A Concurrent Dual-Band Uneven Doherty Power Amplifier with ...

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A Concurrent Dual-Band Uneven Doherty Power Amplifier with Frequency-Dependent Input Power Division Wenhua Chen, Senior Member, IEEE, Silong Zhang, Youjiang Liu, Yucheng Liu, and Fadhel M. Ghannouchi, Fellow, IEEE

Abstract—A concurrent dual-band uneven GaN Doherty power amplifier (PA) for two wide-spacing frequencies application is proposed in this paper. To avoid an early load modulation-drop caused by the soft turn-on characteristic of the peaking device, an adaptive power division is realized by a frequency-dependent uneven power divider as well as the input matching nonlinearities of the two cells in Doherty PA. Due to the adaptive power division, the proposed dual-band uneven Doherty PA achieves a power-added efficiency of 45% and 41% at the 6 dB backoff from the saturation at 850 MHz and 2330 MHz, respectively, the gain of the proposed Doherty PA is also enhanced to 19 dB and 13 dB in the dual bands. Furthermore, a more accurate two-dimensional joint digital predistortion model (2D-JDPD) is applied to linearize the PA and compensate for the in-phase and quadrature (I/Q) imbalance simultaneously. With this new model, the adjacent channel power ratio (ACPR) is improved to better than −47.1 dBc and −49.4 dBc in the lower and upper bands at an average output power of 31.75 dBm, and a drain efficiency of 26.7% is obtained at the same time. Index Terms—Digital predistortion, Doherty PA, dual-band, memory polynomials.

I. INTRODUCTION

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ITH the rapid evolution of communication technologies, mobile communication systems have to accommodate many standards simultaneously. This requirement stimulates the demand for multiband power amplifiers (PAs) and other radio frequency components [1]–[7]. In the conventional multiband PA solutions, several single band PAs are paralleled, and the outputs of each PA are added together using passive

Manuscript received October 25, 2012; revised January 07, 2013 and March 07, 2013; accepted April 30, 2013. This work was supported in part by National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2012ZX03001009-003), National Natural Science Foundation of China (Grant No. 61201043), the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Research Chairs, and Agilent Technologies Foundation (2414-CN11). This paper was recommended by Associate Editor P. Reynaert. W. Chen and S. Zhang are with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). Y. Liu is with the Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China and is also with the Department of Engineering Physics, Tsinghua University, Beijing 100084, China. Y. Liu is with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA. F. M. Ghannouchi is with the Intelligent RF Radio Laboratory (iRadio Lab), Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSI.2013.2268341

combiners or multiplexers. These architectures will lead to a significant power loss, since their power combination is implemented at the high power stages. To enhance the overall efficiencies of the transmitters, concurrent multiband PAs have attracted extensive studies and developments. With respect to concurrent multiband PAs, the signals are added first and then fed to the PAs, the power combination is carried out at the lower power stages, thus the absolute power loss induced by the insertion loss of the combiners will be smaller than before. For the sake of multiband operation and high efficiency PAs, concurrent dual-band Doherty PA (DB-DPA) has been proposed and demonstrated successfully [8]–[12]. In modern wireless communication systems, non-constant envelope modulation schemes are widely used to pursue high transmission capacity. However, non-constant envelope signals usually result in a high peak-to-average power ratio (PAPR), which significantly deteriorates the efficiency of PAs in order to meet the linearity requirements in wireless communication standards. To enhance the average efficiency, the Doherty PA has been studied extensively and adopted widely in base stations [13], [14]. However, the current level of the peaking cell is always lower than that in the carrier cell, because the peaking cell mostly is biased deeper in the Doherty topology, thus the load impedances of both cells cannot be fully modulated to the optimum value of the impedance for a high power match. To achieve a perfect Doherty operation, an asymmetrical power division scheme had been proposed [15], which delivered more power to the peaking amplifier at the cost of the PA gain. Recently Nick et al. [16] invented an adaptive input power division scheme to further enhance the efficiency of Doherty PAs. The divider is designed to deliver more power to the carrier and peaking cells in the low and high power regions, respectively. Digital predistortion technique is trusted as a promising solution for Doherty PA linearization due to its good performance and fast adaption capability [21]–[25]. In order to linearize concurrent multi-carrier and multi-band PAs, many efforts have been made. Roblin et al. [26] proposed a frequency-selective predistortion linearization technique to compensate for intra-band and third-order intermodulation distortion (IMD3) for multicarrier wideband code-division multiple-access (WCDMA) signals. Cidronali et al. [27] proposed a concurrent dual-band IF DPD technique, where the RF signals in each frequency band were down-converted to an IF band using a subsampling technique. Recently, Aidin et

