Arabi, E., De Falco, P. E., Birchall, J., Morris, K., & Beach, M. (2017).
Design of a triple-band power amplifier using a genetic algorithm and
the continuous mode method. In
2017 IEEE Topical Conference on
RF/Microwave Power Amplifiers for Radio and Wireless Applications
(PAWR 2017): Proceedings of a meeting held 15-18 January 2017,
Phoenix, Arizona, USA
(pp. 48-51). (Proceedings of the Topical
Conference on RF/Microwave Power Amplifiers for Radio and
Wireless Applications (PAWR)). Institute of Electrical and Electronics
Engineers (IEEE). https://doi.org/10.1109/PAWR.2017.7875570
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Design of a Triple-Band Power Amplifier Using a Genetic Algorithm and
the Continuous Mode Method
Eyad Arabi, Paolo Enrico de Falco, James Birchall, Kevin A Morris, and Mark Beach
Communication Systems and Networks Research Group
University of Bristol
Bristol, BS8 1UB, UK
Email: eyad.arabi@bristol.ac.uk
Abstract—Dual band power amplifiers use either large and
lossy matching networks, or switches, which do not allow
concurrent operation. In this work, a concurrent, triple-band
power amplifier with a simple matching network is presented.
The theory of continuous modes of operation has been used in the
optimization of the input and output matching networks using a
genetic algorithm. As proof of concept, a design at 0.8, 1.8, and
2.4 GHz has been fabricated and characterized in the laboratory.
A maximum power added efficiency and output power of 70%
and 41 dBm have been achieved using our novel design. The
design described in this paper is based on a solid theoretical
analysis and demonstrates a simplified biasing network. Such
design is highly suitable for next generation wireless systems
with aggregated carriers.
Index Terms—Power amplifier, Multi-band, Triple-band, Ge-
netic Algorithm, Continuous mode
I. INTRODUCTION
T
HE evolution in wireless communications is ever in-
creasing with more users and data-heavy applications
being introduced. As a consequence, the future standards,
such as advanced long-term evolution (LTE), are calling for
considerably increased data rates. Obviously, the wireless
systems currently used (below 6 GHz) will not be able to
accommodate such rates. Moreover, future wireless systems
are also featured by multiple services and applications which
typically require multiple sub-systems. To optimally exploit
the sub-6 GHz bands and reduce the number of sub-systems,
multi-band wireless systems are thus required.
In the design of multi-band wireless systems the most
challenging part is the RF front end. One of the most important
components in the RF front end is the power amplifier (PA). To
address the above-mentioned applications ultra-wideband PAs
can be used. However, if the multiple bands are positioned
wide apart, it becomes very challenging to maintain the per-
formance (linearity and efficiency) of the wide-band amplifier;
therefore, a multi-band design is preferable is such case.
The most critical part of the design of multi-band PAs is
usually the matching networks (MN). An obvious solution is to
design multiple defined MNs with switches [1]. This approach,
however, does not provide concurrent operation and has in-
creased insertion loss due to the use of switches. A conven-
tional way to realize concurrent operation is to design multiple
matching networks and introduce frequency selectivity using
resonators in the form of lumped or distributed components
[2]. These matching networks, however, become large as the
number of bands is increased. They also impose restrictions on
the frequency bands that can be accommodated, and they can
provide the desired impedances at the fundamental frequencies
only. Other designs utilize unified MNs designed to operate
at multiple frequencies, which overcome the restrictions on
the frequency bands and provide the desired impedances at
both the fundamental as well as the second harmonic [3],
[4]. Others are also designed for different classes of operation
at different frequency bands [5], or utilizing the continuous
modes [6]. These designs, however, use very complex methods
to design the matching networks, which limits them to only
two concurrent bands. They also require complex dual band
biasing networks because the bias networks are not part of
the main design [7]. For all of the above-mentioned designs,
increasing the number of concurrent bands either increases
the size, and hence losses, of the MN [2], or considerably
increases the complexity of the MN [3], [4], [6].
In this work, a concurrent triple-band power amplifier is
presented. A very simple and compact output MN is used,
which is optimized by a robust genetic algorithm. The wide
design space provided by the continuous modes has been used
as the goal for the optimizer. Rather than starting from load
pull simulations, this work starts from a theoretical base using
the optimal output impedance at the current generator plane
together with an accurate package model.
II. DESIGN METHODOLOGY
In a conventional class B PA the output current is half-wave
rectified, and the output voltage is a full wave. To achieve
these ideal waveforms the transistor must be biased with zero
quiescent, and the output MN should provide the optimal
impedance at the fundamental frequency and a short circuit
at all the harmonics [8]. It has been shown in [9] that the
linear and efficiency performance of the class B amplifier can
be maintained over a wider impedance space, which is known
as class B-J or continuous class BV. Such wide design space
is very attractive for multi-band designs because the different
bands do not necessarily need to have the same terminations,
which provides flexibility for the optimization of the multi-
band MN.
The theoretical impedance space for continuous class B is
defined at the current generator plane (Z
g en
in Fig. 1) and can
be conveniently expressed as:
C
ds
Z
g en
Z
pkg
PKG
Z
in
L
3
L
1
L
2
L
4
50Ω
(a) (b)
Fig. 1. (a): Schematic of the simple matching network used for both the
input and the output. (b): Block diagram of the transistor with the package
and current generator impedances.
