GaN HEMT Class E2 Resonant Topologies for
UHF DC/DC Power Conversion
José A. García, Member, IEEE, Reinel Marante, Student Member, IEEE, María N. Ruiz, Student
Member, IEEE
Abstract— In this paper, the design and performance of class
E2 resonant topologies for DC/DC power conversion at Ultra
High Frequencies (UHF) are considered. Combining the use of
RF GaN HEMT devices, both for the inverter and the
synchronous rectifier, with high Q lumped-element terminating
networks, peak efficiency values over 70% may be obtained.
Control strategies based on carrier bursting, switching frequency
modulation, or outphasing are also shown to be feasible. Taking
advantage of their improved dynamic response, when compared
to low frequency more traditional switched-mode converters, a
class E3 polar transmitter for the EDGE standard has been
designed and tested at 770 MHz, offering an average global
efficiency over 46% at 4.3 W of output power, through RF-based
amplitude and phase constituting branches. Finally, the potential
of such a high frequency of operation in terms of power density is
explored, absorbing undesired coil parasitics for the original LC
series interconnecting network in a 1 GHz design methodology.
Index Terms— Class E, DC-DC power converters, FETs,
gallium nitride, high power amplifiers, phase control,
predistortion, pulse width modulation, radio transmitters,
rectifiers, resonant inverters, switching converters, UHF circuits,
zero voltage switching.
M
I. INTRODUCTION
ODERN
power
electronics
applications
are
continuously demanding power efficient converting
systems with a very fast transient response and improved
control bandwidth. That has been recently the case, for
instance, of the envelope modulator in envelope tracking (ET),
envelope elimination and restoration (EER) or hybrid ET/EER
wireless transmitters [1], where the amplitude component of a
high data rate digitally-modulated signal (multicarrier
WCDMA, OFDM or similar), with tenths of MHz of spectral
content, has to be linearly reproduced at the output. Together
Manuscript received July 10, 2012. This paper is an expanded paper from
the IEEE MTT-S Int. Microwave Symposium held on June 17-22, 2012 in
Montreal, Canada.
This work was supported by the Spanish Ministries MICINN and
MINECO through the FEDER co-funded project TEC2011-29126-C03-01
and CSD2008-00068. J. A. García and R. Marante acknowledge the funding
received by means of a Mode A Professorship Mobility Grant (ref. PR20100202) and a MAEC-AECID Doctorate Grant Program (ref. 0000524566),
respectively.
J. A. García, R. Marante and M. N. Ruiz are with the Department of
Communications Engineering, University of Cantabria, Plaza de la Ciencia s/n
39005 Santander, SPAIN (Phone: +34-942-202218; fax: +34-942-201488; email: joseangel.garcia@unican.es).
with the interest in miniaturization, associated to the reduction
in the required energy storage and the use of smaller valued
and sized passive components, as to reach the power supplyin-package (PSiP) and power supply-on-chip (PwrSoC)
ultimate targets [2], a great motivation has appeared on the
operation of power converters at switching frequencies quite
over the 0.1-10 MHz range of today’s figures.
Achieving competitive efficiency values in DC/DC
converters at VHF, UHF or higher frequency bands, requires
keeping frequency dependent switching loss mechanisms
under control. Using zero voltage switching (ZVS) [3], they
may be alleviated by mitigating the voltage/current overlap
while also forcing a low voltage across the semiconductor
terminals during the ON/OFF transitions, resulting also in a
reduction of the electromagnetic interference (EMI) associated
to hard-switched more traditional converters [4]. Several
solutions at HF and VHF bands have appeared during the last
years [5], based on class E2 [6] or more recently in class Φ2
topologies [7]. Operation at higher frequencies was also
explored in the past [8], but restricted to small power levels,
mainly due to the non availability of appropriately fast power
transistors and Schottky diodes by that time.
In this paper, the implementation of UHF resonant DC/DC
power converters, following class E2 topologies, is considered.
The use of RF depletion-mode GaN HEMT devices, both for
the inverter and the synchronous (active) rectifier, together
with high Q lumped-element terminating networks allow
improving the operating bandwidth while also preserving a
high efficiency. The output voltage is shown to be perfectly
controlled through different techniques, each with its
advantages and limitations, finding the improvement of the
dynamic response application in a wireless high efficiency
transmitter. A solution is also considered in the
miniaturization direction.
In section II, the selected topology is introduced, described
and adapted according to UHF particular implementation
restrictions with Gallium Nitride transistors. Characterization
results are then presented in section III under different output
voltage control strategies. Special attention is put in the design
of an alternative outphasing scheme, introducing recent
advances on class E load modulation techniques. The use of a
carrier bursting converter as envelope modulator for an EDGE
standard wireless polar transmitter is considered in section IV,
while a small sized topology is finally proposed in section V.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
II. CLASS E2 DC/DC CONVERTER
With the aim of operating at hundreds of kHz or even MHz
frequencies, alternative transistor-based topologies to hardswitched converters were proposed by power supply
specialists in the 80’s [9]. As turn-on and turn-off losses were
associated to the employed rectangular waveforms, the
introduction of a resonant circuit helped shaping either a
sinusoidal voltage or a sinusoidal current. Combining a
DC/AC resonant inverter and a high-frequency rectifier, a
resonant converter first transforms the DC input power into a
controlled AC power, to then turn it back into the desired DC
output [3, 4].
