Frequency and temperature dependence of gain compression inGaN/AlGaN HEMT amplifiers

Arif Ahmed, Syed S. Islam, A.F.M. Anwar *

Department of Electrical and Computer Engineering, University of Connecticut, 260 Glenbrook Road, Storrs, CT 06269-2157, USA

Received 19 March 2002; received in revised form 12 April 2002; accepted 16 April 2002

Abstract

Volterra series analysis is used to determine gain and output power of GaN HEMT amplifiers. Gain compression

defined as the difference between linear and nonlinear gain is reported for varying temperatures. Measured 1-dB gain

compression of 17.5 dBm for a 1 lm � 500 lm Al0:15Ga0:85N/GaN HEMT at 300 K and at 2 GHz is in excellent

agreement with the calculated value of 17 dBm. With the operating frequency increasing from 1 to 6 GHz the 1-dB gain

compression point decreases from 20.5 to 13.8 dBm at 300 K. At 2 GHz the 1-dB gain compression point decreases

from 17.5 dBm at 300 K to 6.5 dBm at 600 K.

� 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction

GaN based HEMTs are pursued vigorously for ap-

plications in high temperature and high power devices.

The advantage of GaN stems from its large band gap

(3.4 eV) and high breakdown field (3 � 106 V/cm). A

high low field mobility (1500 cm2/V/s) makes possible

the application of this family of devices at high fre-

quency. Current gain cutoff frequency (fT) of 101 GHz

and maximum oscillation frequency (fmax) of 155 GHz at

Vds ¼ 16:5 V and Vgs ¼ 5:0 V, minimum noise figure

(NFmin) of 0.42 dB at Vds ¼ 8 V and Ids ¼ 114 mA/mm,

were measured by Lu et al. [1] for a 0.12 lm gate-length

AlGaN/GaN HEMT on SiC substrate. The higher

thermal conductivity of GaN (1.5 W/cm/K) grown on

SiC (4.5 W/cm/K) has made possible the operation of

GaN HEMTs at very high temperatures [2]. Binari et al.

[3] have reported CW power density upto 3.3 W/mm and

a pulsed power density upto 6.7 W/mm at 3.8 GHz for

an AlGaN/GaN HEMT on sapphire substrate by re-

ducing trapping effects in the device. Power density as

high as 9.8 W/mm at 8 GHz from an AlGaN/GaN

HEMT on SiC substrate has also been reported [4].

The ability of GaN based FETs to handle large

power also makes the devices nonlinear. A measure of

nonlinearity is the 1-dB gain compression point. Chum-

bes et al. [5] have shown a reported a 1-dB gain com-

pression point of 12 dBm for a 0:3 lm � 600 lm

AlGaN/GaN HEMT at 837 MHz and 7 dBm at 4 GHz

for a 0:3 lm � 200 lm device. However, the effect of

frequency on gain compression has not been explicitly

addressed. Moreover, the 1-dB gain compression is

sensitive to temperature variation as evident from the

measured data where it decreases from 15 dB at 100 K to

0 dB at 600 K for a 1 lm � 150 lm AlGaN/GaN

HEMT at 2 GHz [6].

The successful application of GaN based HEMTs for

a high power applications rest upon acceptable nonlin-

ear performance. In this paper the temperature and

frequency dependence of 1-dB gain compression point is

investigated using general Volterra series technique

which includes interactions between the nonlinear

parameters and the spectral components at intermodu-

lation frequencies. Volterra series technique has been ex-

tensively used for the analysis of large and small signal

behavior of microwave power amplifier of GaAs MES-

FETs [7], intermodulation distortion of InGaAs/InAlAs/

Solid-State Electronics 47 (2003) 339–344

www.elsevier.com/locate/sse

* Corresponding author. Tel.: +1-860-486-3979; fax: +1-860-

486-2447.

E-mail address: anwara@engr.uconn.edu (A.F.M. Anwar).

