Alexander Deublein, Michael Loose, Andreas Illmer, Christian Musolff, Florian Irnstorfer, Robert Weigel, Thomas Ackermann
IMAGE LICENSED BY INGRAM PUBLISHING
Most RF and millimeter-wave systems for communications and radar include at least one transmitter used to up-convert, amplify, and potentially radiate the desired signal without distortion. Moreover, this part of the system, and in particular its power amplifier (PA), does typically dominate the total power consumption of electronic infrastructure systems. Thus, increasing the PA’s efficiency is the most effective way to enhance the overall power efficiency of such systems.
This common demand was reflected within the competition rules of the 18th High-Efficiency Power Amplifier (HEPA) Student Design Competition (SDC), organized by the IEEE Microwave Theory and Technology Society (MTT-S), which took place in Denver, CO, at the International Microwave Symposium (IMS) 2022. Participants were asked to design and manufacture a linear as well as efficient RFPA supplied by up to two dc voltage rails of their choice [1]. Within the range of 1–10 GHz, the design frequency ${f}_{0}$ could be freely selected.
The figure of merit (FOM) defined in (1) represents the criterion to identify the winning PA and is determined during the linearity test. For convenience, the definition of the power-added efficiency (PAE) as well as its relation with the drain or collector efficiency ${\eta} = {P}_{\text{out}}{/}{P}_{\text{dc}}$ and the power gain G is given in (2). Additionally, to qualify for the linearity test, the PA needs to meet the power criterion specified next.
Given a single-tone excitation with an input power of up to 24 dBm, the PA must deliver an output power of at least 4 W (36 dBm) but no more than 40 W (46 dBm) to qualify for the linearity test.
A two-tone test with a fixed spacing of 20 MHz is utilized to measure both the PA’s linearity as well as its PAE. Therefore, the carrier-to-intermodulation (C/I) ratio is observed given an increasing power sweep ranging from 0 dBm per tone up to 21 dBm per tone. As soon as the C/I ratio falls below 30 dB, the two-tone PAE will be measured and used to compute the FOM according to (1). In case the C/I ratio does not fall below 30 dB, the two-tone PAE will be evaluated at the maximum input power of 21 dBm per tone. \[{\text{FOM}} = {\text{PAE}}\left[{\%}\right]\left\vert_{{\text{two-tone}}}{\cdot}{\sqrt[4]{\frac{{f}_{0}}{\text{GHz}}}}\right. \tag{1} \] \[{\text{PAE}} = \frac{{P}_{\text{out}}{-}{P}_{\text{in}}}{{P}_{\text{dc}}} = {\eta}\cdot\left({{1}{-}\frac{1}{G}}\right){.} \tag{2} \]
Typically, high-efficient amplification requires driving transistors into saturation, which comes along with nonlinearities such as gain compression; amplitude-to-phase modulation (AM-PM); and, in the case of a multitone stimulus signal, intermodulation products. Thus, the competition’s FOM unifies two inherently competing goals omnipresent in PA design to maximize efficiency while ensuring sufficient linearity.
The remainder of the article is structured in the following way. First, the properties of the chosen PA circuit topology will be discussed. Key characteristics about the winning PA demonstrator are summarized afterward, which is followed up by a more detailed description of the design approach. Next, the algorithm used to estimate the PA’s linearity based on single-tone results and the simulation testbench utilized during the design process, including some theory-based features, will be revealed. Finally, measurement results as well as the setup used will be presented before concluding the article.
Before starting any PA design, one needs to identify a promising circuit topology for the given task. For this reason, the winning HEPA demonstrators since 2012, when the PA’s linearity was taken into account the first time, have been reviewed. Figure 1 displays their PAE results versus a frequency axis. Due to the fourth root in (1), lines of constant FOM values have been added to facilitate estimating the demonstrators’ performance within the HEPA-SDC. Furthermore, an examination of their respective circuit topologies reveals a distinct dominance of Doherty’s PA architecture, each of them achieving a considerably higher FOM than the only exception among the winning RFPAs.
Figure 1. The performance data of the winning HEPA demonstrators since 2012.
There are two properties of Doherty PAs that may provide an explanation for this observation. First, Doherty’s primary motivation for the architecture presented in [11] was to amplify modulated signals with high average efficiency despite their fluctuating power levels over time. His circuit topology utilizes two transistors actively modulating each other’s load via a nonisolating output combiner, which is comprehensively explained in [12], [13], and [14]. Since the two-tone stimulus signal used in the linearity test exhibits a peak-to-average power ratio (PAPR) of 3 dB with the power distribution discussed in [3], the aforementioned property of Doherty PAs explains their superior average efficiency compared to single-transistor RFPAs with a constant supply voltage.
There is, however, a single-transistor PA concept promising a similar average efficiency. Envelope tracking PAs modulate their supply voltage according to the envelope of the RF signal, which achieves high efficiency for a wide range of input power levels as well [12, pp. 311–314]. Given the two-tone signal’s low PAPR and the additional circuitry required to sense the RF envelope and to efficiently modulate the supply voltage, the participants’ preference to use Doherty’s architecture instead appears to be reasonable.
In addition, suitable gate biasing of both transistors improves the linearity of the Doherty PA by cancelling intermodulation products, as discussed in detail in [3]. This second feature is crucial as it helps to maintain sufficient linearity up to higher drive power levels, which inherently leads to higher efficiencies.
