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FINAL MANUSCRIPT (MANUSCRIPT NUMBMER:7977) TO IEEE TRANSACTIONS
ON MICROWAVE THEORY AND TECHNIQUES 1
Investigation of a Class-J Power Amplier with aNonlinear Cout
for Optimized Operation
Junghwan Moon, Student Member, IEEE, Jungjoon Kim, and Bumman
Kim, Fellow, IEEE
AbstractThis paper presents the operation principle of Class-J
power ampliers (PAs) with linear and nonlinear output ca-pacitors
(Couts). The efciency of a Class-J amplier is enhancedby the
nonlinear capacitance because of the harmonic generationfrom the
nonlinear Cout, especially the second-harmonic voltagecomponent.
This harmonic voltage allows the reduction of thephase difference
between the fundamental voltage and currentcomponents from 45 to
less than 45 while maintaining ahalf-sinusoidal shape. Therefore, a
Class-J amplier with thenonlinear Cout can deliver larger output
power and higher ef-ciency than with a linear Cout. As a further
optimized structureof the Class-J amplier, the saturated PA, a
recently-reportedamplier in our group, is presented. The phase
difference of theproposed PA is zero. Like the Class-J amplier, the
PA uses anonlinear Cout to shape the voltage waveform with a
purelyresistive fundamental load impedance at the current
source,which enhances the output power and efciency. The PA
isfavorably compared to the Class-J amplier in terms of
thewaveform, load impedance, output power, and efciency.
Theseoperations are described using both the ideal and real
modelsof the transistor in Agilent Advanced Design System. A
highlyefcient amplier based on the saturated PA is designed byusing
a Cree GaN HEMT CGH40010 device at 2.14 GHz. Itprovides a
power-added efciency of 77.3% at a saturated powerof 40.6 dBm (11.5
W).
Index TermsClass-J, saturated amplier, efciency, nonlinearoutput
capacitor, power amplier.
I. INTRODUCTION
H IGHLY efcient power ampliers (PAs) are an essentialRF
component for wireless communication systems toachieve small,
reliable, and low cost transmitters [1] [3].To date, a lot of
topologies have been proposed to providehighly efcient operation.
Among the various PAs, the Class-F delivers a good efciency by
controlling the odd-harmonicimpedances to make a rectangular
voltage waveform [3] [6].However, to get the proper third-harmonic
voltage, the outputcapacitor (Cout) should be accurately tuned out.
Moreover,depending on the capacitance and the operating frequency,
insome cases, the impedance of the capacitance might be a
short-circuit for the third-harmonic frequency. Class-E amplier
pro-vides excellent efciency by acting as a ideal switch [7],
[8].
Manuscript received December 8, 2009; revised June 15, 2010.
Thiswork was supported by the MKE (The Ministry of Knowledge
Economy),Korea, under the ITRC (Information Technology Research
Center) sup-port program supervised by the NIPA (National IT
Industry PromotionAgency)(NIPA-2010-(C1090-1011-0011)), by WCU
(World Class University)program through the Korea Science and
Engineering Foundation funded bythe Ministry of Education, Science
and Technology(Project No. R31-2008-000-10100-0), and by the Brain
Korea 21 Project in 2010.
J. Moon, J. Kim, and B. Kim are with the Department of
Electrical Engi-neering, Pohang University of Science and
Technology, Pohang, Gyungbuk,790-784, Korea (e-mail:
[email protected];
[email protected];[email protected]).
However, the actual ideal switching operation of the
powertransistor might or might not be possible depending on
theoperating frequency and the power transistor. In addition,
thehigh order frequency components of the drain voltage maybe
shorted and the switching time may not be negligible,making the
zero-voltage switching and zero voltage derivativeswitching
difcult. Such limitations degrade the efciency ofthe Class-E PA at
high frequency.
In 2006 [3] and 2009 [9], S. C. Cripps proposed Class-J amplier
that provides the same efciency and linearity asClass-AB or Class-B
ampliers across a broad frequency rangedue to absence of the
resonant impedance condition, such asshort-circuit or open-circuit.
The Class-J PA increases the fun-damental voltage component
assisted by the second-harmonicvoltage by employing a capacitive
harmonic load [10] [12].However, a complex load impedance at the
fundamentalfrequency is required to shape the voltage waveform. As
aresult, the performance of the Class-J PA is degraded dueto the
phase mismatch, making it comparable to that of aharmonic tuned
linear PA, such as a Class-AB or a Class-B, but the reported
Class-J PA provides better efciency thanthe theoretical expectation
[13] [15].