A. Original Topology
Conceived as a class E RF power amplifier (RF PA) in [10],
the idea of using zero voltage and zero voltage derivative
switching (ZVDS) for the inverter in resonant power
conversion is due to Gutmann [11], while a deeper insight into
its operation was later provided in [12]. Forcing soft-switching
conditions not only for the inverter, but also for the rectifier,
the double class E or class E2 converter was later proposed by
Kazimierczuk in [13, 14]. One of its many possible topologies
[13] is presented in Fig. 1, where the rectification is of active
or synchronous type. At high operating frequencies, UHF and
beyond, fast enough Schottky diodes able of handling high
current and voltage levels are rarely available, reason why a
transistor-based rectifier may be the only choice.
Lb
a)
C
Rdc
Cout
b)
Rac
X
Cout
Lb
Rac
Cout
2X
Rac =
(1a)
0.1836
ω ⋅ Cout
X=
0.2116
ω ⋅ Cout
(1b)
Rdc
Cout
(1c)
with D the switching duty cycle, while Rac and X the real
and imaginary components of the impedance to be seen by the
device (including the capacitance) at the fundamental
frequency. Under these conditions, the inverter was proved to
be seen by its DC supply as a load with value,
Rdc =
1
π ⋅ ω ⋅ Cout
(2)
From the inverter circuit, applying the time reversal (TR)
duality principle as described in [16], the class E rectifier of
Fig. 1b) may be easily derived. In this case, optimum
operation is obtained for D, X and Rdc values as in eq. (1a),
(1c) and (2), respectively, while the required phase shift, ∆φ,
between the gate-to-source and the drain-to-source voltage
waveforms should be set to 180º as to obtain the desired
synchronization. The class E rectifier, as inverter TR dual,
would then appear to its AC excitation as a perfectly resistive
load Rac, following eq. (1b).
The class E2 DC/DC converter of Fig. 1c) results from
cascading the above described circuits. The rectifier provides
by itself the load resistance Rac required by the inverter, so
both of them may operate under the desired soft-switching
conditions without adding any further element for the
interconnection. Combining in series the two resonant circuits,
the overall reactance to be presented by the resulting LC
combination [16] should then be:
0.4232
2⋅ X =
ω ⋅ Cout
(3)
For an ideal lossless operation, the output DC voltage
would be equal to the input biasing value, while the DC load
offered by the converter to its power supply would be exactly
its load resistance Rdc.
Lb
c)
Rdc
X
Lb
C
L
L
D = 0.5
Rdc
Fig. 1. a) The class E inverter or PA, b) its time reversal dual, a
class E synchronous rectifier, together with c) a basic class E2
DC/DC converter obtained when cascading a) and b).
The class E inverter of Fig. 1a) was analyzed in detail in
[15], assuming an infinite choke inductance, Lb, in order to
consider the device biasing branch as a DC current source, and
a high enough loaded quality factor for the resonant circuit as
to assure the current through it is a sinusoid at the driving
signal frequency. Tuning the LC series resonant circuit
slightly below the switching frequency, the optimum
conditions, defined as those resulting in the ideal 100%
efficient operation with maximum output power (according to
the voltage and current restrictions imposed by the device
characteristics), were found by Raab [15] to be:
B. Device Model and Simulations
Following this basic topology and concept, a packaged GaN
HEMT from Cree Inc., the CGH35030, was selected to be
employed as the switching element. Besides this technology
offering a very low value for the on-state resistance output
capacitance product, Ron.Cout, its high breakdown voltage (>
120 V) allows alleviating the transistor stress associated to the
voltage peaking waveform (Vpeak = 3.562·VDD) typical of a
class E mode of operation.
