Broadband Sequential Load Modulated Balanced Amplifier With Extended Design Space Using Second Harmonic Manipulation

This article presents the design methodology of a broadband radio frequency (RF)-input sequential load modulated balanced amplifier (SLMBA) with extended high-efficiency design space, by introducing the second-harmonic load manipulation over an enlarged range for the control amplifier (CA). The extension of CA load design space not only can provide the time-domain-varying drain current waveform inside the entire design continuum but also allows maintaining high efficiency at output power back-off (OBO) over an extended operation bandwidth. To validate the theory, a broadband SLMBA operating at 2.05–3.65 GHz was designed and fabricated using packaged gallium nitride (GaN) transistors. The implemented power amplifier (PA) attains a measured 45.2–46.8-dBm peak output power. Drain efficiency (DE) of 61.2%–79.7% at saturation and 50.5%–66.2% at 8-dB OBO is achieved throughout the designed bandwidth. When tested with a 100-MHz long-term evolution (LTE) signal with a peak-to-average-power ratio (PAPR) of 8 dB, the proposed SLMBA achieves 50.7%–63.5% average DE over 2.05–3.55 GHz and better than −45.1 dBc adjacent channel power ratio (ACPR) after digital predistortion (DPD).

The load modulated balanced amplifier (LMBA), a new PA architecture proposed recently, has the potential to overcome the bandwidth and OBO range limitations of DPAs [26], [27], [28], [29], [30], [31]. The CM-LMBA has shown load modulation trajectories in continuous characters using Class-B/J balanced amplifier (BA) as the carrier branch [32]. An RF-input sequential load modulated balanced amplifier (SLMBA) was also proposed [33], [34], where the control amplifier (CA) operates as the carrier branch while the BA becomes the peaking branch. Because there is no load modulation in the carrier branch, the CM CA can be designed to provide high efficiency at OBO over a wide bandwidth. Using the continuous Class-F −1 CA, the design space of the fundamental impedance of the BA can be extended by varying the second-harmonic load impedance of the CA [35], [36]. The recently reported hybrid asymmetrical load modulated balanced amplifier (H-ALMBA) also used harmonic-controlled output matching networks (OMNs) for the realization of hybrid continuous Class-F/F −1 CA operation in carrier branch [37].
In theory, the bandwidth of both the LMBA and SLMBA configurations is only constrained by the bandwidth of the input and output quadrature couplers [26], [33], [34], [38], [39]. However, in practice, the active devices of CA and BA cells require proper source/load fundamental or harmonic impedance tuning to achieve high efficiency with broadband operation [32], [35], [36], [37], [40], [41], [42], [43], [44], [45], [46]. Although the CM theory provides PA design with high-efficiency broadband load design continuum, a fundamental limitation exists that most of the practical  transmission-line (TL)-based matching networks have some impedance mismatch when tracking the design space over a wide frequency band.
In this article, a broadband SLMBA is proposed with the CA operating in an extended high-efficiency CM design space via second-harmonic manipulation. Theoretical analysis shows that the extended CA fundamental load impedance design space not only can provide the time-domain-varying drain current waveform over the design continuum but also contributes to high output OBO efficiency in the proposed SLMBA. Case studies show that the combination of different OBO input driving levels and normalized CA secondharmonic voltage can provide the BA peaking branch with multiple sets of expanded fundamental design space (i.e., either along constant resistance contour or resistively extended contours). Different from the previous work on waveform engineered sequential load modulated balanced amplifier (W-SLMBA) [35], this work focuses on the further extension of broadband operation without deteriorating high efficiency at either OBO or saturation level.
The remaining part of the article is organized as follows. Section II presents the theory of the proposed SLMBA with extended high-efficiency CM design space. Section III shows the detailed design procedure. In Section IV, the experimental results and comparison to the existing LMBA/SLMBA configurations are represented. Finally, this article is concluded in Section V.