The highly efcient PAs have been extensively analyzed inthe
past, but most of these analyses have been carried out underthe
assumption of a linear Cout [3] [15]. However, the Coutpresents a
heavily nonlinear behavior at the low voltage acrossthe capacitor
[16], [17], resulting in unexpected operationand the abstrusity of
the analyses. Although some researchershave made an effort to
describe PA operations accounting thenonlinear capacitor [18] [23],
they only focused on the class-E topology at low frequencies, below
400 MHz.
In this paper, the harmonic-generation property of
thetransistors nonlinear Cout is explored, and the behaviors ofthe
PAs with the linear and nonlinear Cout are investigated.Especially,
Class-J ampliers, which use the output capacitorsas a second
harmonic load, are further analyzed in terms ofthe time-domain
voltage and current waveforms, load-lines,load impedances, and
continuous wave (CW) performances.The Class-J ampliers are compared
with a saturated poweramplier, and it is shown that the amplier is
an optimizedversion of the Class-J PA to obtain better efciency and
outputpower. In [24] and [25], we explained the operation of
thesaturated PA. It uses the nonlinear Cout as a harmonic
load,which is the same of the Class-J amplier, and a
purelyresistive fundamental load, which is different from the
Class-JPA. The resistive fundamental load impedance increases
thepower factor, resulting in better efciency and output powerthan
those of the Class-J amplier.
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ON MICROWAVE THEORY AND TECHNIQUES 2
(a)
(b)
(c)
Fig. 1. (a) Simplied transistor equivalent circuit model. (b)
Capacitancesfor the linear and nonlinear Couts. (c) DC-IV
characteristic.
II. ANALYSIS FOR OPERATION CHARACTERISTICS OF ACLASS-J
AMPLIFIER
A. Ideal Transistor Model for Simulations
To analyze the fundamental behaviors of the PAs, we
haveconstructed a simplied transistor equivalent circuit model
inthe Agilent Advanced Design System (ADS) using the sym-bolically
dened device, as shown in Fig. 1(a). To simplify theanalysis, the
transistor model contains two essential nonlinearparts: Cout and
the drain current source. Cout represents allnonlinear capacitors
of the transistor output, including thedrain-source capacitor Cds
and gate-drain capacitor Cgd. Eventhough Cds and Cgd are modulated
according to both thedrain-source and the gate-source voltages, we
assume only a
TABLE ISUMMARIZED PARAMETERS FOR OUTPUT CAPACITOR Cout
Cout0 A B C
1.9 1192.4 0.0594714 2.94696
Fig. 2. Half-sinusoidal voltage and current waveforms for the
various phasedifferences (In particular, = pi/4 represents the
Class-J PA).
dependence on the drain-source voltage in this model. Thus,Cout
is given by
Cout (Vds) = Cout0+A [1 + tanh (B Vds + C)] [pF] , (1)where
Cout0, A, B, and C are summarized in Table I.Fig. 1(b) illustrates
the characteristic of the nonlinear Cout ac-cording to the
drain-source voltage. The capacitance increasesdramatically as the
drain-source voltage becomes small. Thedrain-source current is
given by
Ids (Vgs, Vds) =
0, Vgs 0gmVgs
(1 exp
(VdsVt
)),
0 < Vgs Vgs,maxgmVgs,max
(1 exp
(VdsVt
)),
Vgs Vgs,max
,
where gm is the trans-conductance, and Vgs,max is the
gate-source voltage when Ids is equal to Imax. For simplicity,
weassume the pinch-off voltage is zero. As depicted in Fig.
1(c),the transistor model exhibits strongly nonlinear effects
ofcutoff and saturation. In the intermediate region between
thecutoff and saturation, the transistor provides a highly
linearoperation. In particular, gm and Imax are set to 1 S and1.5
A, respectively, in this model, and Vk is about 4 V.
Theseparameters are based on the model of the Cree GaN HEMTCGH60015
used for the implementation. It is well known thatthe input
nonlinear capacitor Cgs has nonlinear characteristic,which results
in the generation of harmonic components [10][12], [26], [27].
However, compared with the output nonlinearcapacitor, Cgs has a
minor effect on the performance, as willbe described in Section
III, so the effect of Cgs nonlinearityis eliminated in this
model.
B. Class-J Amplier with Linear Output Capacitor
First, we review the operation of Class-J amplier withlinear
Cout. Linear Cout refers to a constant capacitance, asshown in Fig.
1(b). Class-J amplier can be characterized by
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ON MICROWAVE THEORY AND TECHNIQUES 3
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0 1.0
20
40
60
80
0
100
0.4
0.8
1.2
1.6
0.0
2.0
Time [nsec]
Drain Voltage [V] D
rain Curre
nt [A
]10 20 30 40 50 60 70 800 90
0.5
1.0
1.5
0.0
2.0
Drain Voltage [V]
Drain Current [A]
Fig. 3. Simulated (a) time-domain voltage and current waveforms
and (b)load-lines for Class-B and Class-J ampliers with linear
Cout.
half-sinusoidal voltage and current waveforms with a phaseshift
between them, as depicted in Fig. 2. These waveformscan be
expressed by
I () = Imax (1pi+
12sin 2
3picos 2
)(2)
V () = piVdc (1pi 1
2sin ( + ) (3)
23pi
cos (2 ( + )) ),
where is a phase difference between the voltage and currentfrom
the normal 180. Thus, the load impedances of eachharmonic
frequencies can be calculated by
Zn = VnIn
, (4)
where n denotes the nth frequency component. For Imax = 1and Vdc
= 1/pi, the fundamental and second-harmonic loadsare given by
Z1 = 1, Z2 = 1 (2 pi) (5)For Class-J amplier, is pi/4 because
the second harmonicloading is made by the capacitive component.