In order to construct a very simple model of the device as a
switch, the ON state resistance was estimated from the low
drain voltage slope of the measured I/V curves at high VGS
values, as represented in Fig. 2a). For the equivalent
frequency-dependent output capacitance, the S22 parameter
was measured in Fig. 2 b) at VDS = 28 V (the voltage value
initially selected for operation) and for a VGS slightly below
pinch-off, just before observing any significant increase in the
output conductance.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
a)
3
RON = 1/m = 0.5041 Ω
2.5
VGS = -3.40 V
VGS = -3.30 V
VGS = -3.00 V
VGS = -2.70 V
VGS = -2.40 V
VGS = -2.10 V
VGS = -1.80 V
VGS = -1.50 V
VGS = -1.20 V
VGS = 0 V
IDS (A)
2
1.5
1
0.5
0
0
5
10
20
25
30
1.0
b)
15
VDS (V)
10.0
4.0
5.0
3.0
2.0
0.8
0.4
0.6
0.2
0
1.0
0.25 GHz
COUT = 3.34 pF
2 GHz
C OUT = 3.74 pF
ηd =
Pout _ DC
Pin _ DC
(4)
As expected, the efficiency figure reduces with frequency,
staying above 80% up to 1 GHz. Considering the simplicity of
the model as well as the perfectly ideal terminating conditions
implemented in the simulations, the real performance would
be probably below these predicted curves. The design
frequency was then selected to be 780 MHz, since the
maximum frequency for optimum class E operation [17, 18]
was estimated from the extracted Cout to be around this value.
The drain voltage and current waveforms, obtained from
HB simulations at 780 MHz, are represented in Fig. 4. The
voltage waveforms at the rectifying device in Fig. 4b, as
theoretically described [13, 16], are time-reversed versions of
those for the inverter in Fig. 4a. When one transistor is in its
conduction state, the other is not. The ZVS and ZVDS
conditions may be also appreciated, in the device transitions
from OFF to ON (inverter) or from ON to OFF (rectifier).
S(2,2)
=28 V & VGS
=-3.5 V
CGH35030 @ VDS
DS
GS
4 GHz
COUT = 7.16 pF
The efficiency figure was simply computed as in eq. (4),
with Pout_DC and Pin_DC representing the output and input DC
power, respectively.
0.5 GHz
C OUT = 3.52 pF
1 GHz
COUT= 3.57 pF
-1.0
a)
Fig. 2. Estimated values for Ron and Cout. a) Ron extracted from the
measured I/V curves and b) Cout from the S22 parameter.
With this model, and forcing the required conditions for
both the inverting and the rectifying devices, the class E2
topology was evaluated in terms of the switching frequency
through harmonic balance (HB) simulations. The converter
DC load and the interconnecting reactance were carefully
adjusted according to eq. (2) and eq. (3), respectively, while
open circuit conditions were implemented at both drain
terminals to the second and third order harmonics. The precise
phase shifting angle between the gate driving signals, required
for assuring the desired coherent or synchronous operation of
the rectifier, was also set at each frequency point. In Fig. 3, the
obtained evolution for the output DC voltage and drain
efficiency are plotted.
100
96.3 %
27.5 V
83.75%
VOUT (V)
25
80
24.1 V
20
15
60
35.2 %
12.5 V
40
Efficiency (%)
30
20
109
1010
Frequency (Hz)
Fig. 3. Evolution of (─) output voltage and (--) drain efficiency
with the switching frequency as obtained from HB simulations.
10
108
b)
Fig. 4. Drain voltage and current waveforms for a) the inverting
and b) the rectifying device, as obtained from HB simulations. The
observed ringing may be ameliorated with the number of harmonics.
When turned-on, the rectifying GaN HEMT operates in the
third quadrant of its I/V characteristics, as it should provide
power to the DC load. Most available non-linear models, using
a hyperbolic tangent function over Vds as part of the Ids(Vgs,Vds)
equation, fail in accurately reproducing this “inverse”
operating region.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
4
2nd/3rd Harm.
Termination
C3p
RFIN_INV
RFin
Hybrid
Coupler
00
90
BiasTee
Lin
CB
LB
Cin
L3p
L3s
C3s
VGS
0
C3p
LB
50 Ω
Lin
CB
BiasTee
RFIN_RECT
L3p
L3s
C3s
Cin
Input network
L2p
L2s
VDS_IN
LB
CB
BiasTee
C2s
Lfun
Cfun
L2p
L2s
C2s
2nd/3rd Harm.
Termination
Cfun
LB
Inv./Rect.
Matching
According to the reported evolution of output voltage and
overall efficiency versus the envelope duty cycle, for a pulse
repetition frequency of 500 kHz, a 3.7:1 control range could
be perfectly covered with ηov ≥ 60% [21]. Being the duty
cycle to reconstructed voltage characteristic nearly linear, such
coding results appropriate for reproducing dynamic variations
with high fidelity. However, as the efficiency figure started
degrading when increasing the pulse repetition frequency over
a few tenths of MHz, mainly due to the highly demanding
requirements for terminating the rectifying circuit at the
carrier frequency as an open, while at the PWM frequency
components as a short, excess losses could appear in the
reproduction of wideband communication signal envelopes, as
exemplified with a WCDMA format in [21].
B. Output Voltage Control through Frequency Modulation
Other control techniques may offer alternative performance
to PWM, as described in detail along this and the following
sub-section. Attending to the measured evolution of efficiency
and DC voltage, reproduced from [21] in Fig. 6, the switching
frequency may be used as control variable instead of the
envelope duty cycle. Proposed with the original topology in
[13, 14], advantage may be taken from the reduction in the
output voltage with frequency, typical of class E operation, as
to code the desired voltage variations using frequency
modulation, FM, of the gate driving signals.
