EFFICIENCY OPTIMIZATION IN LINEAR-ASSISTED SWITCHING POWER CONVERTERS FOR ENVELOPE TRACKING IN RF POWER AMPLIFIERS V. Yousefzadeh1, E. Alarcón2, D. Maksimović1 1
2
Colorado Power Electronics Center ECE Department, 425 UCB University of Colorado Boulder, Colorado, USA {yousefza, maksimov}@colorado.edu ABSTRACT Linear-assisted switchers are based on the idea of combining high efficiency of switching converters with wide-bandwidth capabilities of linear amplifiers. Such linear-assisted switching power converters have been proposed for implementation of wide-bandwidth envelope-tracking power supplies for RF power amplifiers in polar modulation architectures. This paper presents modeling of the overall linear-assisted switcher efficiency as a function of the band separation frequency between the signals processed by the switching and the linear parts. The efficiency model, which is based on the statistical amplitude distributions of the signals, is used to derive the optimum band separation frequency to maximize the overall efficiency. Application examples, including a two-tone test and a CDMA signal in a polar modulation RF transmitter, are presented to illustrate the approach.
Department of Electronic Engineering Universitat Politècnica Catalunya Campus Nord – Mòdul C4. 08034 Barcelona, Spain
[email protected]
envelope-tracking power supply voltage Vo(t) for the RF power amplifier. For this linear-assisted switcher scheme, the question arises of how to optimally separate the frequency bands of the envelope command signal into the low-frequency portion through the switching amplifier versus the high-frequency portion through the linear amplifier. This paper presents modeling of the overall linear-assisted switcher efficiency as a function of the band separation frequency between the signals processed by the switching and the linear parts. The efficiency model, which is based on the statistical amplitude distributions of the signals, is then used to derive the optimum band separation frequency to maximize the overall efficiency of the envelope-tracking converter. Examples are given for cases: a two-tone test signal and a CDMA signal.
1. INTRODUCTION Polar modulation architectures, including the schemes based on the Envelope Elimination and Restoration (EER) or Kahn technique, are considered candidates for efficient implementation of RF transmitters capable of supporting multiple communication standards [1-10]. In a polar modulation transmitter, such as the system shown in Fig. 1, the RF envelope and phase signals have separate power amplification paths. The envelope command signal modulates the power supply voltage Vo(t) of the RF power amplifier through an envelope tracking power converter. High efficiency and wide bandwidth of the envelope-tracking power converter are the key challenges in practical system implementations, especially in space and cost constrained lowpower portable electronic devices such as mobile phones. Several power converter schemes have been introduced for the supply of RF power amplifiers [4-9]. Enhancements to the tracking bandwidth vs efficiency trade-offs in switching converter realizations include multilevel modulation [9], or topologies with interleaving [5, 10]. Linear-assisted switchers are based on the idea of combining high efficiency of switching converters with wide-bandwidth capabilities of linear amplifiers [7]. This solution has also been proposed in the field of power amplifiers for audio applications [11, 12]. Figure 1 shows an implementation where the linear-assisted switcher consists of a buck switching amplifier to generate a low-frequency portion VLP(t) of the envelope signal, and a linear amplifier that generates the remaining high-frequency components VHP(t). A passive filter (L1, L2, C1, C2) combines the signals into the
0-7803-8834-8/05/$20.00 ©2005 IEEE.
Figure 1. A polar modulation transmitter including a linear-assisted switcher as the envelope-tracking power supply for the RF power amplifier.
2. BASEBAND AMPLIFIER MODEL Figure 2 shows the overall block-diagram model of the combined switching and linear amplifier that implements the envelopetracking power converter. We assume that the output signal Vo ideally follows the input envelope command. In this system, the switcher operates in an open-loop manner. The input envelopecommand signal is low-pass filtered and the lower band is amplified through the switcher. The low-pass filter bandwidth is fB. The linear amplifier operates in closed loop, amplifying the higher band of the input signal. The two amplified signals in the switching and the linear amplifier path are combined at the output to produce the power-amplified version of the input envelope command signal.