Thus, to shapethe half-sinusoidal voltage waveform, the fundamental
loadimpedance is set to 1(pi/4). This leads to the degradation
ofthe output power by a factor of cos (pi/4).
The operation of the Class-J PA is further investigated byusing
the model described in Section II-A. Since the Class-Joperation
biased at the Class-B condition is assumed in this
(a)
(b)
Fig. 4. Fundamental (a) current and (b) voltage components for
the Class-Band Class-J ampliers with the linear Cout.
work, the Class-B amplier is also simulated for
comparisonpurpose. For the Class-B design, the optimum
fundamentalload impedance is chosen to obtain the maximum
outputpower.
Ropt =Vdc VkImax/2
. (6)
In the simulation, Vdc is set to 30 V, so Ropt is chosen to
be34.6 .
For the Class-J amplier, the voltage waveform is
half-sinusoidal. It consists of all even harmonic voltage
compo-nents. However, the voltage components at the
higher-orderfrequencies are assumed to be zero because of the
deviceslarge output capacitor. We believe that, in the real
designenvironment, the half-sinusoidal voltage waveform is
mainlymade up the DC, fundamental, and second-harmonic volt-age
components. Among the various half-sinusoidal voltagewaveforms
manipulated by up to second-harmonic component,the maximum-voltage
gain condition is assumed in thisstudy [10] [12]. Accordingly, the
magnitude of the funda-mental load impedance should be set to
2Ropt because the
maximum value of the fundamental voltage extracted from
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ON MICROWAVE THEORY AND TECHNIQUES 4
Fig. 5. Simulated efciencies of the Class-B and Class-J ampliers
with thelinear Cout.
Fig. 6. Simulation setup to investigate the behavior of the
ampliers and theharmonic-generation property of the nonlinear
Cout.
the half-sinusoidal waveform is increased by a factor of2
above that of Class-B amplier. In addition, to properly shapethe
half-sinusoidal voltage waveform, the appropriate amountof the
second-harmonic voltage is required. In particular,
themaximum-voltage gain condition can be achieved whenthe ratio of
the second-harmonic to the fundamental voltageis 2/4. Thus,
assuming the ideal half-sinusoidal currenthaving the fundamental
current of Imax/2 and the second-harmonic current of 2Imax/3pi, the
required second-harmonicload impedance is given by
|Z2| = 3pi8 Ropt. (7)Consequently, the load condition for
Class-J amplier isrepresented by
Z1 =2Ropt45, Z2 =
3pi8Ropt 90. (8)
In the simulation of the Class-J amplier, the fundamental
andsecond-harmonic load impedances are selected to be 34.6 +j34.6
and j40.768 , respectively.
C. Class-J Amplier with Nonlinear Output Capacitor
Fig. 3 depicts the simulated time-domain voltage and cur-rent
waveforms and load-lines for the designed Class-J andClass-B
ampliers with linear Cout. Because of the complex
10 20 30 40 50 60 70 800 90
0.5
1.0
1.5
0.0
2.0
Drain Voltage [V]Drain Current [A]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0 1.0
20
40
60
80
0
100
0.4
0.8
1.2
1.6
0.0
2.0
Time [nsec]
Drain Voltage [V]
Drain Curre
nt [A
]
Fig. 7. Simulated (a) time-domain voltage and current waveforms
and (b)load-lines for the Class-J ampliers with the linear and
nonlinear Couts.
Fig. 8. Average capacitance for the Class-J with the nonlinear
Cout accordingto the power level.
fundamental load impedance, the Class-J amplier providesa
loadline having looping-characteristic. Fig. 4 shows thefundamental
current and voltage components for the Class-Band Class-J ampliers.
In the saturated region, the fundamentalcurrent of the Class-B is
slightly larger than that of the Class-J, because the Class-J has
an asymmetric current waveformdue to the complex fundamental load
impedance, as shownin Fig. 3(a). However, the bifurcated current of
the Class-B requires slightly larger DC current than the Class-J,
andthe efciency of the Class-B at the highly saturated region
isslightly lower than that of the Class-J amplier, as depicted
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ON MICROWAVE THEORY AND TECHNIQUES 5
Fig. 9. Simulated efciencies for the Class-J amplier with a
linear Coutand the Class-B and -J ampliers with the nonlinear Cout
according to thepower level.