0038-1101/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0038-1101 (02 )00216-2

InP heterojunction bipolar transistors (HBTs) [8] and

AlGaAs/GaAs HBTs [9]. In this paper, Volterra series

technique has been applied to investigate the frequency

and temperature dependence of gain compression in

GaN based HEMTs. Calculated results are compared

with the experimental results for a 1 � 500 lm2

Al0:15Ga0:85N/GaN HEMT operating at RF and are in

excellent agreement.

2. Theory

The equivalent circuit model of the GaN HEMT

employed in the amplifier circuit is shown in Fig. 1.

Nonlinearities are associated with the output resistance

rds, transconductance gm and gate–source capacitance

Cgs which are expressed as a Taylor series expansion up

to the quadratic term [6]:

gm ¼ gm1 þ gm2vgs þ gm3v2gs

rds ¼ rds1 þ rds2vgs þ rds3v2gs

Cgs ¼ Cgs1 þ Cgs2vgs þ Cgs3v2gs

Details of the nonlinear circuit derivations are shown in

Appendix A. Channel electron concentration and the

transport parameters are both dependent upon temper-

ature and bias [10,11], which makes circuit nonlinearity

temperature dependent. The temperature and bias de-

pendence of channel electron concentration is calculated

by solving Schroedinger and Poisson’s equations self-

consistently [10]. The temperature dependent mobility as

obtained from ensemble Monte Carlo simulation for a 1

lm long sample is: lnðT Þ ¼ �8:7 � 10�5T 2 � 0:4T þ 411

cm2/V s. The above relationship takes into account the

effect of nonstationary transport [11]. The circuit pa-

rameters used in Volterra-series analysis are shown in

Table 1 for an 1 lm � 500 lm Al0:15Ga0:85N/GaN

HEMT and in Table 2 for an 0:23 lm � 100 lm

Al0:13Ga0:87N/GaN HEMT.

The simplified nonlinear circuit of the GaN-based

HEMT amplifier consists of an input signal source ViðtÞwith source impedance ZsðxÞ and terminated by load

impedance ZLðxÞ. Based on Volterra series the Volterra

kernels or linear transfer function H1ðx1Þ and nonlinear

transfer functions H2ðx1;x2Þ and H3ðx1;x2;�x2Þ are

calculated [6]. The output voltage component at fre-

quency x1 is expressed as [6,12,13]:

vo ¼ viH1ðx1Þ þ 34v3

i H3ðx1;x1;�x1Þþ 3

2v3

i H3ðx1;x1;�x1Þ þ � � �

where the input signal of the amplifier consists of two

equal amplitude sinusoidal signals at the incommensu-

rate frequencies x1 and x2:

ViðtÞ ¼ viðcos x1t þ cos x2tÞ

Here it is assumed that

H1ðx1Þ ffi H1ðx2Þ ffi H1ðx3ÞFig. 1. AlGaN/GaN HEMT equivalent circuit model.

Table 1

Circuit parameters for a 1 lm � 500 lm Al0:15ga0:85N/GaN HEMT used in Volterra––series analysis

