
Yuehang Xu
a
, Wenli Fu
b
*, Changsi Wang
a
, Chunjiang Ren
c
, Haiyan Lu
c
,
Weibin Zheng
d
, Xuming Yu
d
,BoYan
a
and Ruimin Xu
a
a
Fundamental Science on EHF Laboratory, University of Electronic Science and Technology of
China (UESTC), Chengdu 611731, P.R. China;
b
National Key Laboratory of Science and
Technology on Space Microwave, China Academy of Space Technology (Xi’an), Xi’an 710100,
China;
c
Science and Technology on Monolithic Integrated Circuits and Modules Laboratory,
Nanjing 210016, P.R. China;
d
Nanjing Electronic Devices Institute, Nanjing 210016, P.R. China
(Received 24 March 2013; accepted 16 July 2014)
This paper presents a large-signal empirical model for GaN HEMT devices using
an improved Angelov drain current formulation with self-heating effect and a modi-
fied non-linear capacitance model. The established model for small gate-width GaN
HEMTs is validated by on-wafer load-pull measurements up to 14 GHz. Moreover,
a scalable large-signal model is presented by adding scalable parameters to drain-
source current and non-linear capacitance equations. The scalable model of a
1.25 mm GaN HEMT has been employed to design a class-AB power amplifier for
validation purposes. The results show that good agreement has been achieved
between the simulated and measured results with 37.2 dBm saturation output power
(P
sat
) and 58% maximum power-added-efficiency at 3 GHz.
Keywords: GaN HEMT; large-signal empirical model; scalable model; power
amplifier
1. Introduction
Nowadays, GaN high-electron mobility transistors (HEMTs) are known to be promising
devices for high-efficiency microwave power amplifiers.[1–3] Accurate linear and non-
linear models are crucial for power amplifier design. Compared with the physical-based
model [4] and table based model,[5,6] the empirical large-signal equivalent circuit model
is more simple and easier to be implemented in commercial simulators and has been
widely used in circuit design.[7] Recently, the Angelov model has been extensively used
in microwave large-signal modelling of GaN HEMTs in consideration of its simplicity
and good accuracy compared with the EEHEMTs model.[8–10] However, the scalability
of the large-signal model has been sidelined, which is important in monolithic micro-
wave integrated circuit designing and power amplifier designing. And the accuracy of
large-signal model at small static DC current bias, which is useful for designing high
power-added-efficiency (PAE) power amplifier, is still unsatisfactory.[11]
In this paper, a large-signal model with an improved drain current model and a
modified non-linear capacitance model is presented. The large-signal model of small
gate-width (400 μm) devices is validated by wafer load-pull measurements up to 14 GHz.
*Corresponding author. Email: wlfu-193@163.com
© 2014 Taylor & Francis
Journal of Electromagnetic Waves and Applications, 2014
http://dx.doi.org/10.1080/09205071.2014.947440
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In addition, the scalability of the proposed model is established by adding scalable
parameters into the drain-source current and non-linear capacitance model, which is dif-
ferent from the conventional scalable modelling method in that the intrinsic elements are
scaled linearly with the periphery of the devices.[12–14] The complete scalable equiva-
lent circuit model is implemented into the Agilent Advanced Design System software.
The small gate-width devices used for modelling are 300 μm(4×75μm) and 400 μm
(4 × 100 μm) AlGaN/GaN HEMTs on SiC substrate with a gate length of 0.25 μm. The
DC current and associated S-parameters have been measured by varying V
ds
from 0 to
35 V with 2.5 V step and V
gs
from –4 to 0 V with 0.1 V step. The scattering parameters
are measured in the frequency range of 0.1–26.5 GHz.
2. Large-signal modelling
The bottom-up technique based on the small-signal equivalent circuit is used to build
the large-signal model for GaN HEMTs. This method has proved to be highly efficient
in modelling large-signal characteristics of FETs.[15–17] The results of the comparison
the measured and simulated S-parameters are shown in Figure 1. These results show
that excellent agreements have been achieved.
The topology of the large-signal model for GaN HEMTs is presented in Figure 2.