Fig. 10. Fundamental and second harmonic-load impedance
trajectoriesaccording to the power level.
in Fig. 5. Although the fundamental voltage of the
Class-Jamplier is increased by a factor of
2 compared to the Class-
B, as shown in Fig. 4(b), the output power and efciency of
theClass-J are equal to those of the Class-B amplier due to
thephase mismatch between the current and voltage waveforms by45.
In short, although the Class-B and Class-J ampliers withlinear Cout
have different fundamental loads and harmonicterminations, the
performances of the two PAs are nearly thesame except at the highly
saturated condition. However, evenat the highly saturated
condition, the difference is very small.
Although Section II-B explains clearly the fundamentaloperation
of the Class-J amplier and provides the properload conditions, it
does not describe the real behavior ofthe amplier because Cout is
not a linear element but anonlinear element, as shown in Fig. 1(b).
In this section,the basic operation of a Class-J amplier with the
nonlinearCout is investigated using the setup shown in Fig. 6.
Here,
(a)
(b)
(c)
Fig. 11. Simulation results to demonstrate the harmonic
generation of thenonlinear Cout. (a) Current owing from the linear
and nonlinear Couts.The resultant capacitor voltage waveforms in
the (b) time- and (c) frequency-domain.
we dene the load impedance at the current source ZLoadand the
capacitance is tuned for the fundamental frequencyat low power
level. Fig. 7 represents the simulated time-domain voltage and
current waveforms and load-lines of theClass-J ampliers with linear
and nonlinear Couts, and Fig. 8describes the average capacitance
according to the outputpower level for the Class-J amplier with the
nonlinear Cout.In the low-power region, below 32 dBm (1.6 W) of
theoutput power, the swing of the drain voltage is within therange
where the nonlinear Cout could be regarded as a linearcapacitance,
as shown in Fig. 7 and Fig. 1. At the outputpower of 32 dBm (1.6
W), the voltage is varied from 20 V to50 V so that the average
capacitance remains around 2.1 pF.Therefore, the waveforms and
load-lines with the nonlinearCout case are the same as those with
the linear Cout case.This results in nearly the same performances
for the output
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ON MICROWAVE THEORY AND TECHNIQUES 6
power and efciency, as shown in Fig. 9. In addition, theoutput
fundamental and second-harmonic load impedances forboth the linear
and nonlinear Couts are the same, properlyshaping the
half-sinusoidal voltage waveforms, as describedin Fig. 10. However,
as the output power increases above32 dBm (1.6 W), the average
capacitance also enlarges witha large capacitance at a low voltage.
Thus, as shown inFig. 7(a), the current waveform has a large dip at
the middle,generating a large third-harmonic current and enhancing
theefciency. Moreover, the magnitude of the fundamental
loadimpedance increases, but the phase decreases as depicted inFig.
10. As a result, unlike the Class-J amplier with the linearCout,
the voltage waveform moves toward the direction toreduce the phase
difference between the current and voltagewaveforms while
maintaining the half-sinusoidal shape of thevoltage. This results
in enhanced output power and efciencyperformances compared to the
Class-J amplier with the linearCout. What is interesting here is
that these waveforms can bemade with of less than 45. However, from
(5), less than45 leads to a negative resistance value of the second
harmonicimpedance. This means that the nonlinear Cout generatesthe
second-harmonic voltage component. This phenomenoncannot be
expected from the operation of a Class-J amplierwith a linear
Cout.
Fig. 11 shows the simulation results to demonstrate theharmonic
generation of the nonlinear Cout. The simulationis carried out
using the circuit in Fig. 6. The simulationresults include the
current owing through the linear andnonlinear Cout and the
resultant capacitor voltage waveformsin the time-domain and
frequency-domain. Differently fromthe linear capacitor, the
nonlinear capacitor generates a voltagewaveform consisting of the
fundamental and harmonic voltagecomponents. Although only the
fundamental current is injectedto the capacitor, the voltage
contains a large second-harmoniccomponent with small higher-order
frequency components.Since the transistor can be regarded as a
voltage controlledcurrent source, the current owing through the
capacitor isdetermined by the input voltage. The voltage across
thecapacitor is proportional to the integral of the current,
thecharge in the capacitor, scaled by the capacitance. It can
beexpressed by
VDS (tx) = VDD +1
Cout (VDS (tx))
tx
i (t) dt
= VDD +Q (tx)
Cout (VDS (tx)). (9)
Q (tx) indicates the charge on Cout until tx. As Q (tx)decreases
with negative i (t), Cout increases rapidly. Aroundthe bottom of
the voltage, the output voltage VDS (tx) cannotchange much because
of the large variation of Cout with thelimited current drive. That
is, Q (tx) /Cout (VDS (tx)) remainsnearly constant, VDD, around the
region. As a result, thevoltage waveform has a attened
characteristic in the lowvoltage region, like the half-sinusoidal
shape, as shown inFig. 11(b). Thus, the second-harmonic impedance
can be inthe negative resistance region as shown in Fig. 10
becausethe second-harmonic component in the voltage waveform
isgenerated not by the second-harmonic current and load but by
the nonlinear Cout. This second harmonic component allowsthe
phase difference between the fundamental current andvoltage less
than 45. Additionally, the harmonic componentsgenerated by the
nonlinear capacitor can be varied according tothe nonlinear Cout
prole. The more the nonlinear capacitorchanges, the more the
second-harmonic is generated. If thesecond-harmonic load impedance
attached parallel to the non-linear Cout is larger than the
impedance of the nonlinear Cout,the half-sinusoidal voltage
waveform can be maintained. Thesecond-harmonic current component
generated by the currentsource can assist this behavior, generating
the half-sinusoidalvoltage waveform. However, the saturated current
with alarge dip at the middle has a signicant third-harmonic
andrather small second-harmonic current. Together with the
lowharmonic impedance, the second-harmonic voltage is mainlybuilt
up by the harmonic voltage generation of the nonlinearcapacitor. We
will revisit this issue in the simulation using areal device model
in Section III.