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Fig. 1. The circuit diagram of the dual-band uneven Doherty PA.

al. [28], [29] proposed a two-dimensional digital predistortion (2D-DPD) to model in-band intermodulation and cross-modulation simultaneously, which achieved excellent linearization results for the dual-band PA. In this paper, a dual-band uneven Doherty PA with frequencydependent power division is proposed and implemented. This scheme realizes an adaptive input power division by considering the nonlinearities of the input impedances of the two cells of Doherty PAs [16], [17]. In this scheme, more power is delivered to the carrier cell to avoid an early load modulation-drop at output backoff (OBO) level caused by the soft turn-on characteristic of the peaking device, which demonstrates higher efficiency and gain for the Doherty PA. Due to the input dynamic nonlinearities of the two cells, the power division rate is degraded for the operation at high power level. To further enhance the linearity of the proposed PA, a joint predistorter for both the in-phase and quadrature (I/Q) impairments and PA nonlinearity is applied. In the joint predistortion structure, not only the desired signals of each band, but also the conjugate components are taken into consideration for the predistorter model. Experimental results confirm the effectiveness and superiority of the proposed algorithm. II. PA ARCHITECTURE AND OPERATION CHARACTERISTICS The circuit diagram of the proposed concurrent dual-band uneven Doherty PA is shown in Fig. 1. It consists of a dual-band frequency-dependent uneven power divider, a dual-band phase compensator, two single-branch dual-band PAs, two dual-band offset lines and two dual-band quarter wavelength transmission lines. As shown in [16], the peaking cell’s output current reaches below that of the carrier cell, due to the lower gain of the deeply biased class-C amplifier, which leads to an insufficient load pull-down at high power levels. On the other side, the carrier amplifier does not achieve the perfect saturated point at backoff power levels since it encounters an early load pull-down caused by the soft turn-on characteristic of the peaking transistor. In an effort to overcome this problem, an analog adaptive power divider was invented in [16] to deliver more power to the carrier cell, and push the carrier device into full saturation at back-off power levels. Define the power division ratio of the power divider between the carrier and peaking cells as , where the subscript stand for the lower and upper bands, respectively. Taking the input matching of the two PA cells of Doherty architectures into account, the delivered input power ratio between the carrier cell and peaking cell can be written as follows:

where and are the input scattering parameters of the carrier cell and peaking cell. It is known that the amplifier’s input impedance is a strong function of the input drive level [17], which can be utilized to realize an adaptive power division in Doherty PA. To evaluate the effect of input power ratios, a simulation for dual-band uneven Doherty PA was carried out in Agilent Design System (ADS). The operating frequencies for the dual bands were selected 900 MHz and 2300 MHz, which are both candidate frequencies for long term evolution advanced (LTE-A) system. The simulated results are illustrated in Fig. 2(a) and (b), the related input power levels are indicated with colorful numbers, it can be noticed that both the cells of Doherty power amplifiers (DPAs) experience a significant input impedance variations, where the input power is swept from 5 dBm to 35 dBm. In the lower input power range, the input matching of the carrier cell is quite better than that in the peaking cell due to the different gate bias levels. The trajectory of the respective input impedances of the carrier amplifier and peak amplifier PA can be divided into an upgrading stage and a degrading stage as the input power of the DPA increases, which are getting closer to and moving away from the associated optimum matching points, respectively. These curve inflection points are defined as the knee points of the trajectories. Due to the nonlinearities of input impedance, the carrier cell will get into degrading stage after saturation starting from the impedance knee point as shown in Fig. 2(a) and (b). Since identical input matching circuits are both used for the carrier and peaking cells, and optimized at the bias level of the carrier cell, thus the optimal input matching point in the peaking cell deviates the ideal 50 further.