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efficiency of a linear amplifier resorts to a particular waveform shape. To generalize this, we note that the information about the shape of any signal can be found provided that the amplitude density distribution of the signal is available. Therefore, the input and the output power of any amplifier can be obtained from: n
Pout =
∑a
p (a k )∆a ,
2 k
(1)
k =1
ak 2 p (a k )∆a . η (a k ) k =1 n
Pin = Figure 2. System model for the linear-assisted switcher.
Given that proper signal combination at the output, questions arise of how the power is processed by the system components, and what is the total system efficiency. Furthermore, the key design question is how to choose the band separation frequency fB. Qualitatively, it can be said that for low values of fB, a small portion of the input signal spectrum is amplified by means of the high efficiency switcher, whereas, conversely, a high fB yields a decrease in the efficiency of the switcher, since its switching frequency (and, in turn, its switching losses) has to increase to be able to track a signal of increased bandwidth. Therefore, it can be argued that an optimal fB can be found that maximizes the overall efficiency.
3. EFFICIENCY MODELING 3.1 Efficiency of a switching amplifier In the model of Fig. 2, we can assume that the switching amplifier efficiency depends only on the frequency fB, which is proportionally related to the required switching frequency fsw for the switching amplifier. This assumption holds provided that the conduction losses of the switching amplifier are approximately independent of the switching frequency. As an example, in the experimental measurements depicted in Fig. 3, which correspond to the switcher detailed in [4], the efficiency of the switching amplifier is measured as a function of the switching frequency fsw while the output voltage is regulated at one half of the input DC supply voltage Vg. It is further assumed that the output filter of the switching amplifier is designed so that the converter has a tracking bandwidth of fsw/20, where fsw is the switching frequency. As expected, the switcher efficiency decreases with increasing switching frequency.
∑
(2)
where p(ak) is the discretized amplitude density distribution of the input signal (a histogram for different values of the amplitude slots of ak, n being the number of amplitude slots in the histogram), and η(ak) is the efficiency of the linear amplifier as a function of the signal amplitude ak. From (1) and (2), the efficiency of the linear amplifier for any given signal can be found as: n
P η = out = Pin
∑a
k =1 n
2 k
p (a k )∆a
2
ak p (a )∆a (a k ) k η k =1
∑
(3)
As an example, for an ideal class-B linear amplifier, such as the one used in the polar transmitter of Fig. 1, the efficiency vs. amplitude is shown in Figure 4.
Figure 4. Efficiency of an ideal class-B linear amplifier as a function of the signal amplitude.
One can verify that (3) gives the classical result of π/4 efficiency for the class-B amplifier when the output signal is a sinusoid.
3.3 Total efficiency of linear-assisted switcher for an arbitrary signal
96
Based on the results of Sections 3.1 and 3.2, we can compute the total efficiency ηtotal of the linear-assisted switcher. From the model given in Fig. 2, the input and the output power for the switching and the linear amplifier are found as functions of the corresponding amplitude density distributions.
92
The switching amplifier input and output power are:
100
88
Pout − sw =
84
nsw
∑a
2 k
p L (a k )∆a ,
(4)
k =1
80 0
n
250 500 750 1000 1250 1500 1750 2000
Pin − sw =
Figure 3. Experimental measured efficiency for the switcher from [4].
3.2 Efficiency of a linear amplifier Efficiency of a linear amplifier depends on the shape of the amplified waveform, but to first order does not depend on the frequency of the waveform. The classical approach to derive the
sw 1 a k 2 p L (a k )∆a . η ( f sw ) k =1
∑
(5)
where pL(ak) is the amplitude density function of the signal at the output of the switching amplifier, and η(fsw) is the efficiency of the switching amplifier, which is a function of the switching frequency as shown in Fig. 3.
