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LINC Power Amplifier Combiner Method Efficiency Optimization Bob Stengel and William R. Eisenstadt
Abstract—Linear amplification using nonlinear components (LINC) is a method of vector summing two constant amplitude phase-modulated signals to achieve power amplification. The theoretical efficiency of the LINC power amplifier has been reported as 100% since highly efficient nonlinear constant amplitude amplifiers can be used. However, the 100% efficiency performance is only possible at one or two loads along the power output curve. The bulk of the papers regarding LINC has focused on clever implementations of the signal vector decomposition as well as methods to achieve highly linear signal separation. There has been little regard in the literature to the signal combiner implementation necessary to achieve the high power-added efficiency (PAE) of the LINC radio frequency (RF) power amplifier. Efficiency is not an intrinsic property of the combiner implementations, however, combiner method is the single biggest contributor to efficient performance of an LINC RF power amplifier. This paper develops an analysis method that determines the efficiency of the LINC power amplifier as a function of the amplitude modulation statistics. This can be employed to design the RF communication system amplitude modulation characteristics and to tradeoff and optimize the RF transmitter PAE.
I. INTRODUCTION
T
HE LINEAR amplification using nonlinear components (LINC) radio frequency (RF) power amplifier is derived from the outphasing modulation technique developed in 1935 by H. Chireix [1]. In this work, two power amplifiers were driven by a phase-modulated carrier and combined in order to produce a highly linear and efficient AM transmission at the carrier frequency. In 1974, Cox introduced the LINC amplifier in which any input signal is decomposed into two phase-modulated signals. Then narrow-band linear amplification was achieved with efficient constant amplitude nonlinear amplifiers [2]. Subsequent articles in the literature examined component signal separation and recombination [3], a VHF implementation of an LINC amplifier [4], an inverse-sine modulator for use in an LINC decomposition circuit [5], an in-phase/quadratic processor for LINC [6], [7], a broad-band combiner for LINC [8], digital signal processor (DSP) for LINC component separation [9], [10], and the effect of imbalances and modulation schemes on LINC performance [11], [12]. A conventional power combiner such as 90 or 180 hybrid, with a summing and difference port presents a constant impedance to each of the LINC amplifier branches independent Manuscript received March 21, 1997; revised October 6, 1998. B. Stengel is with RPG Applied Research, Motorola Labs, Plantation, FL 33322 USA (e-mail:
[email protected]). W. R. Eisenstadt is with the University of Florida, Electrical and Computer Engineering Department, Gainesville, FL 32611-6200 USA (e-mail: wre @tcad.ee.ufl.edu). Publisher Item Identifier S 0018-9545(00)00644–7.
of the phase offset. Assuming the combined port is ideally terminated, the result is a distortion-free constant input power delivered into the power combiner with the output power at the sum and difference port being a function of the phase offset. Reference [13] investigates this configuration with the power diverted away from the antenna port dissipated in a 50-W load. Since this combiner dissipates power its efficiency is simply the numerical average to peak power ratio of the particular modulation method being considered. This value is then multiplied by the efficiency of the nonlinear RF power amplifiers in each branch to determine the composite LINC efficiency. The most relevant previous work related to this paper discusses the LINC combiner efficiency for class-B power amplifiers [14]. The configuration reported is a simple transformer coupler summing circuit and transmission line coupler with a shunt reactance. This type of LINC combiner results in conjugate output load variations applied to the nonlinear power amplifiers. Power delivered into the combiner is now a function of the phase offset and would be ideally 100% if the load was real only (no reactance) and the nonlinear power amplifier efficiency was also 100%. This paper solves for the reactance to maximize efficiency at a desired output level and solves for the average efficiency for several signal conditions assuming a class-B RF power amplifier. This paper develops the LINC combiner circuit efficiency, and the LINC power amplifier efficiency for a simplified implementation with two phase-modulated constant voltage sources added in series. What this provides is a generalized LINC RF power amplifier efficiency analysis and optimization independent of the type of amplifier operation class implemented. Simplified power, voltage, or current LINC signal processing model [15] provides an insight to the active LINC component requirements to achieve optimized LINC efficiency performance and extended to include simplified reactive source optimization [1], [14]. It is shown that the peak-to-average value is not sufficient to determine the optimized LINC amplifier design. II. LINC MODULATION First, this paper will examine the efficiency of the simple LINC combiner circuit shown in Fig. 1. Here, an LINC decomposition circuit provides two constant amplitude phase-moduand [6], [7] from the input signal lated signals where input amplitude modulation; input phase modulation; carrier
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Fig. 1.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 1, JANUARY 2000
The block diagram of a simple LINC combiner circuit.