Z
f
0
= R
opt
(1 − jδ) , (1a)
Z
2f
0
= jδ
3π
8
R
opt
, (1b)
and
R
opt
= 2V
DS
/I
max
, (1c)
where Z
f
0
and Z
2f
0
are the fundamental and second har-
monic impedances, respectively. R
opt
is the optimal resistance,
which allows peak voltage swing at maximum output current.
V
DS
is the peak drain voltage and I
max
is the maximum
drain current. δ is the design space parameter, which can take
any real number between -1 and 1. A lumped model for the
package [10] can be used to transform the impedances to the
package plane (Z
pkg
in Fig. 1).
After the theoretical target impedances are defined, the
next step is to select a suitable matching network that can
transform the 50 Ω of the antenna to the appropriate impedance
termination at each band. In this work, a simple two L-sections
have been used as shown in Fig. 1. For biasing purposes,
the stub closer to the transistor is terminated with a short.
This way, no complex, multi-band network is needed for
biasing. This matching circuit has four lines; therefore, eight
optimization parameters (characteristic impedance and length
of each line).
A. Optimization using Genetic Algorithm
The final step in the design is to optimize the MNs. Three
frequency bands have been selected: 0.8, 1.8 and 2.4 GHz.
These frequencies have been chosen as proof of concept and
due to the many applications using them, but other sets of
frequencies can be targeted using this method. Two types of
parameters are used in the optimization process: the eight
parameters of the lines, which are constant across the different
frequencies, and δ, which can change between the three
frequencies providing great flexibility to the optimizer.
Since both the input impedance of the matching network
and the target impedance can be expressed in closed forms,
mathematical optimizers can be used to design the matching
network. In this work, a genetic algorithm has been used due
to its speed and suitability for such problems. The goal of
the optimization is to minimize the difference between the
Optimization
Theory
1
@
@I
1.8 GHz
0.8 GHz
2.4 GHz
@
@I
2×0.8 GHz
2×2.4 GHz
2×1.8 GHz
Fig. 2. Theoretical and optimized complex impedances (at the package plane)
at the fundamental frequencies as well as the second harmonics.
synthesized and the theoretical input impedances. For each
optimization run, the goals are calculated for all the values of
the variable δ and for all the frequencies (the three frequen-
cies and their second harmonics). The value of δ that gives
the minimum total goal for the three frequencies and their
second harmonics is selected. This process is repeated until
the algorithm converges giving the characteristic impedances
and lengths of the optimized transmission lines. In Fig. 2,
the optimized complex impedances of the output MN are
plotted with the theoretical values. It can be seen that the
genetic algorithm has provided very close values at the three
fundamental frequencies and their second harmonics. It is
worth mentioning that for the case of the input MN, the
same algorithm is used, but for conjugate matching and at
the fundamental frequencies only.
B. Simulation
The genetic algorithm described in the previous section
generates values for ideal transmission lines. The next step
is to provide physical dimensions for the matching network.
First, approximate, microstrip dimensions have been obtained
from empirical formulas. Next, a full wave simulation has been
performed to optimize the MN design. This process has been
performed for both the input and output matching networks;
however, only the fundamental is considered for the case of the
input MN. After the MNs have been optimized, the complete
amplifier design is simulated using the transistor model and
the S-parameters of the MNs from the full wave simulator.
III. IMPLEMENTATION AND MEASUREMENTS
The prototype of the triple-band PA has been fabricated
on an RT/Duroid
R
5880 with a thickness of 0.79 mm. A
GaN FET from Cree has been used (CREE CGH40010F) with
standard lumped components for the DC and RF blocks as
shown in Fig. 4.
A single tone, continuous wave (CW) signal has been used
in the measurement of the amplifier with a constant input
power of 27 dBm. The measured and simulated efficiencies,
output powers and gains are plotted in Fig. 3 for the three
frequency bands. A good agreement between the simulation
0.7 0.75 0.8
0
20
40
60
80
PAE (%), P
out
(dBm)
1
1.65 1.7 1.75 1.8
Frequency (GHz)
PAE, meas P
out
, meas PAE, sim
P
out
, sim Gain, meas Gain, sim
1
2.25 2.35 2.45
0
10
20
30
40
Gain (dB)
1
Fig. 3. Simulated and measured PAE, power gain, and output power across the three frequency bands for constant input power of 27 dBm.
and the measurement can be clearly observed with the mea-
sured results shifted downwards slightly (50 MHz). For the
lower band, the PA provides a maximum PAE of 70 % and
an output power of 40 dBm with a flat gain of about 12 dB.
For the middle and high bands, the maximum PAE is 60%
and 58%, respectively. The output powers for these bands are
41 dBm and 40 dBm, respectively, and the gains are about 12
dB and 11 dB, respectively. It can also be seen that the gain
is very stable especially for the first two bands. These results
verify the capabilities of the design methodology to provide
good performances at three different frequencies with such a
simple matching network topologies.
Fig. 4. Photograph of the fabricated power amplifier.
IV. CONCLUSION
In this work, a new design methodology based on the contin-
uous modes is presented. This design approach eliminates the
need for complex and multiple matching networks typically
used for the design of multi-band PAs. To demonstrate the
impact of the new approach, a triple-band amplifier has been
reported. This amplifier uses a matching network much simpler
than the ones used for most of the reported dual-band designs
with comparable PAEs. This triple-band amplifier is suitable
for future wireless applications, which require multi-carrier
operations.
ACKNOWLEDGMENT
This work is supported by the Engineering and Physical Sci-
ences Research Council (EPSRC), under the FARAD project
with grant number EP/M01360X/1 in collaboration with the
University of Sheffield.
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