II. THEORETICAL ANALYSIS The SLMBA is an inverted architecture of the original LMBA. The general schematic of the RF-input SLMBA configuration is shown in Fig. 1(a), wherein a Class-AB/B biased CA is used as the carrier branch, and the BA composed of two Class-C biased PAs operates as the peaking branch. In the low power level, the BA is turned OFF, while the CA solely contributes to the output power for the entire SLMBA and is saturated at OBO. In the high power level, the CA remains saturated, while the BA starts to turn ON and will continue to provide the output power until it reaches saturation.
As shown in Fig. 1(b), the three amplifiers in SLMBA can be modeled by ideal current sources connected to the output quadrature coupler. According to the SLMBA theory introduced in [33] and [34], the port impedance for BA1 and BA2 can be represented as wherein Z 0 is the characteristic impedance of the coupler, and I 1 = − j I ba and I 2 = I ba represent the currents of two cells (BA1 and BA2) in the BA branch with equal magnitude and quadrature phase difference. The control signal current is denoted as I 3 = j I ca e j θ ca . To ensure optimal power combining, the CA-BA phase shift is assumed to be θ ca = 0. The reported W-SLMBA [35] presented the expansion of BA fundamental port impedance design space by exploiting the varying CA fundamental current component i ca [1] versus the second-harmonic load impedance Z ca,2nd along the opencircuit region on the Smith chart. Such CA-BA harmonic fundamental control can only be realized using continuous Class-F −1 mode in the CA carrier branch, which might create difficulties when aiming for further extension of bandwidth in practical design. The continuous Class-F −1 theory generally provides only one single set of design space with constant fundamental conductance real(Y ca,1st ), while the TL-based OMN usually suffer from impedance mismatch when tracking the design space over the frequency domain [47], [48]. In consequence, more complex OMN structures might be required to track the fundamental and harmonic load design space precisely [35], which in return limits the maximum achievable bandwidth of the PA.
To mitigate the above-mentioned limitation, we revisited the intrinsic drain voltage and current waveforms. It is interesting to note that proper manipulation of second-harmonic load impedance Z ca,2nd not only can generate different time-domain current waveform but also bring alteration to the time-domain drain voltage waveform. This provides a solution that can further extend the high-efficiency CA design space beyond the previously reported continuous Class-F −1 operation, via the manipulation of second harmonic. To obtain the performance of the proposed SLMBA configuration in detail, the effect from the proposed CA with second-harmonic manipulation and the behavior of the proposed SLMBA are analyzed below.

A. CA With Second-Harmonic Manipulation Overextended Range
It is known that manipulating the second-harmonic load impedance Z ca,2nd can result in the amplitude change to the drain voltage of the transistor [10]. To better illustrate this manipulation and quantify the performance improvement, in [10], the parameter k 2 is introduced and defined as the ratio of the second-harmonic component to the fundamental component of the CA drain voltage, namely, k 2 = v ca [2]/v ca [1]. Assuming the third harmonic is terminated to a short circuit, the generalized time-domain CA drain voltage waveform can be expressed as where V dc,ca is the DC voltage, and v ca [1] is the fundamental voltage. Meanwhile, as analyzed in [49] and [35], the shaped CA intrinsic drain current waveform varies as a function of second-harmonic load reactance imag (Z ca,2nd ) and k 2 .
Based on the analysis in [35], [47], and [49], the generalized time-domain drain current waveform of the CA, i d,ca , can be derived and expressed as where I max,ca is the maximum current limit of the CA device and V dck,ca = (V dc,ca −V knee,ca ). V dc,ca and V knee,ca are the drain supply voltage and device knee voltage, respectively. δ(k 2 ) is the voltage gain function and can be expressed according to the analysis in [10] δ( As the peak drain current i d,ca excursion should not exceed I max,ca , the second-harmonic load impedance Z ca,2nd must be constrained by a boundary condition [18], [35], [49]. Such a condition with limit on Z ca,2nd can be derived by referring equations (41)- (44) in [49] i ca [2, q] wherein i ca [n, r ] and i ca [n, q] (n = 1, 2) represent the real and reactive current components, respectively, which can be calculated using the Fourier transformation of (3). Therefore, we can obtain the expression as Finally, the boundary condition of CA second-harmonic load impedance Z ca,2nd can be obtained as Fig. 2(a) shows the CA drain voltage with high swing and the square-wave-shaped drain current waveform with k 2 = − √ 2/4 ≈ −0.35, which is for the specific continuous Class-F −1 . In comparison, as shown in Fig. 2(b), when the value of k 2 changes, alternative drain voltage waveform swings can be provided with the same set of drain current waveforms. It is interesting to see that the drain voltage waveform is unchanged with alternative Z ca,2nd and the drain current waveform keeps constant with different values of k 2 . Therefore, the corresponding fundamental and second-harmonic load impedance continuum can be relaxed from the strict requirement from that of continuous Class-F −1 , resulting in an extended design space.