Fig. 3. The LINC combiner realized as a pair of voltage sources in series.
signal into constant amplitude phase-modulated vectors. This vector decomposition and recomposition are done across the entire Cartesian plane. III. LINC COMBINED VOLTAGE SOURCES
Fig. 2. The graphic representation of the decomposition and addition of signals that occur in an LINC power amplifier.
(1)
(2)
This paper focuses on the efficiency of the LINC power amplifier combiner as realized by summing two constant voltage amplifiers. A similar analysis can be performed for summing two constant current amplifiers in parallel. The LINC configuration with ideal combined voltage sources is shown in Fig. 3. In provides a constant voltage signal modulated this figure, provides a constant voltage signal modulated by and , where is set between 0–90 . The output of the series by to voltage sources is added and applied as and creates a current, . This combiner can be realized with some loss using a transformer with two signal inputs and one combined signal output. The phasor signals of the circuit are as defined (7)
(3) (8) (4) (9) (5)
(6) Then, the narrow-band constant amplitude phase-modulated RF amplifier outputs are summed to reconstruct the original signal. The advantage of the LINC configuration is high-efficiency constant amplitude nonlinear RF power amplifiers can be employed as opposed to lower efficiency class-A and class-B RF power amplifiers for an amplitude-modulated transmitter application. The LINC configuration offers linear amplifier distortion performance at power added efficiency of a nonlinear RF power amplifier. Fig. 2 shows graphically how (1)–(5) are used to decompose the amplitude and phase-modulated input
From this point, there are two ways to analyze the efficiency of the LINC amplifier. One method is to calculate the power and from each of the constant voltage sources and the power on the load . However, the equations from this analysis are complicated and do not provide strong insight into the optimal circuit design and the efficiency tradeoffs. The authors find it beneficial to recast the circuit as its Norton equivalent circuit. This is shown in Fig. 4. Here, the current genbecomes a Norton erated by the two series voltage sources equivalent current source. The output voltage is and the load is defined as two parts and . For the simple circuit developed here (10)
STENGEL AND EISENSTADT: LINC POWER AMPLIFIER COMBINER METHOD EFFICIENCY OPTIMIZATION
(with positive real part) its efficiency from
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can be calculated
(18)
Fig. 4. The Norton equivalent circuit of the pair of series LINC voltage sources.
(11) A check on this calculation shows as . The impedances derived from
, and
are (12)
(13) These results are consistent with simulations performed with the Hewlett-Packard Microwave Design System (MDS) circuit simulation software. IV. LINC EFFICIENCY ANALYSIS In order to do efficiency calculations, it is beneficial to model and as a conductance in parallel with a susceptance. Later in the paper, a compensating susceptance will be added to the circuit to raise the overall LINC efficiency (14)
(15) Similarly (16)
(17) and are inThis analysis assumes the voltage sources dependent of both real and reactive loading. What this implies is the high-efficiency power amplifier can be modeled simply as a voltage source which has a voltage amplitude that is constant and unaffected by the value of output load impedance. The ability to efficiently achieve this or the dual of a load independent current source is the objective of most RF power amplifier designs. Assuming the ideal source exists over all impedance
There are no separate resistances in the systems of Figs. 3 or 5 to account for the power that is not dissipated in the load ( ) (an undesired dissipation with a corresponding reduction in the efficiency). When the phase offset has a value other than zero the voltage sources are terminated with loads that have equal real values ( ) and series-connected conjugate reactive values. These reactive terminations result in reactive currents drawn from each of the voltage sources, a phase shift between the source voltage and current flowing within the source results. Examination of the specific implementation of the voltage or current source will reveal whether storage or dissipation occurs within the dc supply to RF source conversion accounting for the efficiency reduction. This may leave some practical considerations needed for the ideal signal source used in an LINC application, which are left for future efforts. One objective of this analysis is to determine and quantify the combiner efficiency of LINC linearization application using ideal signal current