40
VDS_OUT
28.88 V
LUMPED ELEMENT VALUES IN THE CONVERTER SCHEMATIC
Inductor
Lin
L3p
L3s
L2s
Lfun
LB
3.85 nH 5.6 nH 2.5 nH 8 nH 5.6 nH 43 nH
Value
Capacitor
Cin
C3p
C3s
C2s
Cfun
CB
8.2 pF
0.5 pF 0.8 pF 0.6 pF
3 pF
82 pF
Value
L2p was implemented with a small length of transmission line.
III. DC/DC CONVERTER PERFORMANCE
Considering the overall efficiency, ηov, as the figure of
merit, where the required RF gate driving power, Pin_RF, is
accounted for as in eq. (5), a peak value of 72% was reported
in [21], in the state-of-the-art for DC/DC converters in this
frequency band.
η ov =
(P
Pout _ DC
in _ DC
+ Pin _ RF )
(5)
A. Output Voltage Control through Carrier Bursting
In [21], a pulse width modulation, PWM, over the envelope
of the gate driving signal (an ON/OFF type of output voltage
control strategy [5]) was proposed. This mode of operation,
with bursts of the carrier exciting the device gate terminals,
has been also suggested for high efficiency transmitters [22].
The switching frequency and its optimum duty cycle, D = 0.5,
were kept fixed as to have switching losses under control.
VOUT (V)
Fig. 5. Simplified schematic of the UHF converter from [21].
TABLE I
100
65.52 %
72.38 %
75
24.1 V
50 %
20
15.1 V
720 MHZ
770 MHZ
50
25
Efficiency (%)
C. UHF Converter Design
As the simple LC series network of Fig. 1 may turn
inappropriate for RF operation, due to the undesired reactive
parasitics generally associated to the coil and the capacitor, a
multi-harmonic terminating network was proposed in [19], as
a lumped-element version of the widely used microwave
transmission line topology suggested in [20]. Based on this
technique, the topology selected for the UHF converter and
already introduced in [21] is reproduced in Fig. 5. Using Air
Core “Spring” series inductors from Coilcraft and 100B
multilayer capacitors from ATC (values included in Table I),
the desired drain termination at the fundamental, second and
third harmonics were forced. A commercial hybrid coupler
from Anaren allowed distributing the gate excitations with the
required phase shift. A photograph with implementation
details may be also found in the IMS paper [21].
815 MHZ
0
750
800
850
Frequency (MHz)
Fig. 6. (─) Output voltage and (--) efficiency versus the switching
frequency for a continuous wave excitation (VDD = 28 V).
0
700
A maximum value of 72% could be obtained for a voltage
0.83 times the peak value, while the efficiency could be kept
over 50% for a 1.9:1 voltage relation (corresponding to a
peak-to-average power ratio, PAPR, of 5.6 dB, if thinking on
its possible use as envelope modulator). Although for such
specific application, the efficiency would be preferred to peak
at a lower voltage value, this strategy would avoid the impact
of a reconstruction filter in terms of the dynamic response.
C. Output Voltage Control through Outphasing
A third possible alternative for output voltage control, also
employed for low frequency DC/DC converters using class D
or class DE topologies, is based on phase coding. Following
the outphasing principle [23], two amplifiers are combined in
a phase controlled inverting topology, followed by a rectifier.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
5
1.0
Advantage is usually taken from class D relative independence
on the appearance of reactive components in the load.
At the frequencies of our interest, where single-switch
inverters are preferred, the impact of a non purely resistive
termination at the inputs of a Chireix combiner may seriously
degrade the performance of class A, AB, B, C, F or inverse F
based outphasing transmitters [24]. However, as it has been
recently proved in [25], that is not necessarily the case for the
class E topology. If properly transforming the load modulation
paths, imposed by the combiner, into impedance loci at the
drain terminals as close as possible to the optimum, where the
ZVS condition may still be kept, through the addition of a
carefully selected length of transmission line, the output power
may be controlled while also conserving a high efficiency.
Impressive results, following this strategy, have been reported
for a wireless transmitter in [26].
Based on these works and using the simplified switch
model of section II.B, a load-pull simulation at the
fundamental was performed over the basic class E inverting
topology of Fig. 1a) at 780 MHz. Open circuit terminations
were forced at the second and third harmonics. The efficiency
and output power circles are represented in Fig. 7, together
with the trajectories to be obtained after properly transforming
the impedance at both inputs of a simple reactive combiner
with X = 35 Ω (see Fig. 8 for details). From this very simple
simulation, an efficiency value over 80% could be expected
for such outphasing class E inverter along a power range
greater than 8 dB.