Parameter T ¼ 100 K T ¼ 200 K T ¼ 300 K T ¼ 400 K T ¼ 500 K T ¼ 600 K

Cgs1 (pF) 0.5795 0.6226 0.6754 0.7309 0.8191 0.9663

Cgs2 (pF/V) �0.1581 �0.1814 �0.2086 �0.2315 �0.28 �0.3668

Cgs3 (pF/V2) 0.0567 0.0565 0.0573 0.0567 0.0653 0.0878

gm1 (mS/mm) 263.75 221.79 177.33 133.73 89.488 51.64

gm2 (mS/mm/V) 275.46 244.63 206.74 163.72 115.68 69.768

gm3 (mS/mm/V2) �49.085 �32.556 �14.5 2.7313 18.302 24.601

rds1 (kX) 395.1 491.992 450.457 588.175 851.343 1000

rds2 (kX/V) �316.772 �398.615 �322.077 �421.463 �616.374 �705.210

rds3 (kX/V2) 84.249 104.863 77.955 100.664 146.691 156.079

Cgd (pF) 0.07 0.07 0.07 0.07 0.07 0.07

Cds (pF) 0.05 0.05 0.05 0.05 0.05 0.05

Rd (X) 2.5 2.5 2.5 2.5 2.5 2.5

Ri (X) 1 1 1 1 1 1

Rs (X) 1.7 1.7 1.7 1.7 1.7 1.7

340 A. Ahmed et al. / Solid-State Electronics 47 (2003) 339–344

In practice, the two-tone measurement of an amplifier is

used when the frequency

H3ðx1;x1;�x1Þ ffi H3ðx1;x2;�x2Þ ffi H3ðx3;x3;�x3Þ

separation between two input signals is a few megahertz.

Following the above assumptions the output compo-

nents can be written in more general form as [12,13]

vo ¼ viH1ðx1Þ þ 34ð2N � 1Þv3

i H3ðx1;x1;�x1Þ þ � � �

where the number of exciting signals N ¼ 1; 2; . . . etc.

From above equation we obtain the nonlinear transfer

function of amplifier in terms of Volterra kernels

TNLðx1Þ ¼vo

vi

¼ H1ðx1Þ þ 3ð2N � 1ÞPavH3ðx1;x1;�x1ÞReðZsÞ

where

Pav ¼v2

i

4Re½Zs

is the available input power. The nonlinear output

power is

PONL ¼ jVONLðx1Þj2

Re½ZL

Here the load and source impedances are ZL ¼ RL þ jXL,

ZS ¼ RS þ jXS, respectively and VONL is the nonlinear

output voltage across ZL. The amplifier nonlinear power

gain in decibels is

GPNLðdBÞ ¼ 20 log10 jTNLj þ 20 log10

RL

RL þ jXLðx1Þ

��������

þ 10 log10 4ReZs

ZL

� ���������

Voltage compression ratio is the deviation of the am-

plifier voltage gain from its small signal value of

viH1ðx1Þ and is expressed in the following form:

Kðx1Þ ¼ 1 þ 3ð2N � 1ÞPavRe½ZsReH3ðx1;x1;�x1Þ

H1ðx1Þ

� �;

with ½Kðx1Þ2 being the magnitude of the gain com-

pression ratio which is a function of input power and

circuit parameters.

3. Results and discussion

In Fig. 2, the calculated and measured gain com-

pression and the corresponding input power are shown

for a 1 � 500 lm2 Al0:15Ga0:85N/GaN HEMT [12] device

operating at 300 K and at 2 GHz. As observed the

measured 1-dB gain compression point of 17.5 dBm is in

excellent agreement with the calculated value of 17 dBm.

Gain compression increases from 1 to 6 dB when input

power is raised from 17 to 24 dBm. With increasing

input power level the device nonlinearity increases which

causes the nonlinear gain to deviate more from the linear

gain and gain compression increases.

In Figs. 3 and 4, the 1-dB gain compression point is

plotted as a function of frequency. It is observed that the

1-dB gain compression point decreases from 20.5 to 13.8

dBm for the 1 lm � 500 lm Al0:15Ga0:85N/GaN HEMT

with frequency increasing from 1 to 6 GHz. For the

0:23 lm � 100 lm Al0:13Ga0:87N/GaN HEMT the 1-dB

compression point decreases from 12.8 to 4 dBm for 2–

20 GHz frequency increment. With increasing frequency

the magnitude of the third order transfer function in-

creases and the magnitude of the first order transfer

function decreases within the useful operating frequency

Table 2

Circuit parameters for a 0:23 lm � 100 lm Al0:13Ga0:87N/GaN HEMT used in Volterra––series analysis