Since the proposed SLMBA can be described according to the normalized input driving level, β, where 0 ≤ β ≤ 1, we define β bo as the input driving level corresponding to OBO [32], [33], [35]. Herein, the CA design space is analyzed when it hits saturation, which is also at the OBO level with β = β bo in the proposed SLMBA. According to (2)- (7), the intrinsic CA fundamental load impedance Z ca,1st varies as a function of second-harmonic reactance imag (Z ca,2nd ) and normalized drain voltage second-harmonic component k 2 , and it can be expressed as Hence, the intrinsic CA fundamental admittance Y ca,1st can be calculated as which shows that the intrinsic CA fundamental conductance can be varied along real axis on the Smith chart with proper control of k 2 , corresponding to different values of CA second-harmonic impedance Z ca,2nd . When k 2 = −0.35, the operation described in (2)-(9) degenerates to that for the conventional continuous Class-F −1 PAs. Fig. 2(c) illustrates that the alternative value of k 2 can provide different sets of CA second-harmonic load impedance Z ca,2nd , which means the second-harmonic tuning range is extended, which, in return, provides more choices on the CA fundamental load impedance Z ca,1st to extend high-efficiency CM operation. Since only CA is turned ON when β = β bo , the OBO performance in terms of output power and efficiency can be expressed as [47] To better illustrate the performance with the variation in normalized second-harmonic drain voltage k 2 , the theoretical efficiency and output power are plotted in Fig. 3(a)  In this case, the normalized intrinsic drain voltage waveform exhibits an overshooting behavior at peaks along with high ripples at the minima, as shown in Fig. 3(b). This forces the device to operate near breakdown, which might impact its reliability. As a result, it is preferably to select the k 2 values within the range of [−0.35, −0.20] to provide a good tradeoff in terms of voltage level at the peaks, ripples at the minima, and bandwidth extension in the high-efficiency design space.

B. BA Behavior Analysis
The BA starts to turn ON when the input power level β keeps increasing from β bo at OBO level. To better analyze the performance of BA, we focus on the behavior at peak power level, where both CA and BA operate at the saturation with β = 1. Since two BA cells are biased in Class-C mode, the fundamental components of the BA current i ba,peak [1] at peak power level can be calculated as [35] i ba,peak [ where I max,ba is the maximum current limit of the BA device. (−θ b , θ b ) defines the turn-on phase range of the BA and θ b can be obtained as The BA fundamental port impedance at saturation can be calculated as where Substituting (7) into (13), the reactive part of BA fundamental impedance varies in the range of From (13) to (15), it can be seen that the BA fundamental port impedance can be expanded due to the injection of the varying CA fundamental current which is shaped by the intrinsic CA second-harmonic reactance over the extended range. What is more, for the fixed CA and BA devices and supply voltages, the BA fundamental design space expansion is only dominated by the parameter σ , which is actually determined by the input driving threshold, β bo , at OBO.
While β bo and k 2 are relatively independent of each other, when selecting different settings of β bo and k 2 , the power scale between peak power level and OBO level, defined as OBO d B dB, would vary. Case studies under different scenarios are conducted to investigate the impact on the entire performance in terms of efficiency, output power, and design space of BA fundamental impedance.
At peak power level when β = 1, the output power from two BA cells in the peaking branch can be calculated as where Re [Z ba,pt,1st ] is the real part of BA fundamental port impedance. Therefore, the OBO level of the proposed SLMBA can be calculated as OBO · P obo = P ca,sat + P ba,peak .