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The input and the output power of the linear amplifier are given by (1) and (2), except that the notations for the amplitude density distribution and the number of amplitude slots are changed to pH(ak) and nLin.
P = 0.48, normalized to the maximum instantaneous output power. 1.2 1
Combing these results, the total efficiency ηtotal can be obtained:
=
∑a
2 k
p L (ak )∆a +
k =1
nsw
nLin
∑a
2 k
k =1 n
2
(6)
0.2 0
p H (ak )∆a
-0.2
(7)
2
Lin ak ak p L (ak )∆a + p H (ak )∆a ( ) f η η sw k =1 k =1 (a k )
∑
∑
n
ηtotal
P = out = Pin
∑a
2 k
nLin
2
k =1
L
k
2
sw
k =1
k
VHP(t)
-0.4
po (ak )∆a
a a ∑ η ( f ) p (a )∆a + ∑ η (a ) p (a )∆a k
Vo (t)
2.55
2.6
2.65
2.7 -3 x 10
t (ms)
Figure 5. Time waveforms for the two-tone test simulation. Blue: signal at the output of switching amplifier, green: signal at the output of the linear amplifier, red: recovered rectified sinusoidal signal.
k =1
nsw
0.4
H
(8)
8
20
6
15
4
10
2
5
k
k
Here it is assumed that the signal is perfectly reconstructed at the output, n, nsw and nLin are the total number of the amplitude slots for the signals in the output of the system, switching and linear amplifier, respectively, and po, pL, pH are the amplitude density distributions at the system output, switching and linear amplifier, respectively (according to the model of Fig. 2). It should be noted that the overall efficiency in (8) is obtained for an ideal linear amplifier with no quiescent power. To account for this, a quiescent power PQ can be added to the total input power Pin. Changing the filter bandwidth fB affects the amplitude distributions po, pL, pH and the switching frequency of the switching amplifier. As a result, the total efficiency depends on the band separation frequency fB, as illustrated by the examples in the Sections 4 and 5.
4. COMPUTATION OF EFFICIENCY AS A FUNCTION OF THE BAND SEPARATION FREQUENCY The setup for the examples in this section, including a two-tone test signal, and a CDMA signal, corresponds to the model shown in Fig. 2. After obtaining the amplitude density distributions for the switching and the linear amplifier paths (by simulation), the total efficiency of the system is found from (8). 4.1 Two-tone test signal envelope
In this section a rectified sinusoidal signal (the two-tone test signal envelope) is considered as the envelope command input to the system shown in Fig. 2. Simulation is performed with the frequency of the low pass filter located at fB = 25 kHz, and consequently the switching frequency of the switching amplifier is chosen to be 500 kHz. The switcher efficiency, according to Fig. 3, is 93.5%.
0 0
0.2
0.4
0.6
0.8
1
0 -0.25 -0.2 -0.15 -0.1 -0.05
1.2
0
0.05
0.1
ak Figure 6. Two-tone test envelope signal. Amplitude density distribution of: (a) switcher output signal (b) linear amplifier output signal.
Figure 6(b) shows the amplitude density distribution of the signal at the output of the linear amplifier. The total power provided by the linear amplifier is P = 0.01, normalized to the maximum instantaneous output power. The total efficiency ηtotal obtained from (8) is ηtotal = 87%. It can be observed that the system efficiency is affected by the linear amplifier even though the output power provided by the linear amplifier is relatively small. 4.2 CDMA signal envelope
In this section a CDMA signal (IS-95 standard) is considered as the input of the system shown in Fig. 2. Simulation is performed with the frequency of the low pass filter located at fB = 30 kHz, hence the switching frequency of the switching amplifier is chosen to be 600 kHz. Figure 7(a) shows the amplitude density distribution of the signal at the output of the switching amplifier. The total (normalized) power provided by the switching amplifier is P = 0.23. Figure 7(b) shows the amplitude density distribution of the signal at the output of the linear amplifier. The total (normalized) power provided by the linear amplifier is P = 0.02. The total efficiency ηtotal is obtained using (8) and is ηtotal = 70%. 3.5
50
3
40
2.5
The simulated signal waveforms at the output of the switching and the linear amplifier as well as the recovered-amplified input signal are shown in Fig 5. Figure 6(a) shows the amplitude density distribution of the signal at the output of the switching amplifier. The power provided by the switching amplifier is
30 20
pH(ak)
nsw
0.6
Pout − sw + Pout − Lin Pin− sw + Pin− Lin
pL(ak)
ηtotal =
VLP(t)
0.8
2 1.5 1
10 0 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53
0.5 0 -0.5 -0.4 -0.3 -0.2 -0.1 0
0.1 0.2 0.3 0.4 0.5
Figure 7. CDMA signal envelope. Amplitude density distribution of (a) switcher output signal (b) linear amplifier output signal.