The non-linear elements in the model are: the drain source current (I
ds
), bias-dependent
gate-source capacitance (C
gs
) and gate-drain capacitance (C
gd
).
The proposed drain-source current I
ds
based on the Angelov model is given as
follows:
Ids ¼Ipk ð1þtanhðwÞÞ  expðkVdsÞtanhðaVds Þ 1kDT
T

(1)
w¼p1ðVgs VpkÞþp2ðVgs VpkÞ2þp3ðVgs Vpk Þ3(2)
Vpk ¼Vpk0 þcVds (3)
DT¼Rth Ids Vds (4)
Figure 1. Comparisons of simulated (solid line) and measured S-parameters (circle line) at
V
gs
=−2.8 V, V
ds
= 27.5 V in the frequency range from 1 to 20 GHz.
2Y. Xu et al.
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where V
ds
is the drain-to-source voltage, V
gs
is the gate-to-source voltage, I
pk
is the
drain current at which the transconductance is maximum, V
pk
is the gate voltage at
maximum transconductance,[18]λis the channel length modulation parameter and αis
the saturation voltage parameter. γis used to describe the weak dependence of V
pk
on
V
ds
in the saturated region. p
1
,p
2
and p
3
are fitting parameters. ΔTis the equivalent
temperature change and R
th
is the thermal resistance.[19] Figure 3shows comparisons
Figure 2. Large-signal model topology for GaN HEMTs including self-heating effect.
Figure 3. Comparison between calculated I–Vresults using proposed model and measurement
data (cricles) of 300 μm(4–75 μm) device.
Journal of Electromagnetic Waves and Applications 3
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of simulated and measured results. Good agreement has been achieved with the
consideration of the self-heating effect.
The modified models of C
gs
and C
gd,
based on the Angelov model, are given
below:
Cgs ¼Cgs0 þCgs0 ðM2þtanhð/1ÞÞð1þcosð/2ÞÞ þ M4ðVds ðVgs VpÞÞ (5)
/1¼P111 Vds þP112 Vds2þP113 Vds 3(6)
/2¼M1Vgs2þP21 Vgs þM5Vgs 3(7)
Cgd ¼Cgd0 þB1ð1þexpð/3ÞÞð0:2þexpð/4ÞÞ (8)
/3¼AVgs þB(9)
/4¼A1Vds þA0(10)
All the parameters in the equations are obtained by fitting the capacitance values
extracted from the small-signal model. The calculated parameters of drain-source cur-
rent and capacitance models are provided in Table 1. Figure 4shows the comparison
between the calculated and measured results of C
gs
and C
gd
.
3. Scalable large-signal model
A non-linear model of a 4 × 100 μm HEMT with the same process has been developed.
The non-linear model of the 4 × 100 μm GaN HEMT was assessed under large signal
excitations over an input power (P
in
) ranging from 0 to 19.5 dBm at 14 GHz. The output
power and PAE were measured under these excitations. Figure 5shows comparisons
between the measured and simulated large-signal characteristics, which indicate that the
model is capable of predicting large-signal behaviour. The scaling rules are listed in
Table 2, where the superscripts “sc”and “ref”indicate the scaled parameter and the
reference parameter, respectively. The scaling factors are defined as follows [20]:
SFX¼Wsc
g=Wref
g;SFY¼Nsc
g=Nref
g;(11)
where W
g
sc
,W
g
ref
,N
g
sc
,N
g
ref
are the gate widths and the number of gate fingers of the
scaled and reference devices, respectively. SF
X
is applied when there is a change of the
gate width along the direction of propagation. SF
Y
is applied when there is a change of
the number of paralleled fingers in the transverse direction.
Table 1. Parameters of drain-source current and gate capacitance models.
I
pk
/A 0.2255 p
1
0.3624 k 0.3388 V
pk0
/V −0.1023
λ0.032 p
2
0.0347 R
th
/K/W 8.37 γ0.0094
α1.1524 p
3
0.0559 M
5
0.12 P
21
0.21
C
gs0
/pF 0.068 P
111
0.007 C
gd0
/fF 0.8 A 0.1
M
1
0.27 P
112
0.003 A
0
1.25 B 4.1
M
4
9×10
−16
P
113
0.003 A
1
−0.18 B
1
0.813 × 10
−15
M
2
1.3
4Y. Xu et al.