or voltage vectors in place of power signal vectors. If the results of this vector analysis show promising efficiency, future efforts will focus on ideal LINC source development. LINC amplifier consists of several elements: generation of and voltage signals, amplification of these signals level as an ideal source, and vector summing of to these signals. Each of these elements has an efficiency associated with them, the product of all three individual efficiencies is power-added efficiency (PAE). This paper is focused on the vector summing efficiency only, similar to the output matching elements insertion loss of a conventional linear RF power amplifier. V. REACTIVE TERMINATED VOLTAGE SOURCE The key observation from the previous analysis is the series representation of the Norton equivalent load impedance (12), ) independent of the and (13) has a constant real value ( phase offset. If additional conjugate reactances are supplied in series with the constant voltage sources they would have no net effect on the real part of the Norton equivalent source load and . impedance and However, the equivalent shunt representation of shows a load variation with that has a real and reactive variation as a function of phase offset (14)–(17). This means that if shunt conjugate reactive elements are placed across the and , they can result in compensating susvoltage sources ceptance in the Norton equivalent circuit. These shunt conjugate reactive elements may be optimized for power amplifier efficiency at a particular output power level other than the peak output power. The new circuit with shunt conjugate reactive elements is and are shown in Fig. 5. Here, parallel admittances and . If we calculate the Norton equivalent curadded to rent sources for this circuit, we can partition the circuit into two back to back current sources and loads as shown in Fig. 6.
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Fig. 5. The LINC combiner of series voltage sources with parallel admittances to improve efficiency.
Fig. 7. LINC efficiency as a function of the parallel admittanceB for constant phase offset, Pi/4 QPSK, and Quad-QAM modulation examples.
gives average efficiency as a function of allel admittance Efficiency
the additional par(23)
In order to do this, (21) is inverted to give (24)
Fig. 6. Norton equivalent circuit of the series voltage sources LINC with parallel admittances.
In this figure,
and
A critical value for can be found by taking (24) and setting the imaginary part equal to zero
become (25) Setting the numerator equal to zero reduces to the following relationship: (19) (26)
Similarly (20) The loads (20)
and
are defined using (12), (13), (19), and
(21)
(22) The efficiency of the amplifier load can be examined as the phase offset of the LINC is varied. VI. EFFICIENCY OPTIMIZED REACTIVE TERMINATED SIGNAL SOURCES In order to evaluate the average LINC efficiency, the expression in (18) must be integrated over the phase offset region. The following example assumes that the phase offset has equal probability for all values of phase offset ( ) between 0–90 . This
This expression allows the designer to find the phase offset where maximum efficiency occurs in the LINC combiner, given a load and shunt reactive element. Evaluating the LINC efficiency for a number of different shunt reactive B values is critical to constructing a good design. Fig. 7 shows the LINC combiner average efficiency evaluated from (23) as a function of the parallel admittance . For this example, the most efficient operation is at Siemens. Fig. 8 shows how the LINC efficiency varies with and . Although tradiphase offset for are efficient at , the tional LINC designs with efficiency drops quickly as goes above 45 . For an application with a peak-to-average transmitter output power of 3 dB ) or less, an ideal lossless combiner design would have ( an efficiency of 0.707 times the nonlinear RF power amplifier design has very high efficiency value. The (greater than 0.7264 multiplier) until the phase offset tops 75 . This offset phase of 75 would amount to a peak-to-average value of 11.7 dB using 20 log of the result of (9) normalized to the peak value of two when the phase offset is zero. Fig. 9 shows these relations on a plot of efficiency versus power with a log scale, the phase offset has been mapped to power.
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However, another look at the previous example may be insightful before proceeding. Equal phase offset probability translates to amplitude probability function using (5). Peak-to-average for a constant phase offset probability is equal to Peak Average
Fig. 8. LINC efficiency as a function of the phase offset for (B optimum parallel admittance (B = 0:012 535 1).