To guarantee an adaptive and dynamic power division for the dual-band Doherty PA, an appropriate power division rate should be optimized, in which the carrier cell gets into the degrading stage (less power into the carrier cell) while the peaking cell starts to turn on. For circuit design and implementation purposes, we can get the swept trajectories of the input mathing in simulation for the carrier and peaking cells, respectively, thus the knee point of the carrier cell and the turn-on point of the peaking cell can be obtained, and the difference between the two points indicates the optimum power division ratio. As shown in (2), the power division ratio can be calculated for the power divider design based on the simulated trajectories, where and stands for the input power at the knee point of the carrier cell and at the turn-on point of the peaking cell, respectively. As illustrated in Fig. 2, the in the lower band is 20.1 dBm, while the in the lower band is 13.6 dBm, thus we can obtain that the optimum power division ratio should be 6.5 dB. Similarly, the optimized power division ratio for the upper

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. CHEN et al.: A CONCURRENT DUAL-BAND UNEVEN DOHERTY POWER AMPLIFIER WITH FREQUENCY-DEPENDENT INPUT POWER DIVISION

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Fig. 3. Input power ratio of the proposed Doherty PA.

turns on, while the input impedance of the carrier PA starts to move away from the optimum matching point cross a degrading stage, thus the power division ratio can be changed dynamically because of the input impedance variations. Specifically, will be increased starting from the turn-on of the peaking PA, while becomes smaller. Based on the (1), the overall input power ratio will be decreased as the input power increases. As a result, the power divider delivers more power to the carrier cell at a low power level to guarantee a better active load pull in Doherty PAs, while the power delivered to the peaking cell is increased to perform a higher efficiency at the high power level. Simulated input power ratio between the carrier cell and the peaking cell are presented in Fig. 3, it can be figured out that an adaptive power division is implemented by using an uneven power division ratio as well as the nonlinearities of input impedances of two cells. III. ANALYSIS OF PA PERFORMANCE Fig. 2. Input matching trajectory at the input of the carrier and peaking cells in proposed Doherty PA as the input power increases. (a) Lower band. (b) Upper band.

band can be derived as 5.5 dB according to the indicated power levels. These power division ratios are calculated and good enough for low drive levels to the drive level needed to turn-on the peaking cell. Beyond the turn-on point of the peaking cell, these drive levels change dynamically as shown in Fig. 3 to insure the closest possible optimum load-modulation effect taking place at the output of the carrier and peaking cells. By carefully selecting an appropriate power division ratio for the two cells and combining the nonlinearities of the input impedances, an adaptive input power division can be realized to maximize the load-modulation effects taking place at the output of carrier and peaking cells. To fulfill the adaptive division, the carrier PA is designed to reach the optimum matching point as the peaking PA starts to turn on. Due to the uneven power division ratio, the input impedance of the peaking cell is located at the upgrading stage going toward better matching condition at back-off power level (the peaking PA is off) and going closer to the optimum matching point as the peaking PA