D. Optimization of Class-J Amplier with Nonlinear
OutputCapacitor: Saturated Amplier
The Class-J amplier can be further optimized to achievehigher
efciency and output power by reducing the phasemismatch between the
fundamental voltage and current com-ponents, adopting the resistive
fundamental loading condition.This is possible due to the
second-harmonic voltage generationby the nonlinear Cout. To obtain
the highly efcient operation,the voltage waveform should be shaped
to minimize thedissipated power of the device by reducing the
concurrent non-zero voltage and current. However, as mentioned in
SectionII-C, if the external second-harmonic loading is greater
thanthe impedance level generated by the output capacitor,
thehalf-sinusoidal voltage waveform can be generated by
thenonlinear Cout. In [24] and [25], we proposed a novel
highefciency PA, saturated power amplier, taking advantage ofthe
nonlinear Cout to shape the voltage waveform with theresistive
fundamental load, and it is the optimized operationof the Class-J
amplier. Since its waveform is similar to thatof the Class-F1, the
fundamental load impedance is adjustedbetween
2Ropt to 2Ropt to achieve the highest efciency
with an acceptable output power [6]. The harmonic load haslarge
tolerance because the voltage waveform is mainly shapedby the
nonlinear Cout. It means that the half-sinusoidal voltagecan be
generated if the second harmonic load impedanceis larger than the
impedance level of the nonlinear Cout.The harmonic load impedance
comparable to or less thanthe nonlinear Cout disturbs the
generation of the harmonicvoltage. However, to achieve the maximum
efciency, thesecond harmonic should be carefully matched to a
particularimpedance.
Fig. 12 shows the simulated time-domain voltage and cur-rent
waveforms and load-lines for the Class-J and saturatedampliers with
nonlinear Cout. Unlike the waveforms of theClass-J amplier depicted
in Fig. 7(a), the phase differencebetween the current and voltage
is nearly zero due to theresistive fundamental load impedance, as
shown in Fig. 13.Moreover, since the second-harmonic voltage to
shape the
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10 20 30 40 50 60 70 800 90
0.5
1.0
1.5
0.0
2.0
Drain Voltage [V]
Drain Current [A]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0 1.0
20
40
60
0
80
0.5
1.0
1.5
0.0
2.0
Time [nsec]
Drain Voltage [V]
Drain Curre
nt [A
]
Fig. 12. Simulated (a) time-domain voltage and current waveforms
for thesaturated amplier and (b) load-lines for the Class-J and
saturated ampliers.
half-sinusoidal voltage waveform is generated mainly by
thenonlinear Cout, the second-harmonic impedance remains in
thenegative resistance region. However, in the low-power
regionwhere the nonlinear Cout can be regarded as a linear
capacitor,the phase of the fundamental-load impedance of the
saturatedamplier is not 45 while the phase of the second-harmonicis
90, so it does not provide the half-sinusoidal voltagewaveform.
Fig. 14 shows the simulated efciencies for theClass-J and saturated
ampliers. Since the saturated amplierhas a smaller phase mismatch
between the voltage and currentcompared to the Class-J amplier, it
produces a higher outputpower and efciency than the Class-J
amplier.
In short, for the linear Cout, the Class-J amplier doesnot have
any merit compared to the Class-B amplier withrespect to the output
power and efciency because of thephase mismatch between the voltage
and current waveforms.However, for the nonlinear Cout case, the
Class-J amplier hasa chance to improve the performance because the
nonlinearcapacitor generates harmonic-voltage components,
especiallythe second-harmonic voltage component. Thus, the
phasedifference can be reduced below 45. A further improvementcan
be achieved by selecting a purely resistive load forthe fundamental
frequency to eliminate the phase mismatchbetween the voltage and
current, while maintaining the half-sinusoidal voltage waveform.