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Figure 4. (a) The comparison results between calculation (solid line) and measurement
(symbols) results for the C
gs
. (b) The comparison results between calculation (solid line) and
measurement (symbols) results for the C
gd
.
Figure 5. Comparison of Measured (symbols) and simulated (lines) results with different input
powers at 14 GHz.
Table 2. Model scaling rules for GaN HEMT.
Extrinsic parameters Intrinsic parameters
R
g
sc
=R
g
ref
·SF
X
/SF
Y
C
ds
sc
=C
ds
ref
·SF
X
·SF
Y
I
pk
sc
=I
pk
ref
·SF
X
·SF
Y
R
d
sc
=R
d
ref
/SF
X
/SF
Y
R
i
sc
=R
i
ref
/SF
X
/SF
Y
lamda
sc
= lamda
ref
/SF
X
/SF
Y
R
s
sc
=R
s
ref
/SF
X
/SF
Y
C
gs0
sc
=C
gs0
ref
·SF
X
·SF
Y
R
th
sc
=R
th
ref
/SF
X
/SF
Y
L
i
sc
=L
i
ref
·SF
X
/SF
Y
A
sc
=A
ref
·SF
X
·SF
Y
gama
sc
= gama
ref
/SF
X
·SF
Y
(i=g,d,s)B
1
sc
=B
1
ref
·SF
X
·SF
Y
alpha
sc
= alpha
ref
·SF
X
/SF
Y
Journal of Electromagnetic Waves and Applications 5
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The non-linear model of the 10 × 125 μm HEMTs is obtained by exploiting the
scaling rules in Table 2. Considering the difficulty of on-wafer measuring, a class-AB
amplifier module, realized on a Taconic RF-60 substrate (ε
r
= 6.15, h= 0.635 mm),
has been designed for validation purposes. The design of the amplifier comprises gate
and drain bias networks, as well as synthesis of the input and output matching net-
works. The input and output impedances are 16.54 + j*23.88 and 78.352 + j*40.815,
which is determined by a load-pull simulation. The input and output fundamental
matching networks are achieved using a single L-section. The bias networks are com-
posed of a low-impedance bypass capacitor and a λ/4-line with 100-Ωcharacteristics
impedance to provide high impedance at RF. There is also a 56-Ωresistor at the gate
bias to enhance low-frequency stability. Figure 6shows the fabricated amplifier.
Single-tone large-signal measurements are performed for the amplifier at different
input driving levels. The corresponding simulated results have been compared with the
measurements, as shown in Figure 7. A fundamental output power of 37.2 dBm
Figure 6. Photograph of class-AB amplifier at 3 GHz using 10–125 μm GaN HEMTs.
Figure 7. Power sweep measurement (symbols) and simulation (lines) of the class-AB amplifier
at 3 GHz (V
ds0
=28V,V
gs0
=−2.6 V, IDS0 = 70 mA).
6Y. Xu et al.
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(5.2 W at P
sat
) and PAE of 58% has been measured at 3 GHz, and good agreement
between the simulated and measured fundamental output powers has been found, which
indicates the accuracy of the scaled non-linear model. Figure 8shows the measured
and simulated results of the second and thirdharmonic output power for the
4 × 100 μm GaN HEMT at 3 GHz, indicating that the developed scalable large-signal
model is also capable of predicting harmonic output power characterization.
4. Conclusions
A scalable large-signal model with self-heating effect for GaN HEMTs has been pre-
sented in this paper. The developed model is validated by on-wafer load-pull measure-
ment with 400 μm gate-width devices. A class-AB amplifier has been designed and
fabricated with the proposed scalable model for demonstration purposes. The results
show that good agreement has been achieved between the simulated and measured
results. The result of this paper is useful for high-efficiency GaN power amplifier
designing (i.e. class AB, class E, class F etc.).
Acknowledgements
The authors would like to render their thanks for the assistance and support of the National
Natural Science Foundation of China [grant number 61106115].
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