A. Efficiency Enhancement As more power is delivered to the carrier cell, the carrier PA will approach the saturation faster, thus the soft turn-on effect will be weaker than before. Thereby, the efficiency of the proposed PA at the backoff level will be increased. In Fig. 4, the simulated PAE results show the proposed uneven power divider leads to higher and flat efficiencies, as compared to the considerable efficiency drops between two peaks, presented by the even power division. This feature is attributed to the appropriate turn-on level of peaking PA jointly tuned by both the power division ratio and the nonlinearities of the input impedance. As more power delivered to the peaking cell, the optimized bias level gets deeper since we want the peaking PA to turn on right away when the carrier PA starts to saturate. These result in a more severe soft turn-on attribute for the peaking cell, and an efficiency drop in the backoff region. With more power delivered to the carrier branch, the input impedance of the peaking PA goes forward optimum matching point, with a rapid current increase in the peaking cell in compensation for the compressed current of the carrier cell as the carrier cell begins to saturate. Also the soft turn-on characteristic of the peaking PA is extenuated considerably. Hence, we obtain a higher and more flat efficiency before and after the carrier cell saturates.



Fig. 5. Gain of the Doherty PA with frequency-dependent division ratios.

Fig. 4. PAE of the proposed and conventional even Doherty PAs.

Moreover, according to the probability that a spectrum density function of the signal with a non-constant envelope such as WCDMA, the output signal mostly appears around the average output power level, thus the efficiency with no-constant envelope modulated signal will approach the efficiency at the average power level for CW signal. Thereby, the proposed power division scheme mainly contributes to the efficiency and gain enhancement in the average power level, this technique will leads to a significant improvement in the overall performance, when the PA is driven with a modulated signal having PAPR equal to the difference between the PA’s peak power and the average power level However, it should be noticed that the peak output power is decreased slightly. As shown in Fig. 4, there is a 0.6 dB degradation in the peak output power. Since more input power is delivered to the carrier cell and the carrier cell is driven into saturation easilier, the carrier cell will be pushed into a deep saturation, as a result, the total output power could be a little bit lower than the conventional even power division scheme. Fortunately, this is accompanied with a better power efficiency B. Gain Enhancement The total gain of Doherty PA depends on the power division ratio and the gain of the two cells simultaneously. The total gain of the proposed PA without phase misalignment in two cells can be expressed as [14]: (3) , , are the total gain, the gain of where the carrier cell and the gain of the peaking cell, respectively. Generally the peaking cell is biased deeper to perform an active load modulation, the gain of the peaking cell is smaller than that of the carrier cell. For the uneven power division, the imbalance of power division are 6.5 dB and 5.5 dB for the lower band (LB) and upper band (UB), respectively. In the new power division scheme, more power is delivered to the carrier cell, as shown in Fig. 5, the total gain of the proposed PA can be enhanced efficiently compared to the conventional topology. Since a smaller portion of the input power is delivered to the peaking cell, and the gain at high power levels are mainly deter-

mined by the peaking cell, the proposed uneven power division scheme will result in a higher gain compression than the conentional even power division. However, as assigned less power to the peaking cell, the turn-on point of peaking device will be delayed and the peak power is not significantly decreased, thus the backoff power range of Doherty PAs will be extended. To ensure an appropriate backoff range, the bias voltage of the peaking cell should be tuned shallowly. In this situation, the gain compression in the proposed power division can be compesated to some degree. As shown in Fig. 5, it can be seen that the gains do not exhibit a significant compression in the saturation region compared to the even power division. IV. UNEVEN DUAL-BAND DOHERTY PA IMPLEMENTATION A. Frequency-Dependent Power Divider Since the soft turn-on characteristic of the device is frequency-dependent for the dual bands, the power division ratios of the dual bands should be optimized individually. Wilkinson power dividers are commonly used in Doherty PAs to perform input power division. To realize dual-band Wilkinson power dividers, it is essential to develop an equivalent dual-band transformer at the targeted two frequencies. Recently many approaches [18]–[20] have been proposed to achieve impedance transformation for the dual bands, including even and uneven power division. However, their power division ratios are all identical in dual bands. Since the characteristic of the transistors is varied with the operating frequencies, it is necessary to design a dual-band power divider with frequency dependent power division ratios to optimize the proposed Doherty PA performance. To fulfill different power division ratios at two frequencies, a frequency dependent power divider is proposed as in Fig. 6(a), four frequency dependent dual-band impedance transformers , , , and are used to implement power division and impedance matching. (4) (5) (6)


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Fig. 6. (a) Complete structure of the proposed frequency-dependent power divider. (b) -shaped dual-band transformer.