90%
45dBm
10.0
5.0
4.0
3.0
2.0
70%
1.0
0.8
0.6
0.4
0
0.2
80%
50dBm
Circles 90:-10:70
Efficiency (%)
Circles 50:-5:30
Pout (dBm)
Class E Circuit
C3p
RFin
Lin
1
Rin
Cin
L2p Lf0
L3p L L Cf0
3s 2s
C3s C2s
2
LCh
VDS_IN
VGS
Chireix
Combiner
CCh
Class E Circuit
C3p
RFin 1
Lin
Rin
Cin
L2p Lf0
L3p L L Cf0
3s 2s
C3s C2s
2
VGS
Class E Inverter
Class E
Synchronous
Rectifier
Tx Line
Length
Tx Line
Length
Lph
Lph
Cph
Cs
2
Class E Circuit
High Power
Load (50 Ω)
1
+
–
VDS_OUT
Component values
Lph
Cph
LCh
CCh
CS
9.85 nH
1.4 pF
3.85 nH
8.2 pF
0.1 pF
Fig. 8. Schematic for the proposed UHF class E2 outphasing
converter. Added lumped element values have been tabulated.
This sample should be correctly dimensioned as to force a
switched-mode operation of the rectifier over a range as wide
as possible. To avoid device damage at high power values, the
resistance in its gate DC path may be correctly dimensioned in
such a way that the gate-to-source voltage is reduced with
respect to the applied biasing value when a small rectifying
current appears at this terminal. In the proposed design, a
small valued capacitor, Cs, was used to take the sample,
followed by the introduction of a T Lph-Cph-Lph network in the
drain-to-gate interconnecting branch as to assure the
appropriate phasing between the drain-to-source and gate-tosource voltages. Since the selected GaN HEMT is able to
provide a very high gain at this frequency band, close to 20
dB, the impact on overall efficiency when taking such a small
sample of the inverter AC output (the rectifier AC excitation)
may be neglected.
In Fig. 9, a photograph with details of this alternative double
class E UHF converter, implementing the outphasing control
voltage technique, is presented. No special attention was paid
to produce a compact design, only to validate the topology.
Rac+j.X
Zd(f0)opt.
40dBm
Chireix -X=-35 Ω
Input 1
-1.0
35dBm
30dBm
Chireix X = 35 Ω
Input 2
Fig. 7. Class E PA load-pull simulation including the output power
and efficiency circles. The transformed impedance trajectories due
to the combiner and the transmission line are also included.
Based on these results, an alternative class E2 DC/DC
converter to the one in [21] has been designed, following the
schematic represented in Fig. 8. Two class E UHF PAs are
asymmetrically combined through a reactive lumped-element
topology and lengths of transmission line, constituting an
outphasing inverter, followed by a class E rectifier. As when
controlling the inverter output power, the resulting phase
component of the RF (our AC) signal also varies with the
outphasing angle, the phase of the rectifier gate driving
excitation would need to be consequently adjusted. A possible
solution to this problem comes from taking a sample of the RF
signal at the rectifier input to excite its device gate terminal.
Fig. 9. Photograph with details of the UHF DC/DC converter,
implementing the outphasing principle, and the employed test setup.
After characterizing the converter in terms of the
outphasing angle, the output DC voltage and the overall
efficiency have been represented in Fig. 10.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
6
23 V
20
40
17 V
10
20
0
150 200 250 300 350
Phase (degree)
Fig. 10. (─) Measured output voltage and (--) efficiency profiles
versus the outphasing angle at VDD = 28 V and f = 780 MHz.
0
0
50
100
A peak overall efficiency also of 72% has been obtained, but
in this case for an output voltage 1.52 times below the
maximum (corresponding to a 3.66 dB PAPR signal if
thinking again on an envelope modulating application). The
overall efficiency was kept over 50% for a 2:1 voltage control
range. Although this range is reduced with respect to the
results using the carrier bursting control technique, no
reconstruction filter is here required. This makes this topology
highly attractive in terms of the dynamic response. Through a
careful selection of the reactance value and the use of an
alternative solution for the rectifier gate driving signal, the
voltage range might be extended as to reproduce signals with a
higher PAPR.
DSP Unit
60
50 %
50 %
AM DPD
PM DPD
RFin_PWM
DAC
Pre-Distorting
Functions
VOUT(V)
30
Cartesian-to-Polar
Converter
35 V
VDD_in
80
Tx - Base-Band
72 %
Efficiency(%)
40
Sampling
clock
DAC
Class E2
DC/DC
Converter
Reconst.
filter
RF Carrier
Oscillator
PM
Modulator
RFin_PM
Class E
RF PA
RFout
Fig. 11. Diagram of the proposed UHF class E3 polar transmitter.
In Fig. 12, a photograph with details of the RF part of the
scheme may be appreciated. Three similar GaN HEMT
devices, the CGH35030 from Cree Inc., are employed, two for
the converter plus the one for the RF PA. The CLC
reconstruction filter, with a 1 MHz bandwidth and a
maximally flat response may be also distinguished. A 5 MHz
pulse repetition frequency was employed for PWM coding the
envelope variations. Since this frequency is quite below the
carrier value, optimum rectifier terminations are possible.