This can be carried out if theexternal second-harmonic impedance is
greater than the levelof the nonlinear Cout, which is a saturated
PA, the furtheroptimized version of the Class-J amplier for highly
efcientoperation.
Fig. 13. Fundamental and second-harmonic load impedance
trajectories forthe Class-J and saturated ampliers according to the
power level.
Fig. 14. Simulated efciencies of the Class-J and saturated
ampliers.
III. IMPLEMENTATION AND EXPERIMENTAL RESULTS
To validate the voltage waveform shaping by the nonlinearCout
and the highly efcient operation, a saturated ampli-er was designed
and implemented at 2.14 GHz using aCree GaN HEMT CGH40010 package
device containing aCGH60015 bare chip. Since the commercial device
modelincludes packaging effects, due to bonding wires,
packageleads, and parasitics, the simulation is conducted using a
bare-chip model to show the inherent operation of the saturatedPA.
In addition, the simulation for the implementation isconducted
using the model of the packaged-device. Fig. 15shows the simulated
second-harmonic load-pull contours of theoutput power and efciency
when the fundamental and third-harmonic impedances are set to 18.23
+ j25.15 and 0 ,respectively, at the drain pad of the bare chip.
The load-pullsimulation was carried out using Agilent ADS 2008
Update 1.The device model, CGH60015 and package information,
were
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Fig. 15. Simulated second-harmonic load-pull contours of the
output powerand efciency when the fundamental and third-harmonic
impedance are setto 18.23+ j25.15 and 0 , respectively, at the
drain pad of the bare chip.
Fig. 16. Simulated second-harmonic source-pull contours of the
efciencywhen the fundamental source impedance is conjugate-match
condition andthe output load terminations are set to the condition
of the saturated PA. Thecharacteristic impedance of the smith chart
is 5 .
provided by Cree Inc.. As mentioned in Section II, a
highefciency and output power can be achieved when the
second-harmonic load impedance is large, proving that the
nonlinearCout is enough to shape the voltage to the
half-sinusoidal.Since a large second-harmonic load impedance
provides a highefciency, it is set to 2 + j80 . For the high
efciency andoutput power operation, a fundamental-load impedance at
thedependent current source is determined to be about 60 . Sincethe
efciency changes a little according to the third-harmonicmatching
impedance, the impedance is set to 0.
(a)
(b)
Fig. 17. Simulated (a) Vgs and (b) Vds waveforms at the marked
pointson the Smith chart in Fig. 16 (A = 0 , B = 0.01 + j1.3 , C
=0.01 + j2.8 , D = 0.01 j2.8 , E = 5 , and F = 100 ).
So far, the fundamental and harmonic-load impedances atthe
output have been considered to achieve high power andefciency
capabilities, and the fundamental input componentis conjugately
matched. However, it has been observed that theinput harmonic
terminations should be properly placed due tothe nonlinear input
capacitor Cgs. In particular, to preservethe sinusoidal input drive
at the gate, the input harmonicterminations are frequently set to
be short-circuit [26], [27].On the other hand, in [10] [12], they
make an effort to shapethe output voltage waveform by using the
nonlinear effect ofCgs. To nd the optimum input termination for the
secondharmonic, the source-pull simulation for the second
harmonicis carried out, as shown in Fig. 16. During the
simulation,the fundamental source impedance is conjugately
matched,and the output load terminations are set to the condition
ofthe saturated amplier. A simulation of source-pull for
thesecond-harmonic termination indicates only a minor effect onthe
efciency if the termination is not in the gray coloredregion. This
result supports that the output voltage waveform ismainly shaped by
the nonlinear output capacitor. Fig. 17 showsthe simulated Vgs and
Vds waveforms for second harmonic
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ON MICROWAVE THEORY AND TECHNIQUES 9
impedances at the marked points on the Smith chart in Fig.
16.Except for the points marked by A and C, the Vgs waveformsare
very similar due to the harmonic voltage generation of Cgs.Not just
for these points, almost regions of the smith chart,except for the
gray colored part, provide the analogous Vgswaveforms. For the
point marked by A, due to the short-circuitfor the second harmonic,
the sinusoidal voltage is presented.In spite of the different Vgs
waveforms, the output voltages atthe drain are similar shapes.
Those waveforms clearly showthat the output voltage shape is not
much affected by theharmonic generation of Cgs while considering
the nonlinearCds. However, even though most of regions provide the
sameperformance, the output power and efciency deterioratedwhen the
source impedance for the second harmonic is locatedat the
gray-colored region. In this region, the conduction angleof the
drain current is reduced, resulting in low output powerand
efciency. Therefore, in this work, the input terminationfor the
second harmonic is set to the short-circuit.