TABLE I DIMENSIONS OF -SHAPED TRANSFORMERS

,

)

where is the isolation resistor, are the power division ratios in dual bands, is the impedance of the ports, , , , and are the equivalent characteristic impedances of the four transformers in the LB and UB, respectively. Once power division ratios for the dual bands are determined, the next tasks are to design the demanded dual-band impedance transformers. Due to good frequency response and compact size, -shaped microstrip networks with shorted stubs as in Fig. 6(b) are selected. By applying an odd-even modes analysis method [20], the design parameters of the structure can be derived. The design equations are present in the (4) to (6), the values of impedance transformers , , , and can be calculated by substituting the optimized uneven power division ratios 6.5 dB and 5.5 dB in the lower and upper band, respectively. Based on these derivations, a dual-band power divider with frequency dependent division ratio is implemented. The dimensions of the -shaped networks are listed in Table I, the isolation resistor is 100 , and the simulated and measured results are presented in Fig. 7(a) and (b). It can be seen that the imbalance of power division are 6.5 dB and 5.5 dB for the LB and UB, respectively. These imbalanced power division ratios are optimized by the aforementioned analysis in Section II. The discrepancies between simulated and measured results at 900 MHz and 2300 MHz are less than 0.5 dB in average. B. Dual-Band PA Cell The proposed Doherty PAs are dedicated to dual-band applications, thus the PA cell in each branch should also exhibit dual frequencies property. The circuit design and simulated performances of the single-branch dual-band power amplifier are shown in Fig. 8(a) and (b). The output network includes a T-network with a shorted shunt line in the center, which realizes the

Fig. 7. Simulated and measured results of the uneven dual-band power divider. (a) s21 and s31. (b) s11 and s32.

dual-band impedance transformation from the output load to the optimum impedances. Since the end of shunt line T2 is shorted, the DC supply can be connected to the drain of the transistor through this line directly. At the input port, a multi-section network is employed to perform dual-band matching. C. Dual-Band Offset Line To guarantee full load modulations in Doherty PAs, additional offset lines (OLs) are connected after the matching circuits of the carrier and peaking cells. As the input power in the peaking amplifier is lower than the threshold, the phase adjustments of the OLs cause the peaking cell to be open circuited. To adjust the output impedance of the peaking cell to the high impedance so that current leakage is prevented, a 50 -shaped network with electrical lengths of and in the LB and UB is added to the peaking branch, in order to transfer the impedance presented to the load in peaking cell to the open-circuited point. The offset line for the carrier branch is optimized for PAE at 3 dB power backoff level. As illustrated in Fig. 9, a -shaped network and design method can be used to develop a dual-band offset line. The phase delays required for dual-band offset lines are 53 and 80 for peaking branch and 86 and 219 for carrier branch, the design equations are derived easily by replacing the 90 phase angles with the desired angles. A simple transmission line phase



Fig. 10. Prototype of the proposed dual-band Doherty PA.

V. MEASUREMENT RESULTS

Fig. 8 Dual-band PA cell. (a) Schematic circuit. (b) Simulated performances.

Fig. 9. Impedance adjustment of the dual-band offset line.

compensation can be used for the carrier branch due to the accidently close ratio of 86 and 219 to 900 MHz and 2330 MHz. Due to the phase delay induced by the transformer and different carrier and peaking output offset line, a similar offset line should be added before the peaking cell to achieve identical phase delays for the two branches at the power combiner. Herein a dual-band transmission line with 96 and 76 phase shifts are used for the phase compensation, and the -shaped equivalent transformer as discussed in power dividers can be also employed directly. The dimensions of the input and output offset lines can be found in Table I. The transformer is implemented by a T-shaped microstrip network [19], which introduces an additional phase shift of 90 and 90 at dual bands, respectively.