= 0) and the
dB
Motorola’s Quad-QAM signal modulation used in the integrated digitally enhanced network (iDEN) for 6.25-KHz channel bandwidth products has a peak-to-average value of 5.6 dB. One might expect that the constant phase offset distribution with a peak-to-average of 3 dB would have an very different to that of Quad-QAM. optimized value of Since it is difficult to develop a phase offset or amplitude level distribution function for a given modulation system, a numerical alternative to (23) is needed. Using (23) with phase offset variable is replaced with (5) and the integral replaced with a numerical summation factored by the number of time samples ( ), a statistically representative signal sample can be used to determine the optimized efficiency value of Efficiency
Fig. 9. LINC efficiency as a function of the output power down from peak output power for (B = 0, B = 0:0122, B = 0:012 535 1, and B = 0:0156).
Equation (26) shows that the point of highest effiis and again ciency for . The peak average efficiency using (23) is 0.8285 at and 0.65 for . For a different for modulation system statistical distribution objective, such as equal probability of all output levels, there will be a different and the corresponding peak average optimized value for efficiency. VII. APPLICATION WITH
QPSK AND QUAD-QAM SIGNAL SAMPLES
Equal phase offset assumption of the previous example leaves one asking if this is a practical example of signal statistics. If the amplitude probability function is known (5) can be used to determine the phase offset probability function. Variable would be replaced with the normalized amplitude probability with the phase function, as the peak amplitude value, and offset probability function.
(27)
(28)
For a single slot of Motorola’s time-division multiple-access (TDMA) Quad-QAM signal sample with a peak-to-average of 5.7 dB, the efficiency result of (28) is 78.22% with . While the optimized efficiency value was . Since the uniform phase offset ex78.24% with ample and Quad-QAM have very different amplitude statistical distributions and peak-to-average values, the above function was needed to determine the efficiency optimized value of . A random Pi/4 QPSK signal sample using a root raise cosine impulse truncated at ten symbols on each side, and a rolloff of 0.35 results in a peak-to-average of 4.38 dB for 1024 symbols. Processing ten samples per symbol with (28) results in an . optimized efficiency of 93.11% with a value of Efficiency versus the value of is plotted for all three signal examples in Fig. 7. Optimized or maximum efficiency occurs at a value of that is a function of the modulation signal statistics. VIII. CONCLUSION LINC amplifiers are a vector combining technique where the vectors can be power, voltage, or current signals. To achieve a load modulation as a function of the desired output power level the vectors must be voltage or current signals. An LINC system based on ideal voltage sources can have some independence in power output level and efficiency characteristics. A means has been provided that optimizes LINC transmitter efficiency as a function of the amplitude modulation statistics. It is shown that adding appropriate shunt admittance at the voltage source greatly improves the peak-to-average efficiency. This result can be recalculated for different LINC power amplifier phase modulation schemes optimizing the LINC efficiency across the output power range associated with the application modulation. Two signal samples with significantly different amplitude statistics were numerically applied using the analysis
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routine and compared with a constant offset phase example. The results indicated the optimized efficiency value for , the shunt reactance across each LINC voltage source, cannot be determined form the modulation method peak-to-average value only. Another conclusion from the results, it is not strictly true that optimized LINC voltage source RF power amplifiers will have higher efficiency for signals with smaller peak-to-average values. Constant phase offset signal with 3-dB peak-to-average has an optimized efficiency of 82.85% while Pi/4 QPSK signal with 4.3-dB peak-to-average has an optimized efficiency of 93.11%. However, implementation of an ideal voltage or current source may