IV. CLASS E3 POLAR TRANSMITTER
In order to test the potential of the carrier bursting class E2
converter of [21] in a real fast response application, as the
above mentioned bias adaptation wireless transmitters, a polar
architecture has been selected. Since in a pure EER technique,
the load impedance presented by the RF PA stays constant,
there would be no need for regulating the converter output
voltage despite its finite output impedance. Such regulation
would be instead required in ET or hybrid ET/EER schemes.
Taking also into account its bandwidth limitations, in terms
of efficiency, related to the minimum required ratio to be
conserved between the desired converter frequency response
and the pulse repetition frequency (for PWM coding such
voltage variations), as well as between this frequency and the
carrier, an EDGE standard signal was selected. Having a
moderate 200 kHz bandwidth, a 3.8 dB PAPR and a hole in its
constellation, to avoid the feedthrough effect, this format is
certainly amenable for polar transmission.
A. UHF Polar Transmitting Scheme
In Fig. 11, a simplified diagram of the proposed class E3
polar transmitter is represented. The class E2 resonant power
converter is used to high level amplitude modulate a class E
RF PA, in an analogous way to [27], excited with a constantenvelope phase modulated (PM) signal. The same carrier
frequency is used, both for the PM and the AM branches,
resulting in a fully RF-based implementation. One of the
advantages of handling the envelope with a RF switching
frequency is the reduced size of the implemented transmitter.
Fig. 12. Photograph with details of the implemented EDGE class E3
polar transmitter at 770 MHz.
A second advantage of using this type of converter has to
do with the correction of the differential delay between the
AM and PM paths, one of the main nonlinear distortion
sources in this type of architectures [28, 29]. Being the AM
component processed also at the frequency used for the PM
modulation, the differential delay was not significant at all.
B. RF PA Stage
For the RF PA, a stage similar to those integrating the
converter has been selected. In Fig. 13, the measured static
(with CW RF excitation) Vdd-to-AM and Vdd-to-PM profiles
are plotted, together with the probability density function, pdf,
for the EDGE AM component and the PAE evolution. A peak
drain voltage value of 28 V was assumed. As typical from
class E operation [30], the most significant part of the
envelope variation coincides with a nearly linear amplitude
characteristic and a minor undesired phase modulation.
Although the voltage and current waveforms have not been
measured, these profiles may show that the device is operating
close to the desired ZVS and ZVDS conditions.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
7
1
75
50
0.75
25
0.5
0
PAE
EDGE pdf
-25
-75
0
0.25
|Vout |
∠ Vout
-50
5
10
15
20
VDS (V)
25
30
0
35
Normalized EDGE pdf
and PAE
|VOUT| (V) and ∠VOUT(º)
Fig. 13. Vdd-to-AM, Vdd-to-PM and PAE static profiles for the class
E RF PA. The EDGE envelope pdf function has been also plotted.
Cartesian-to-Polar
Converter
C. DPD and Characterization Results
After implementing the transmitter, a static characterization
of output amplitude, ay, and phase variations, φy, with the
envelope voltage, ax, was made (see Fig. 11 for notation). The
input DC biasing voltage was fixed to 35 V, as to obtain a
peak voltage at the converter output close to 28 V. A simple
memoryless digital predistortion, DPD, based on [31], was
then implemented as a look-up table, LUT, in order to
reproduce the desired signal. As described in Fig. 14, the
digitally generated amplitude component, ax(n), should
include corrections to the AM-to-AM profile, including PWM
modulation, DC/DC converter and RF PA Vdd-to-AM
nonlinearities. After that, the parasitic phase variations, ∆φ, to
be introduced by the AM modulating signal, from the
characteristic in Fig. 13, were digitally subtracted from the
desired PM component, φy(n).
-10
Original EDGE
Recovered EDGE
-20
Pout (dBm)
Taking also into account the nearly linear Duty Cycle-toAM characteristic measured for the class E2 converter in [21],
a low predistortion effort could be required for transmitter
linearization. Most part of the envelope also fits in the region
where the power added efficiency, PAE, is over 75%, reason
why a high average figure could be expected.
-30
-40
-50
-60
-70
769
769.5
770
Frequency (MHz)
770.5
771
Fig. 15. Spectrum of the output signal, as compared to the original.
A summary of the measured output power, linearity and
efficiency figures is also included in Table II. The linearity
specifications, -58 dBc at 400 kHz and -60c dB at 600 kHz,
are satisfied with an average transmitter efficiency figure over
46% (including envelope modulator and RF PA). In these
specific operating conditions, the average efficiency of the
DC/DC converter was estimated to be over 60%.