A concurrent dual-band Doherty PA prototype was designed to verify the design methodology. The prototype PA using a GaN HEMT (CREE, CGH40010) is shown in Fig. 10. The transistor is unmatched and has a breakdown voltage of 84 V, and its typical saturation power is 13 W. The frequencies for the two bands were 850 MHz and 2330 MHz, which are both candidate frequencies for Long Term Evolution (LTE). Both the carrier and peaking cells employed the same matching topology of the dual-band PA discussed in Section IV. The supply voltages of the carrier and peaking PAs were both set to 28 V. The gate bias voltages of the carrier and peaking cells were set as 3 V and 3.8 V, respectively, which are optimized for the power ratio of 4:1. Since the uneven power divider delivers more power to the carrier cell, the gate bias of the peaking cell is elevated slightly from that in conventional deep class-C modes to make the peaking device turn on appropriately at 6 dB power backoff point. Fig. 11 plots the drain currents of the carrier and peaking cells in dual bands. It can be figured out that the carrier and peaking cells approach the same saturated power level by using frequency dependent power division, which will lead to desired load modulations at the two frequencies. Fig. 12 shows the measured drain efficiency, power-added efficiency (PAE) and gain of this PA at 850 MHz and 2330 MHz, using a single continuous wave signal. The measured results show PAEs of 45% and 41% at the 6 dB OBO point from power saturation at 850 MHz and 2330 MHz, respectively. The gains of this Doherty PA were increased to 19 dB and 13 dB at the 6 dB OBO, which is attributed to the optimized uneven power division scheme. It can be found that a discontinuity is existed in the measured efficiency at 2330 MHz, which is due to the delayed turn-on effect in the peaking cell. As shown in Fig. 11, the peaking amplifier still does not turn on after the carrier cell get into the saturation region, thus the output power of the PA will drop drastically, and this misalignment leads to an obvious discontinuity in the efficiency in the upper band. On the contrary, this misalignment is not existed in the lower band, so we do not observe the phenomenon. To avoid this discontinuity, the uneven power


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TABLE II PERFORMANCE COMPARISON OF 2-WAY DUAL-BAND DOHERTY PAS

Note: The PAE of Ref [8] and [11] are calculated by the drain efficiency and gain.

transistors in the reference techniques. Bathich [11] and Saad [12] also demonstrated high efficiency DB-DPAs for dual-band applications. However, their frequency spacing is still narrow and the frequency ratio (FR) of is around 1.3 1.4. In this prototype, a FR of 2.74 has been developed for the scenario wherein a wide frequency spacing is demanded. VI. JOINT DIGITAL PREDISTORTION FOR DUAL-BAND PA

Fig. 11. The drain currents of the cells in dual bands.

The performance of wireless transmitters is very sensitive to the I/Q balance in the modulator. I/Q impairment and local oscillator leakage are known to cause extra intermodulation terms to appear at the PA output, as well as to degrade the performance of adaptive PA predistorters. For the concurrent dual-band transmitters including two I/Q modulators, I/Q impairments show cross-modulation effects between the two signals in each band. The I/Q impairments problem in the single-band direct-conversion transmitters has been widely addressed in the literatures [31]–[36]. It is shown that when DPD is employed to linearize transmitters that has I/Q impairments and PA nonlinearity, the I/Q impairments must be compensated in advance. Or in another way, one can adopt a joint predistortion structure by inverse modeling the I/Q impairments and PA nonlinearity jointly [32], [33]. To meet this demand, a joint two-dimensional digital predistortion (2D-JDPD) concept is studied and verified by a dual-band transmitter for the dual-band Doherty PA with about 1.5 GHz frequency spacing, and the prototype is driven to saturate nearly. The general forms of the 2D-JDPD model are as follows:

Fig. 12. Drain efficiency, PAE and gain of the dual-band Doherty PA at (a) 850 MHz and (b) 2330 MHz.

division for the upper band should be decreased in the real implementation, thus a little bit more power will be delivered to the peaking cell to guarantee it turns-on appropriately. A performance comparison of published works is provided in Table II. It shows that the proposed dual-band Doherty PA operates concurrently at two frequencies with the widest frequency spacing, and achieves much higher gain than other works. As a result, the proposed PA outputs 42.5 dBm and 44 dBm power with 10 W devices, which needs to be realized by higher power

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TABLE III MODEL ACCURACIES OF DIFFERENT METHODS

Fig. 13. The model structure of 2D-JDPD.