Fig. 18 indicates the simulated time-domain voltagewaveform and
the fundamental and second-harmonic loadimpedance trajectories
according to the power level. Likethe simulation conducted in
Section II-D, the half-sinusoidalvoltage waveform is achieved at
the high power level wherea large amount of the second harmonic is
generated bythe nonlinear Cout, so that the second-harmonic
impedanceremains in the negative resistance region. For comparison,
theClass-B amplier is also simulated using the same device.
Toprovide the sinusoidal voltage waveform, all harmonics
areshort-circuited. In addition, the fundamental-load impedanceof
the Class-B PA is set to 36.5 at the maximum powerlevel to provide
the full swings of the voltage and currentwaveforms. Fig. 19 shows
the simulated gain and efciencycomparisons between the saturated PA
and Class-B amplier.Because the load impedance of the saturated PA
is larger thanthat of the Class-B amplier, the saturated PA
provides highergain than the Class-Bs one in the low power region.
At thehigh power level, compared with the Class-B amplier,
thesaturated PA delivers the better efciency performance
withcomparable output power, resulting from the
second-harmonicmanipulation caused by the nonlinear Cout. In
particular, themaximum efciency of the saturated PA is 81.5%, which
isan improvement of 9.3%.
Fig. 20(a) shows a photograph of the designed PA imple-mented on
a Taconic TLY-5 substrate with r = 2.2 andthickness of 31 mil. The
detailed microstrip dimensions areshown in Fig. 20(b). In the
experiment, the gate bias is setto 3.1 V (IDSQ = 94 mA) at a
supplied drain voltage of30 V. Unlike the conventional high
efciency PAs, any specialharmonic-loading circuit is not used in
the output matching.The simulated and measured output power,
efciency, andgain characteristics for a CW signal are well matched,
asshown in Fig. 21. In particular, the implemented PA providesa
maximum PAE of 77.3% at a saturated output power of40.6 dBm (11.5
W). Fig. 22 depicts the measured adjacentchannel leakage ratio
(ACLR) and PAE for LTE signal with6.6 dB PAPR and 10 MHz signal
bandwidth. The proposedPA delivers a PAE of 42.3% and a power gain
of 21 dBat an average output power of 34.2 dBm (2.6 W). To val-
(a)
(b)
Fig. 18. (a) Simulated time-domain voltage waveforms of the
saturated am-plier and Class-B PA. (b) Fundamental and
second-harmonic load impedancetrajectories of the saturated amplier
and Class-B PA according to the powerlevels.
Fig. 19. Simulated gain and efciency comparison between the
saturated PAand Class-B amplier.
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ON MICROWAVE THEORY AND TECHNIQUES 10
(a)
10pF
10pF
50Ohm
10pF
10pF
0.2pF
10uF
10uF
r=2.2,31milthickMicrostripdimension
(width/lengthinmm)
8.8/4.414.8/5.415.6/22.8
15.6/2.38 15.6/3.0
2.38/22.2
3.2/1.63.2/2.38
3.2/6.5211.2/3.3513.75/3.05
5.9/12.6
2.38/25.0
(b)
Fig. 20. (a) Photograph and (b) circuit schematic of the
implemented PA.
idate potential of the proposed PA as a main block of alinear
power amplier (LPA), the linearization of the PA iscarried out by
employing the digital feedback predistortiontechnique (DPBPD) [28].
Fig. 23 shows the measured outputspectra before and after the
linearization. The ACLR at anoffset of 7.5 MHz is 45.1 dBc, which
is an improvementof 23 dB at an average output power of 34.2 dBm
(2.6 W).The linearization results are summarized in Table II.
Theseexperimental results clearly show that the proposed
saturatedamplier can provide excellent efciency without any
specialharmonic loading circuit. Moreover, by applying the
lineariza-tion technique, it is well suited to be a highly efcient
mainamplier of a LPA for use in a LTE transmitter.
Comparison of the performance among the designed PAwith
state-of-the-art results for high-efciency is summarizedin Table
III. The comparison shows the excellent performanceof the saturated
PA, the optimized Class-J PA, without anyharmonic control
circuitry.
IV. CONCLUSION
The operation principles of Class-J ampliers with linearand
nonlinear Couts are analyzed using a simple transistormodel in an
ADS simulator. The performance of the Class-J
Fig. 21. Simulated and measured (a) output power, (b) efciency
and gaincharacteristics for a CW signal.
Fig. 22. Measured ACLR and PAE characteristics for an LTE
signal.
TABLE IILINEARIZATION PERFORMANCE AT AN AVERAGE OUTPUT POWER
OF
34.2 dBm (2.6 W) FOR LTE SIGNAL
ACLR [dBc] ACLR [dBc] PAE
at 7.5-MHz at 12.5-MHz [%]
Before Linearization 22.3 33.1 42.3
After Linearization 45.1 47.9 43.8
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ON MICROWAVE THEORY AND TECHNIQUES 11
Fig. 23. Output spectra before and after the linearization using
DFBPD.