1) Case I (Varying OBO and Peak Power
Value for Different k 2 ): As shown in Fig. 4(a), when the entire SLMBA hits peak power level with β = 1, BA port impedance Z ba,pt,1st at the coupler port plane is expanded in the constant resistance contour, which is similar to Class-B/J or continuous Class-F fundamental impedance design continuum. According to Fig. 3, with constant value of β bo , CA has different saturation output P ca,sat power for k 2 over [−0.35, −0.20]. This leads to the slight variation in output power value at OBO level and peak power level. Fig. 4(c) shows different OBO values and first peak efficiencies with constant input driving level (β bo = 0.5) at OBO.
2) Case II (Constant OBO and Peak Power Value for Different k 2 ): To ensure constant OBO and peak power value with different k 2 , the value of input driving threshold β bo needs to be varied as well. According to (13) and (15), the BA fundamental port impedance can be expanded not only reactively but also resistively in the Smith chart, as shown in Fig. 4(b). Fig. 4(d) shows different β bo values and first peak efficiencies with constant OBO level.
Given the expanded BA fundamental port design spaces from the above two cases, it is worth mentioning that such extended harmonic-to-fundamental control still follows the mechanism that the variation in CA secondharmonic impedance Z ca,2nd manipulates the fundamental port impedance Z ba,pt,1st . The second-harmonic impedance Z ba,pt,2nd at BA ports needs to be properly controlled to achieve optimal peak power level performance in terms of efficiency and output power. As the BA fundamental port impedance naturally tracks the design space of the Class-B/J operation mode, the second-harmonic impedance at BA port Z ba,pt,2nd should be properly tuned following the Class-J theory such that: where δ max is the CM design space parameter that controls the second-harmonic design of Class-J BA. By substituting (13) and (15) to (18), δ max can be calculated and expressed as From the above analysis we can see, the design space for CA and BA can be extended while maintaining the good performance in terms of efficiency and output power.

III. DESIGN OF THE PROPOSED BROADBAND SLMBA
To validate the proposed theory, an RF-input SLMBA was designed and fabricated using commercial gallium nitride (GaN) HEMTs (CG2H40010F) from Wolfspeed. The target frequency range is from 2.05 to 3.65 GHz to cover the 5G NR bands, e.g., N22 of 3410-3590 MHz, N40 of 2300-2400 MHz, and N41 of 2496-2690 MHz for cellular communication systems. Similar to the reported SLMBA configurations [33], [35], the input driving threshold β bo = 0.5 was used and the target 8-dB OBO level was set for the design. While using the same CG2H40010F transistor for both CA and BA, larger drain supply voltage was used to achieve the required output power for the BA cell. The designed SLMBA was realized on a 31-mil-thick Taconic TLY-5 substrate with 2.2 dielectric constant. The schematic of the proposed SLMBA is shown in Fig. 5.
A broadband coupler was designed for both the input and output sections of the proposed SLMBA. The coupler was implemented using a three-section branch-line hybrid structure to cover the target bandwidth over 2.05-3.65 GHz, with the characteristic impedance of 50 . The parameters of coupler are shown in Fig. 5.
According to the theoretical analysis of the proposed SLMBA in Section II, the value of design parameter k 2 was chosen within [−0.35, −0.20], which can expand the fundamental load design space resistively and enlarge the second-harmonic load tuning range, while avoiding the overshooting behavior at the peaks and the high ripples at the minima for the drain voltage waveform.
A CG2H40010F transistor was used as the active device for CA with a drain supply of 20 V. Co-design of the CA OMN and coupler was required because the port impedance of the designed coupler cannot be maintained constant 50 over such a wide bandwidth of 2.0-3.65 GHz. As shown in Fig. 6(a), the output port of OMN is connected to port 3 of the designed coupler. The parasitic and package parameters in commercial transistors usually limit the access to the device intrinsic plane. To extract the intrinsic drain current and voltage and intrinsic impedance, the de-embedded network for CG2H40010F transistor was used in the practical OMN design [40], [50], [51]. The topology and parameters of the CA OMN are shown in Fig. 5. During the design, both manual tuning and algorithm optimization were used for obtaining the good performance. The intrinsic CA load impedance trajectory is shown in Fig. 6(b), which follows the theoretical design space presented in Section II. Typically, the fundamental impedance has large value at low-frequency points, and vice versa at high-frequency points.