(8) are the coeffiwhere cients of the proposed model, which correspond to the original signal, the conjugate counterpart and the DC offset; and are the complex baseband signals at the two carrier frequencies; and, is the absolute value of the complex signal. The (7) and (8) can be written in matrix format for easier model’s coefficients extraction as [28]. The model structure of the proposed 2D-JDPD is illustrated in Fig. 13, where complex-conjugation and absolute value are denoted by and . Unlike the 2D-DPD model, the proposed model not only considers the desired components of the input signal, but also takes into account the conjugate components of that. Thereby, the 2D-JDPD can compensate for the PA nonlinearity and the I/Q impairment jointly, which finally leads to better linearization performances. In the 2D-JDPD technique, inverse model identification procedure is same as that in 2D-DPD, which is based on an indirect learning approach. However, the input signals are the complex envelopes of the signals at the output frequency bands, and the output signals are the complex envelopes of the signals intended to be transmitted over that frequency band. In this way, the extracted coefficients represent an approximate inverse behavior of the nonlinear transmitter. VII. LINEARIZATION RESULTS Based on the DPD evaluation platform [29], a test bed formed by two identical and time-aligned vector signal generators (ESG 4438C), a spectrum analyzer (E9030A), and 89600 vector signal analyzer and MATLAB software were utilized. The two signal generators synthesized the baseband signals and then up-converted them to the targeted carrier frequencies at 850 MHz and 2330 MHz. These two RF signals were merged together before being fed into the driving PA. Finally, the output signal was captured by the spectrum analyzer. According to the sampled input

signal and output signal with de-embedding time delay, the reverse model for DPD was derived; thus, the predistorted signal could be generated and downloaded into the two signal generators for verification. To evaluate the linearization performance of the 2D-JDPD model, the dual-band Doherty PA prototype was concurrently tested by a 10 MHz LTE signal at 850 MHz and 15 MHz LTE signal at 2330 MHz. The PAPR of the two signals are both 7.5 dB, and The I/Q imbalance parameters are as follows: gain imbalance 1 dB, phase imbalance 2 . The average output power was driven to 28 dBm and 28.8 dBm in the LB and UB, respectively. In this experiment, the nonlinearity of the PA was characterized with the 2D-DPD and 2D-JDPD models with 5th-order nonlinearities and 5th-order memory depth. As given in Table III, the 2D-JDPD achieves NSME of 38.6 dB and 41.0 dB for the dual bands, which outperforms the conventional 2D-DPD with better than 13.9 dB. The predistorted signals for linearization were obtained by swapping the input and output signals. As shown in Fig. 14(a) and (b), the output spectra after linearization in the LB and UB are presented, respectively. Clear performance improvement over the uncompensated case and the 2D-DPD techniques can be obtained with the proposed method, the 2D-JDPD achieves a more flat out-of-band spectral correction. The detailed performances of linearization are presented in Table IV, the 2D-JDPD model achieves the ACPR of better than 47.1 dBc at each frequency, it has 3.2 dB and 5 dB improvements when compared to the conventional 2D-DPD model, the corrections of ACPR are approximately 13.8 dB and 17.1 dB in the LB and UB, respectively. With digital predistortion, the proposed PA outputs 31.75 dBm average output power, and a drain efficiency 26.7% is achieved at the same time. Since the PAPR of the concurrent signals is higher than that in the single-band mode, the proposed PA should be backed off further and delivers a little lower average output power. VIII. CONCLUSION In this paper, a concurrent dual-band uneven GaN Doherty power amplifier (PA) for two frequencies with wide spacing is proposed and demonstrated to further enhance the efficiency and gain performance. A frequency dependent power divider is designed to deliver more power to the carrier cell, which can avoid an early load pull-down at backoff power levels caused by the soft turn-on characteristic of the peaking device and demonstrates higher gain. Experimental results show that the proposed asymmetrical dual-band PA successfully achieves a power-added efficiency (PAE) of 45% and 41% at the 6 dB backoff point from the saturated output power at 850 MHz and 2330 MHz, respectively. Furthermore, an accurate 2D-JDPD method is applied to the PA prototype, linearization results