TABLE IIISTATE-OF-THE-ART HIGH EFFICIENCY PAS USING GAN HEMT
DEVICE
ABOVE 2 GHz
Referencefo* Psat VDC PAE Topoplgy
[GHz] [W] [V] [%]
[29] 2.10 11.2 50.0 79.7 Class-E
[30] 2.00 11.5 50.0 74.3 Class-E
[31] 2.00 16.5 42.5 85.5 Class-F[32] 2.10 12.0 28.0 79.6
Class-F1
[33] 2.14 7.2 28.0 68.0 HT PA[34] 2.14 12.0 40.0 74.0
Class-E
This work 2.14 11.5 30.0 77.3 Saturated PA
*fo denotes the operating frequency.HT PA denotes the
harmonically tuned PA.Internal matching circuitry is optimized for
the class-E.PA is fabricated using bare-chip.Performance is
measured on the load-pull measurement setup.
PA with linear Cout is comparable to that of the
conventionalClass-B amplier. However, due to the harmonic
generationproperty of the nonlinear Cout, the half-sinusoidal
voltagewaveform can be properly shaped while the phase overlap
be-tween the voltage and current components are reduced below45.
This allows the improvement of the efciency beyondthat of a Class-J
amplier with a linear Cout. The furtheroptimization of the amplier
can be carried out by adoptingthe phase difference to zero degree
using the purely resis-tive fundamental load impedance. It
minimizes the dissipatedpower caused by the concurrent non-zero
voltage and currentwhile maintaining the half-sinusoidal voltage
waveform. Sincethe voltage shaping is achieved by the nonlinear
Cout, effortsto control the harmonic components are unnecessary. If
theexternal harmonic load impedances are larger than the level
ofthe capacitor, a highly efcient voltage waveform is obtained.This
is supported by the ADS simulation using both ideal andreal models
of the transistor. This is the optimized version ofClass-J PA,
which is the saturated PA we have reported. Ahighly efcient
saturated PA is implemented by using a CreeGaN HEMT CGH40010 device
at 2.14 GHz. It provides a PAEof 77.3% and a saturated output power
of 40.6 dBm (11.5 W)
without any special harmonic loading network.
ACKNOWLEDGEMENT
The authors would like to thank Cree Inc. for providing theGaN
HEMT transistors and models used in this work.
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Junghwan Moon (S07) received the B.S. degreein electrical and
computer engineering from theUniversity of Seoul, Seoul, Korea, in
2006 andis currently working toward the Ph.D. degree atthe Pohang
University of Science and Technology(POSTECH), Pohang, Gyungbuk,
Korea.
His current research interests include highly linearand efcient
RF PA design, memory-effect com-pensation techniques, digital
predistortion (DPD)techniques, and wideband RF PA design.
Mr. Moon was the recipient of the Highest Ef-ciency Award at
Student High-Efciency Power Amplier Design Competitionin IEEE MTT-S
International Microwave Symposium (IMS), 2008.
Jungjoon Kim received the B.S. degree in electri-cal engineering
from Han-Yang University, Ansan,Korea, in 2007, and the Master
degree in electricalengineering from the Pohang University of
Scienceand Technology (POSTECH), Pohang, Gyungbuk,Korea, in 2009.
He is currently working toward thePh.D. degree at the POSTECH,
Pohang, Gyungbuk,Korea.
His current research interests include RF PA de-sign and supply
modulator design for highly efcienttransmitter system.
Bumman Kim (M78-SM97-F07) received thePh.D. degree in electrical
engineering from CarnegieMellon University, Pittsburgh, PA, in
1979.
From 1978 to 1981, he was engaged in ber-opticnetwork component
research with GTE LaboratoriesInc. In 1981, he joined the Central
Research Labo-ratories, Texas Instruments Incorporated, where hewas
involved in development of GaAs power eld-effect transistors (FETs)
and monolithic microwaveintegrated circuits (MMICs). He has
developed alarge-signal model of a power FET, dual-gate FETs
for gain control, high-power distributed ampliers, and various
millimeter-wave MMICs. In 1989, he joined the Pohang University of
Science andTechnology (POSTECH), Pohang, Gyungbuk, Korea, where he
is a POSTECHFellow and a Namko Professor with the Department of
Electrical Engineering,and Director of the Microwave Application
Research Center, where he isinvolved in device and circuit
technology for RF integrated circuits (RFICs).He has authored over
300 technical papers.
Prof. Kim is a member of the Korean Academy of Science and
Tech-nology and the National Academy of Engineering of Korea. He
was anassociate editor for the IEEE TRANSACTIONS ON MICROWAVE
THEORY ANDTECHNIQUES, a Distinguished Lecturer of the IEEE
Microwave Theory andTechniques Society (IEEE MTT-S), and an AdCom
member.