The IMN was also designed according to the source impedance extracted from the load-pull simulation. A 100-pF capacitor was used for DC blocking. A 10-resistor is added to the gate bias line and ensure the stability of the transistor.
Two CG2H40010F transistors were also used as the active devices for the realization of the BA cells. In this case, the drain supply was set to 36 V. To simplify the design, we considered the BA impedance at saturation. The topology and parameters of BA OMN are shown in Fig. 5. It transformed the BA port impedance Z ba,pt,1st (when β = 1) to BA transistor intrinsic impedance Z ba,1st at saturation when the BA load modulation trajectory was on the real axis. The de-embedded network was also used for the BA OMN design so that intrinsic BA load impedance trajectory can be achieved, as shown in Fig. 7.
Similar to the design process in [32], [33], [34], and [38], a practical TL based phase shift network was designed to mimic the optimal phase shift value at each frequency point over the entire bandwidth of 2.05-3.65 GHz. The two-section equal ratio power divider (PD) was also designed and included in the schematic, as shown in Fig. 5.  1%-69.1% is achieved 6-and 8-dB OBO. A 9.6-12.0-dB gain was obtained at around 28-dBm output power level. Fig. 9 shows the simulated power-added efficiency (PAE) of 53.2%-64.5%, 47.4%-60.7%, and 49.0%-62.3% at saturation, 6-, and 8-dB OBO power level, respectively. Moreover, the simulated intrinsic BA fundamental load modulation trajectories at selected frequency points are plotted in Fig. 10, which is in good consistency with the theoretical design space continuum shown in Fig. 4(a) at saturation power level. Fig. 11 presents the photograph of the fabricated SLMBA. The board is in a size of 22.25 cm × 12.8 cm. The drain supply voltage of 20 V and quiescent current of 30 mA for the carrier CA were set during all the measurements. The drain voltage of the peaking BA was set to 36 V to ensure good linearity, and the peaking bias voltage was set to −5.2 V. During the measurements, the CW and modulated signals were generated by a vector signal generator, and the output power was measured with a spectrum analyzer. A broadband linear driver amplifier was used to drive the SLMBA with enough input power. A broadband circulator was added between the driver and SLMBA to improve isolation.

A. Measurements With CW Signal
The SLMBA was first measured under CW signal stimulation at different operation frequencies with different input power levels. Fig. 12 presents the measured DE and gain versus output power at different operation frequencies. It can be seen that the Doherty-like behavior was achieved by the implemented SLMBA within the desired frequency band. Fig. 13 is the measured PAE versus output power at different operation frequencies. To better present broadband performance, the measured DE at different output power levels and output power at saturation versus the operation frequency are presented in Fig. 14. Over the realized bandwidth, the proposed SLMBA achieves a measured DE of 50.5%-66.2% at 8-dB OBO, 51.2%-65.8% at 6-dB OBO, and 61.2%-79.7% at peak power, with output power from 45.2 to 46.8 dBm.
The measured PAE and the gain at different output power levels over the bandwidth are also plotted in Fig. 15 with a measured PAE of 40.5%-57.7% at 8-dB OBO, 40.0%-56.3% at 6-dB OBO, and 43.5%-62.2% at peak power level, respectively. A 7.8-10.8-dB gain was obtained at around 28-dBm output power level. It should be noted that the transducer power gain of this SLMBA prototype is relatively low, i.e., 4.9-7.1-dB at peak output power. This leads the PAE to be much lower than DE reported above. To directly use this  PA prototype in a real system, a large driver amplifier would be required to keep the system efficiency [39]. Besides the tradeoff in gain versus frequency versus bandwidth [40], the low gain is a general issue for the SLMBA-based architectures [33], [34], [37], [38], [39]. At least half of the input power is steered to drive large peaking BA and wasted at OBO level. This leads to the low gain for the carrier CA and also insufficient gain for peaking BA. This issue needs to be addressed in future research.