TABLE II
CLASS E3 TRANSMITTER FIGURES OF MERIT
Figure
Measured Value
Output Power, Pout
4.3 W
Adjacent Channel Power Ratio, AdCPR
- 61 dBc
Alternate Channel Power Ratio, AlCPR
- 64 dBc
Average Error Vector Magnitude, EVMave
1.39%
46.33%
Average Tx Efficiency, ηave
Average Tx Power Added Efficiency, PAEave
43.61%
Attending to these results, appropriately dimensioning a
class E2 power converting topology, a linear reproduction of a
time-varying voltage envelope may be assured with low
losses. If interested in efficiently handling signals with a wider
envelope, such as WCDMA, LTE or similar, using this
particular PWM resonant converter, a pulse repetition
frequency of at least 100 MHz would be required. If using a
higher carrier switching frequency, such as the 2.14 GHz
required for base stations, the desired filter terminations would
be feasible at the expense of a reduction in the achievable peak
efficiency value (at least for the here employed devices).
V. UHF POWER CONVERSION FOR MINIATURIZATION
Fig. 14. Diagram representation of the implemented DPD.
Having described the benefits of a UHF power converter in
terms of frequency response enhancement, attention may be
paid to the second benefit of a high frequency conversion for
power density improvement (size and weight reduction). The
above proposed implementations are not exactly compact,
mainly due to the selection of a multi-harmonic network to
properly terminate the inverting and the rectifying devices, as
well as the use of packaged versions for the transistors.
Once this simple predistortion strategy was applied, the
spectrum of the output EDGE modulated signal was compared
to the spectrum of the original version in Fig. 15. As it may be
appreciated, the recovered signal nearly fits the original. Outof-band emission components were also measured at ± 5 MHz
from the carrier and 55 dBc below its level. They are due to
the PWM spectral components and the attenuation offered by
the implemented reconstruction filter.
A. LC Series Class E2 Converter using Coil Self-Resonance
To reduce the footprint and volume, the original LC series
topology in [13, 14] is a very attractive candidate. If taking
advantage of the lumped-element parasitics, selecting a high Q
coil with a self-resonant frequency between the second and
third harmonic, while carefully tuning the capacitance value as
to provide the desired 2·X reactance of eq. (3), the converter
size could be significantly reduced.
+
–
⁺
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
8
1.0
1 GHz
r 14.2402 Ohm
x 28.9213 Ohm
1 GHz
r 10.766 Ohm
x 24.816 Ohm
2 GHz
r 222.793 Ohm
x 471.223 Ohm
30
24.9 V
75
71.7 %
50 %
63.7 %
20
50
25
Efficiency (%)
100
29.3 V
VOUT (V)
After characterizing, as in section II.B, a die GaN HEMT
with similar power capability, the CGH60030, also from Cree
Inc., a simple network with an 8 nH Air Core “Spring”
inductor from Coilcraft and two 8.2 pF 100B ATC capacitors
was adjusted. In Fig. 16, the evolution with frequency of the
impedance as seen in one of its port, when loading the other
with the desired AC resistive component is shown. As it can
be appreciated, the impedance at the fundamental frequency
nearly fits the desired Rac + j·2·X value, while the second and
third order harmonic terminations are relatively close to the
open circuit condition thanks to the coil parasitic capacitance.
12.7 V
10
0
0.94 0.96 0.98 1
1.02 1.04 1.06
Frequency (GHz)
Fig. 18. (─) Measured output voltage and (--) efficiency versus the
switching frequency at VDD = 28 V for the converter in Fig. 17.
10.0
3.0
4.0
5.0
2X
2.0
0.8
1.0
0.4
0.6
0.2
0
VI. CONCLUSION
Rac
Ref. Coef .
Series LC network
-1.0
Ref. Coef .
Rac+j.2.X
3 GHz
r 16.8319 Ohm
x - 222.727 Ohm
Fig. 16. Measured evolution with frequency of one port impedance,
when loading the other with the optimum resistance value, Rac.
In Fig. 17, a photograph of the suggested 1 GHz
implementation is shown. The input and output DC networks
have been included, as well as gate matching capacitors. The
gate driving signal was externally split using a commercial inphase power divider, also from Anaren. The desired phasing
between the inverter and rectifier excitations was set by
adding a few SMA transitions. The gate biasing voltage was
also applied to both die devices through an external bias tee.
VDD_in
Vout
VGS+RFin|inv.
VGS+RFin|rect.
CGH60030 Dies
2
Class E resonant topologies for DC/DC power conversion
at Ultra High Frequencies (UHF) have been designed and
characterized in this paper, considering their benefits for
improving the response speed and power density over current
lower frequency solutions. In the first case, a class E3 polar
transmitting application for the EDGE standard has been
proposed and tested at 770 MHz, offering an average global
efficiency of 46% for more than 4 W of output power, with
amplitude and phase branches fully implemented at the carrier
frequency. Further considerations for obtaining a higher
bandwidth have been also suggested, such as the use of an
outphasing output voltage control strategy. In the
miniaturization direction, a compact implementation, taking
advantage of passive element parasitics and die device
versions has been also proposed. A peak value for the overall
conversion efficiency over 70% has been measured, at 12.4 W
of output power and 1 GHz. Comparing this work with
previously published converters (see Table III) the obtained
efficiency results are in the state-of-the-art according to the
switching frequency and power level.