have some practical limitations for an LINC application. LINC is the only transmitter technology that offers both efficiency and linearization performance. However, achieving these benefits in sufficient levels with practical low-cost implementations have been limited to less than 3-dB peak-to-average signal modulation applications with less than 50-dBc adjacent channel coupled power ratio (ACCPR). Extending the efficiency benefit of an LINC RF PA system to signal applications with peak-to-average values up to 10 dB are needed for LINC to find widespread use in the industry. In addition, there is a need for simpler LINC architectures that will aid in overcoming imbalance imperfections limiting linearization performance with lower cost and size while operating over a broad frequency range. Once ideal signal source implementations are practical with a low-cost high-linearization LINC system, this modulation independent technology could become the preferred transmitter architecture of future multi-mode communication systems. REFERENCES [1] H. Chireix, “High power outphasing modulation,” Proc. IRE, vol. 23, no. II, pp. 1370–1392, Nov. 1935. [2] D. C. Cox, “Linear amplification with nonlinear components,” IEEE Trans. Commun., vol. 22, pp. 1942–1945, Dec. 1974. [3] D. C. Cox and R. P. Leck, “Component signal separation and recombination for linear amplification with nonlinear components,” IEEE Trans. Commun., vol. 23, pp. 1281–1287, Nov. 1975. [4] , “A VHF implementation of a LINC amplifiers,” IEEE Trans. Commun., vol. 24, no. 9, pp. 1018–1022, Sept. 1976. [5] A. J. Rustako, Jr. and Y. S. Yeh, “A wide-band phase-feedback inverse-sine phase modulator with application toward a LINC amplifier,” IEEE Trans. Commun., vol. 24, pp. 1139–1143, Oct. 1976.
[6] R. O. Mendez, “Linear amplification using nonlinear amplifying devices,” Master’s thesis, Univ. Florida, Gainesville, FL, 1978. [7] L. Couch and J. L. Walker, “A VHF LINC amplifier,” in IEEE Southeastlon 82 Proc., Destin, FL, Apr. 4–7, 1982, pp. 122–125. [8] A. K. Johnson and R. Myer, “Linear amplifier combiner,” in Proc. 37th IEEE Veh. Technol. Conf., Tampa, FL, June 1–3, 1987, pp. 421–423. [9] S. A. Hetzel, A. Bateman, and J. P. McGeehan, “A LINC transmitter,” in Proc. 41st IEEE Veh. Technol. Conf., St. Louis, MO, May 19–22, 1991, pp. 133–137. [10] L. Sundström, “The effect of quantization in a digital signal component separator for LINC transmitter,” IEEE Trans. Veh. Technol., vol. 45, pp. 346–352, May 1996. , “Automatic adjustment of gain and phase imbalances in LINC [11] transmitters,” Electron. Lett., vol. 31, no. 3, pp. 155–156, Feb. 1995. [12] F. J. Casadevall and A. Valdorinos, “Performance analysis of QAM modulations applied to the LINC transmitter,” IEEE Trans. Veh. Technol., vol. 42, pp. 399–406, Nov. 1993. [13] L. Sundström and M. Johansson, “Effect of modulation scheme on LINC transmitter power efficiency,” Electron. Lett., vol. 30, no. 20, pp. 1643–1644, Sept. 1994. [14] F. H. Raab, “Efficiency of outphasing RF power-amplifier systems,” IEEE Trans. Commun., vol. 33, pp. 1094–1099, Oct. 1985. [15] H. L. Krauss, C. W. Bostian, and F. H. Raab, Solid State Radio Engineering. New York, NY: Wiley, 1980.
Bob Stengel received the B.S.E.E. degree from the University of Florida, Gainesville, in 1976 and the M.S.E.E. degree from Florida Atlantic University, Boca Raton, in 1980. He joined Portable Product Development, Motorola, Plantation, FL, in 1976 and has been involved in the design of narrow-band FM communications circuits. In 1989, he joined Motorola Labs, Plantation, where he is currently working on integrated wireless transceiver technology. He has 26 issued U.S. patents and three published works.
William R. Eisenstadt received the B.S., M.S., and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 1979, 1981, and 1986, respectively. In 1984, he joined the faculty of the University of Florida, Gainesville, where he is now an Associate Professor. His research is concerned with high-frequency characterization and simulation and modeling of integrated circuit devices, packages, and interconnects. In addition, he is interested in large-signal microwave circuits and analog circuit design. He has published more than 50 conference and journal papers. Dr. Eisenstadt received the NSF Presidential Young Investigator Award in 1985.