Compared with the simulation results presented in Figs. 8 and 9, the measured results slightly deviated from the simulation results. This can be attributed to fabrication   tolerances of the prototype board and inaccuracy of the largesignal model of the device in deep Class-C bias [31].

B. Measurements With Modulated Signal 1) Single-Band Measurements:
To evaluate the linearity and efficiency performance under modulated signals' stimulation, 60-and 100-MHz LTE signals with 8-dB peak-to-averagepower ratio (PAPR) were used to test the SLMBA from 2.05 to 3.65 GHz.      Fig. 17(b), (d), and (f).
In Fig. 18  2) Concurrent Dual-Band Measurements: The proposed SLMBA was also measured under concurrent dual-band signal stimulation. Concurrent dual-band modulated signal with 7-dB PAPR was used with 20-MHz signal bandwidth at each band. To validate the performance under different scenarios, the PA was measured under different carrier frequencies with different frequency spacing between the bands. During the measurement, the average output power of the two frequency bands was kept almost equal. Dual-band memory polynomial (MP) model-based DPD was performed to linearize the proposed SLMBA under concurrent operation [53].
a) Frequency spacing of 500 MHz: In this scenario, the center frequencies of the two signals were 2.15 and 2.65 GHz for LTE B1 and B7 bands, respectively. Fig. 20 represents the corresponding output spectrum. The average efficiency of 54.6% was achieved with around 35.5 dBm average output power at each band. The ACPRs were −29.5 and −27.9 dBc without DPD correction and improved to −48.1 and −46.9 dBc with DPD, at 2.15 and 2.65 GHz, respectively.  b) Frequency spacing of 1000 MHz: In this scenario, the center frequencies of the two signals are 2.55 and 3.55 GHz corresponding to 5G NR N7 and N48 bands, respectively. Fig. 21 represents the corresponding output spectrum. The average efficiency of 45.4% was achieved with around 34.2 dBm average output power at each band. The ACPRs   c) Frequency spacing of 1300 MHz: In this scenario, the center frequencies of the two signals are 2.15 and 3.45 GHz, corresponding to 5G NR N1 and N48 bands, respectively. Fig. 22 represents the corresponding output spectrum. The average efficiency of 45.2% was achieved with around 32.8 dBm average output power at each band. The ACPRs were −25.8 and −25.9 dBc without DPD correction and improved to −47.5 and −47.5 dBc with DPD, at 2.15 and 3.45 GHz, respectively.
Although the main target of this design was focused on continuous bandwidth extension, the above measurements show that the proposed SLMBA can also support concurrent operation with different frequency distributions and large frequency spacing. The proposed SLMBA presents promising performance in terms of efficiency, output power, and linearity, at the concurrent dual-band scenario with various frequency spacing.  Table I summarizes the performance of some recently reported LMBA and SLMBA-based configurations. Compared with other published work, the proposed SLMBA shows excellent efficiency performance at both saturation and 6/8-dB OBO levels. Particularly, it achieves 56.1% fractional bandwidth over 2.05-3.65 GHz. Compared with W-SLMBA reported in [35], the proposed SLMBA design approach enables significant improvement in fractional bandwidth (improved approximately by 34%), without adding extra complexity. Furthermore, the proposed SLMBA achieves good average efficiency under both the single-band and concurrent dual-band scenarios, proving that it can be a good candidate for the 5G NR band, e.g., N7, N22, and N40 bands.

V. CONCLUSION
An RF-input broadband SLMBA is proposed with extended high-efficiency design space, via proper manipulation of CA second-harmonic load impedance over an expanded range. The enlarged CA load design space not only can provide the time-domain-varying drain current waveform over the design continuum, but also allows maintaining high OBO efficiency over an extended operation bandwidth. To validate the theory, a broadband SLMBA operating at 2.05-3.65 GHz was designed following the proposed design methodology and fabricated using packaged devices. The implemented SLMBA achieves a measured DE of 61.2%-79.7% at saturation and 50.5%-66.2% at 8-dB OBO.