Although the employed GaN HEMTs have not been
conceived for this mode of operation and the efficiency figures
are not currently competitive with more traditional kHz
converters, the great potential of RF conversion using this
technology has been proved.
TABLE III
STATE-OF-THE-ART HIGH FREQUENCY DC/DC CONVERTERS
LC network
Fig. 17. Photograph with magnified details of the miniaturized
implementation at 1 GHz.
B. Measured Performance
The characterization results in terms of frequency are finally
represented in Fig. 18. A good performance has been obtained,
with a peak overall efficiency over 70%, through a much more
compact and simple implementation. The voltage and
efficiency profiles measured versus the duty cycle
approximately followed those reported for the converter in
[21]. Frequency or carrier bursting modulation for output
voltage control would be also feasible.
Switching
Frequency
(GHz)
Output
Voltage
(V)
Output
Power
(W)
Overall
Efficiency
(%)
Reference
0.02
7
6
84
[32]
0.03
65
472
83
[33]
0.03
33
220
87
[7]
0.05
42
35
90
[34]
0.1
23.7
1.7
55
[6]
0.15
3.3
3.3
84
[35]
0.78
24
11.5
72
This work.
1
25
12.5
72
This work.
4.5
2.15
0.053
64
[8]
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
ACKNOWLEDGMENT
J. A. García wants to acknowledge all the advice and
suggestions on the treated topics received from Prof. Z.
Popovic and Prof. D. Maksimovic, Univ. Colorado at Boulder,
Prof. J. Sebastian, Univ. Oviedo, Prof. D. Perreault,
Massachusetts Institute of Technology, Prof. J. C. Pedro,
Univ. Aveiro, and Dr. F. Raab, Green Mountain Radio
Research Co. The contributions to this research line from
previous members of the group, Dr. L. Cabria and Ms. L.
Rizo, are also appreciated, as well as the support received
from Mrs. Sandra Pana, Univ. Cantabria, with die mounting
and bonding, and from Mr. Ryan Baker, Cree Inc., related to
the GaN HEMT devices. Finally, the authors want to thank the
editor and the reviewers by their kind comments and detailed
suggestions to improve this manuscript.
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Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
José A. García (S’98, AM’00, M’02) received
the Telecommunication Engineering degree
(with honors) from the Instituto Superior
Politécnico “José A. Echeverría” (ISPJAE) in
1988, and the Ph.D. degree (with a University
Prize) from the University of Cantabria in 2000.
From 1988 to 1991, he was a Radio System
Engineer at a High Frequency Communication
Center, where he designed antennas and HF
circuits. Between 1991 and 1995, he was an
Instructor Professor in the Telecommunication
Engineering Department, ISPJAE. He worked
also as a Radio Design Engineer on base station arrays for Thaumat Global
Technology Systems (1999-2000), and as a Microwave Design
Engineer/Project Manager for TTI Norte from 2000 to 2001, being in charge
of the research line on SDR while involved in amplifying active antenna
design. From 2002 to 2005, he was a Senior Research Scientist at the
University of Cantabria, where he is currently an Associate Professor. He was
a Visiting Researcher at the Microwave & RF Research Group (Prof.
Popovic), Univ. Colorado at Boulder, during 2011.
His main research interests include nonlinear characterization and modeling of
active devices, as well as the design of power RF/microwave amplifiers, high
efficiency transmitting architectures (incorporating arrays), and RF DC/DC
power converters. He has been a reviewer for the MTT Transactions as well as
many other international journals and conferences.
Reinel Marante Torres (S’12) was born in
Havana, Cuba, on June 14, 1980. He received
the B.S. degree in Telecommunication
Engineering from Instituto Superior Politécnico
“José A. Echeverría” (ISPJAE) in 2004 and
MsC. degree from University of Cantabria in
2009. He is currently working toward the Ph.D.
degree at Dpt. of Communications Engineering
(DICOM), University of Cantabria. His research
interests include active devices nonlinear
modeling and highly efficient transmission
technologies.
María de las Nieves Ruiz Lavín (S’12) was
born in Santander, Spain, on September 19,
1983. She received the B.S.E.E. degree in 2010
and she is currently working toward the
M.S.E.E. degree at the University of Cantabria,
in Spain. Her research interests include highefficiency microwave power
amplifiers,
rectifiers, oscillators and converters.
Copyright © 2012 IEEE. Reprinted from IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 12, DECEMBER 2012
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of
Cree’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
pubs-permissions@ieee.org By choosing to view this document, you agree to all provisions of the copyright laws protecting it.