Parameter T ¼ 100 K T ¼ 200 K T ¼ 300 K T ¼ 400 K T ¼ 500 K T ¼ 600 K

Cgs1 (pF) 0.0371 0.0368 0.0366 0.0364 0.0358 0.0408

Cgs2 (pF/V) 0.0037 0.0035 0.0032 0.0029 0.0008 �0.00794

Cgs3 (pF/V2) �0.0007 �0.0006 �0.0005 �0.0004 0.0004 0.0028

gm1 (mS/mm) 802.63 772.73 732.72 676.85 648.38 461.56

gm2 (mS/mm/V) 343.91 341.46 336.11 318.7 357.61 371.32

gm3 (mS/mm/V2) �79.96 �77.306 �73.046 �67.24 �58.388 10.896

rds1 (kX) 156.237 172.982 198.031 228.183 368.609 2000

rds2 (kX/V) �384.114 �442.544 �529.547 �628.207 �1000 �6000

rds3 (kX/V2) 164.129 189.791 228.078 271.292 509.204 2000

Cgd (pF) 0.07 0.07 0.07 0.07 0.07 0.07

Cds (pF) 0.05 0.05 0.05 0.05 0.05 0.05

Rd (X) 2.5 2.5 2.5 2.5 2.5 2.5

Ri (X) 1 1 1 1 1 1

Rs (X) 1.7 1.7 1.7 1.7 1.7 1.7

A. Ahmed et al. / Solid-State Electronics 47 (2003) 339–344 341

range. Therefore, 1-dB compression point, which is a

function of the ratio of the first order to third order

transfer functions, decreases with increasing frequency.

The decrease of the first order transfer function with

increasing frequency is a result of the reduction of the

capacitive reactance due to Cgs. On the other hand the

increase in the third order transfer function with in-

creasing frequency is due to the increased feedback

through Cgd.

In Fig. 5, 1-dB compression points are plotted as a

function of temperature at 2 GHz for the 1 lm

� 500 lm Al0:15Ga0:85N/GaN HEMT [14] and at 5 GHz

for the 0:23 lm � 100 lm Al0:13Ga0:87N/GaN HEMT.

Circuit parameters for different temperatures are shown

in Tables 1 and 2 [6]. 1-dB compression point decreases

from 17.5 to 6.5 dBm and from 9.2 to 6.4 dBm re-

spectively when temperature changes from 300 to 600

K for the above mentioned devices. With increasing

temperature the decrease in 1-dB gain compression

point is correlated to the behavior of the fundamental

and third order transfer functions. The linear transfer

function is proportional to the device fundamental

transconductance that decreases with increasing tem-

perature. Whereas, the third order transfer function is

proportional to the device third order transconductance

that increases with increasing temperature. This in-

creases the distortion power and decreases the funda-

mental power. Therefore, the available transducer gain

deviates from the linear value with increasing temper-

ature.

Fig. 2. Input power versus gain compression at f ¼ 2 GHz for

1 lm � 500 lm Al0:15Ga0:85N/GaN HEMT at 300 K.

Fig. 3. Gain compression versus frequency for 1 lm � 500 lm

Al0:15Ga0:85N/GaN HEMT at 300 K.

Fig. 4. Gain compression versus frequency for 0:23 lm�100 lm Al0:13Ga0:87N/GaN HEMT at 300 K.

342 A. Ahmed et al. / Solid-State Electronics 47 (2003) 339–344

4. Conclusion

Gain compression of a GaN amplifier operating at

RF is reported. General Volterra series representation is

used to take into account device nonlinearities. Theo-

retical results are in excellent agreement with experi-

mental data.

Appendix A. Derivation of transfer functions H1, H2 and

H3

Using a Volterra series expansion the output voltage

voðtÞ of the nonlinear circuit is expressed as:

voðtÞ ¼Z x

�xh1ðs1Þvsðt � s1Þds1

þZ Z x

�xh2ðs1; s2Þvsðt � s1Þvsðt � s2Þds1 ds2

þZ Z Z x

�xh3ðs1; s2; s3Þvsðt � s1Þvsðt � s2Þ

� vsðt � s3Þds1 ds2 ds3 þ � � � ðA:1Þ

where hnðs1; s2; s3; . . . ; snÞ is the nth order Volterra ker-

nel, whose Fourier transform Hnðx1;x2;x3; . . . ;xnÞ are

the corresponding nth order nonlinear transfer functions

in the frequency domain. Assuming low distortion and

mild nonlinearities the first three terms of the Volterra

series are used to characterize the HEMT [15].