Fig. 14. Linearization results (a) 850 MHz and (b) 2330 MHz.

TABLE IV LINEARIZATION RESULTS WITH DIFFERENT METHODS

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Wenhua Chen (S’03–M’07–SM’11) received the B.S. degree in microwave engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, in 2001, and the Ph.D. degree in electronic engineering from Tsinghua University, Beijing, China, in 2006. From 2010 to 2011, he was a Postdoctoral Fellow with the Intelligent RF Radio Laboratory (iRadio Lab), University of Calgary. He is currently an Associate Professor with the Department of Electronic Engineering, Tsinghua University, Beijing, China. His main research interests include power-efficiency enhancement for wireless transmitters, PA predistortion, and smart antennas. He has authored or coauthored over 100 journal and conference papers, and serves as an associate editor for the International Journal of Microwave and Wireless Technology and as a guest lead editor for the International Journal of Antenna and Propagation. He holds two U.S. patents and was the co-recipient of the Student Paper Award of 2010 APMC.

Silong Zhang received the B.S. degree in electronic engineering from Tsinghua University, Beijing, China, in 2011, where he is currently working toward the M.S. degree in electronic engineering. His main research interests are in the area of wireless communication, with a focus on high efficiency RF power amplifiers design, digital predistortion linearization, and nonlinear modeling.

Youjiang Liu received the B.S. degree in engineering physics in 2008 from Tsinghua University (THU), Beijing, China, where he is currently working toward the Ph.D. degree in engineering physics. From Oct. 2011 to April 2012, he was a Visiting Student with the Intelligent RF Radio Laboratory (iRadio Lab), Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada. His main research interests are in the area of wireless communications, with a focus on high efficiency RF power amplifiers design, digital predistortion linearization, and nonlinear modeling.

Yucheng Liu was born in Nanning Guangxi, China. He received the B.S. degree in electronic engineering from Tsinghua University, Beijing, China, in 2011. He is currently pursuing the Ph.D. degree in Purdue University, West Lafayette, IN, USA. His research interests include development of microwave dual-band passive device, high-efficiency dual-band power amplifier design based on Doherty architecture, and nonlinear behavioral modeling for power amplifier application. Mr. Liu’s work on dual-band unbalanced Doherty PA design received the Outstanding Thesis Award from Tsinghua University in 2011. He also received the Outstanding Graduate Award from Tsinghua University and the Ross Fellowship from Purdue University in 2011.

Fadhel M. Ghannouchi (S’84–M’88–SM’93–F’07) is currently an iCORE Professor and Senior Canada Research Chair with the Electrical and Computer Engineering Department, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada, and Director of the Intelligent RF Radio Laboratory (iRadio Lab), University of Calgary. He has held several invited positions at several academic and research institutions in Europe, North America, and Japan. He has provided consulting services to a number of microwave and wireless communications companies. He has authored or coauthored over 450 publications. He holds 12 patents (with five pending). His research interests are in the areas of microwave instrumentation and measurements, nonlinear modeling of microwave devices and communications systems, design of power- and spectrum-efficient microwave amplification systems, and design of intelligent RF transceivers for wireless and satellite communications. Prof. Ghannouchi is a Fellow of the Institution of Engineering and Technology (IET), and a Distinguish Microwave Lecturer for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).