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5. EFFICIENCY OPTIMIZATION Following the model given by (8) and the procedure illustrated in Section 4, the optimum band separation frequency fB can be found to maximize the efficiency ηtotal of the linear-assisted switcher. Two examples are described in this section. 5.1 Two-tone test signal In this example, the linear-assisted switcher amplifies a 20 kHz rectified sinusoidal signal. The band separation frequency fB of the low-pass filter is swept from 10 kHz to 100 kHz. It has been assumed that the supply voltages of the linear amplifier are fixed to the normalized values of –1 and 1, and that the quiescent power consumption of the linear amplifier is negligible.
The simulated total efficiency ηtotal vs. fB is shown in Fig. 8. It is observed that the total efficiency has the maximum of about 88% when the band-separation frequency is placed at fB = 30 kHz.
based on the switcher efficiency as a function of the switching frequency, as well as the linear amplifier efficiency as a function of the amplitude distribution of the output signal. It is shown how the total efficiency depends on the selection of the bandseparation frequency, which is the frequency that separates the low-frequency portion of the signal processed by the switching amplifier and the remaining high-frequency portion processed by the linear amplifier. Based on the efficiency model, the optimum band-separation frequency that maximizes the efficiency of the linear-assisted switch can be found. Examples of efficiency computation and efficiency optimization based on finding the optimum band separation frequency are shown for two cases: a two-tone test signal, and a CDMA signal in a polar modulation RF transmitter. Acknowledgements. This work was supported by DARPA under the Intelligent RF Front Ends (IRFFE) program, Grant N0001402-1-0501.
100
REFERENCES
90 80 70 60 10 20 30 40 50 60 70 80 90 100 Figure 8. Total efficiency ηtotal vs. fB for the two-tone test signal example.
5.2 CDMA signal
In this example, the linear-assisted switcher amplifies the envelope of a CDMA signal. The total efficiency ηtotal of the system is calculated for different band separation frequency fB sweeping from 10 kHz to 100 kHz. It is found that the maximum ηtotal is achieved for the lowest fB, i.e., when the switching amplifier passes only the DC component of the signal. Because of the nature of the envelope signal in this case, increasing the band separation frequency does not significantly affect the amplitude density distributions or the output power of the switching and the linear amplifiers. Therefore, increasing the value of fB in the range up to 100 kHz does not decrease the power provided by the linear amplifier significantly. A significant change in the output power of the switching and the linear amplifiers would require a much higher band-separation frequency. However, the high value of fB would require a correspondingly high value of the switching frequency fsw (in the 10 MHz range), which would likely result in low efficiency (as illustrated by the trend in the example of Fig. 3).
6. CONCLUSIONS One of the approaches to implement the wide-bandwidth, highefficiency envelope-tracking power supply for polar modulation RF transmitters is based on a combination of a linear amplifier (for wide bandwidth) and a switching amplifier (for high efficiency). In this paper we address the question of efficiency modeling and efficiency optimization for the linear-assisted switcher. A method is proposed to compute the overall efficiency
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