The first order transfer function H1ðx1Þ expresses the

linear response of the amplifier in the frequency domain.

The second and third order transfer functions H2ðx1;x2Þand H3ðx1;x2;x3Þ are expressed in terms of the circuit

parameters to investigate nonlinearity [13].

H1ðxÞ ¼ �gm

YoðxÞH1CðxÞ ðA:2Þ

H2ðx1;x2Þ ¼ �H1Cðx1ÞH1Cðx2ÞYoðx0Þ

�gm1 1=Zgs2

� �Yiðx0Þ

�

þ gm2 þYds2g2

m1

Yoðx1ÞYoðx2Þ

�ðA:3Þ

H3ðx1;x2;x3Þ ¼�1

Yiðx0Þ H1Cðx1ÞH1Cðx2ÞH1Cðx3Þ"

� gm3

(�gm1 1=ðZgs3ðx00ÞÞ

� �Yiðx0Þ

� Yo3g3m1

Yoðx1ÞYoðx2ÞYoðx3Þ

)

þ H1Cðx1ÞH2Cðx1;x2Þ

� 2gm2

�� 2gm1ð1=ðZgs2ðx00ÞÞÞ

Yiðx00Þ

�

þ 2Yo2H1ðx1ÞH2ðx1;x2Þ#

ðA:4Þ

where

H1CðxÞ ¼ YsðxÞYsðxÞ þ YEðxÞ ðA:5Þ

H2Cðx1;x2Þ ¼ �1=Zgs2

� �Yiðx0Þ H1Cðx1ÞH1Cðx2Þ ðA:6Þ

H3Cðx1;x2;x3Þ ¼�1

Yiðx0Þ 21

Zgs2

�H1Cðx1ÞH2Cðx1;x2Þ

�

þ 1

Zgs3

�H1Cðx1ÞH1Cðx2ÞH1Cðx3Þ

�

ðA:7Þ

and

YsðxÞ ¼ 1

ZSðxÞ þ ðRg þ jxLgÞðA:8Þ

YEðxÞ ¼ 1

ZgsðxÞ ðA:9Þ

YiðxÞ ¼ YsðxÞ þ YEðxÞ ðA:10Þ

Fig. 5. Gain compression as a function of temperature for

0:23 lm � 100 lm Al0:13Ga0:87N/GaN HEMT at 5 GHz (tri-

angle) and 1 lm � 500 lm Al0:15Ga0:85N/GaN HEMT at 2

GHz (square).

A. Ahmed et al. / Solid-State Electronics 47 (2003) 339–344 343

YoðxÞ ¼ YdsðxÞ þ 1

ðRd þ jxLdÞ þ ZLðxÞ ðA:11Þ

YdsðxÞ ¼ gdsðxÞ þ jxC0ds ðA:12Þ

C0ds ¼ Cds þ C00

gd ðA:13Þ

Zgs ¼1 þ jxCgsRi

jxCgs þ jxC0gd � x2CgsRiC0

gd

ðA:14Þ

Zgs2 ¼1 þ jx0Cgs2Ri

jx0Cgs2 þ jx0C0gd � x02Cgs2RiC0

gd

ðA:15Þ

Zgs3 ¼1 þ jx00Cgs3Ri

jx00Cgs3 þ jx00C0gd � x002Cgs3RiC0

gd

ðA:16Þ

Yo2 ¼ ðgds2 þ jx2C0dsÞ þ

1

ðRd þ jx2LdÞ þ ZLðx2ÞðA:17Þ

Yo3 ¼ ðgds3 þ jx3C0dsÞ þ

1

ðRd þ jx3LdÞ þ ZLðx3ÞðA:18Þ

C0gd and C00

gd are the Miller capacitances replacing Cgd,

x0 ¼ x1 þ x2 and x00 ¼ x1 þ x2 þ x3.

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