Based on the previous analysis as well as further aspects discussed in [4], the authors decided to design a single-stage Doherty PA at 3.6 GHz. A photograph of the final PA demonstrator is shown in Figure 2. In Denver at IMS2022, in the two-tone test scenario, it did not fall below a C/I ratio of 30 dB and achieved a two-tone PAE of 61.9% given the specified maximum input power of 21 dBm per tone. This corresponds to a FOM of 85.3. For a single-tone excitation, the Doherty PA has a small-signal gain of 15.5 dB, an output power of 40.9 dBm, and a PAE of 64.7%, both at 1-dB gain compression. It utilizes a shared drain bias voltage of 32 V and a second dc voltage rail of −5 V, used to supply both gate bias drivers. With a gate voltage of ${V}_{{\text{G}},{\text{Mn}}} = {-}{2.98}\,{\text{V}}$ and a quiescent current of ${I}_{\text{DQ}} = {29.7}\,{\text{mA}}$, the main (Mn) transistor operating in class ${F}^{{-}{1}}$ is biased in deep class AB. For the peak (Pk) transistor, ${V}_{{\text{G}},{\text{Pk}}} = {-}{4.36}\,{\text{V}}$ turned out to be a suitable class C bias voltage suppressing C/I ratios smaller than 30 dB for a wide input power range.
Figure 2. A photograph of the Doherty PA winning the 18th HEPA-SDC.
Because of a close industry cooperation, unpackaged high-electron-mobility transistors (HEMTs) of Infineon’s latest RF gallium nitride (GaN) on a silicon (Si) sub-6-GHz process were chosen for this Doherty design. Compared to GaN devices processed on silicon carbide (SiC), GaN-on-Si transistors exhibit a higher thermal resistance between the junction and baseplate because of Si’s reduced specific thermal conductivity compared to SiC. In consequence, the junction temperature of GaN-on-Si HEMTs rises higher for a given amount of dissipated power.
To partially compensate for Si’s thermal properties, the unmatched transistors were planned to be soldered directly onto a copper block to minimize the additional thermal resistance. Later, due to better machinability, a gold-plated brass block was used instead, resulting in a significantly increased thermal resistance between the devices’ baseplates and the heatsink, which, according to simulations via SolidWorks, is about 6.2 K/W instead of 1.8 K/W. The alternative of soldering the transistors directly onto capped thermal vias on the 20-mil printed circuit board (PCB) used would have been barely worse as simulations predict about 7.5 K/W for the same thermal resistance.
Moreover, passive RF structures and biasing circuits have been realized on two two-layer PCBs, both using Isola’s ultra low loss substrate Astra MT77, which exhibits a Dk of 3.0 and a loss tangent of ${1.7}\times{10}^{{-}{3}}$ up to 10 GHz [15]. Necessary bonding transitions to connect the HEMTs with both PCBs have been simulated via CST Studio Suite’s Frequency Domain Solver and were taken into account within PathWave Advanced Design System (ADS) via an imported four-port touchstone file, not shown in all figures for better clarity.
For the Doherty design, two 1.92-mm transistors with estimated output powers of 9.6 W $({V}_{\text{DD}}$ of 28 V) at 3-dB gain compression were selected such that high efficiency can be reached given the available stimulus power. In contrast to idealized theory [13, pp. 37–39], biasing the main transistor in class AB and the peak one in class C, given a symmetric power division, will not result in a symmetric Doherty PA but leads to an operation mode called Doherty Lite by Cripps [13, pp. 46–49] without a characteristic efficiency peak in the power back-off region.
Given the design frequency of 3.6 GHz, the tone spacing of 20 MHz specified by the competition rules corresponds to a relative bandwidth below 1% such that the following single-frequency PA design approach, consisting of five steps, could be applied.
A general Doherty architecture, used to identify design goals for the passive networks as well as suitable biasing of both transistors, is shown in Figure 3. Except for the GaN HEMTs’ compact models, it consists only of tuners, discussed in a later section, capable of emulating a variety of multiharmonic impedance environments, including load modulation at the fundamental frequency. ADS’s Harmonic Balance (HB) simulation algorithm and the iterative tuning of different parameters allow one to identify desired configurations promising both sufficient linearity as well as a high average PAE.
Figure 3. A generalized block diagram of a Doherty PA.
As the initial combiner model emulates the load modulation mechanism only in a simplified way, an actual combiner was implemented in the next step. It absorbs terminations of higher harmonics as well as drain-biasing networks. Furthermore, to model parasitic phenomena and losses as accurately as possible, the resulting representation is exclusively based on Modelithics’ models for SMD capacitors and electromagnetic (EM) simulation results of the RF layout.
Afterward, the implemented Doherty combiner substitutes its corresponding tuner within the testbench shown in Figure 3. In contrast to the S-parameter simulations executed in the previous step, reliable estimates of the combiner losses may be extracted only from HB simulation results because of the transistors’ nonlinear nature and the active load modulation mechanism. This is likely to detune the PA’s behavior, including linearity and efficiency. In consequence, the designed Doherty combiner, as well as the goals for the single input matching network (IMN) utilized for both amplifier branches and the drive function, should be retuned or reoptimized based on HB simulation results. Prior division of the combiner layout into multiple sections and their modeling via ADS’s Advanced Model Composer are very likely to be beneficial for gradient-based optimizations due to their inherent monotonicity.
Stability Parameters
The stability parameters ${\mu}$ and ${\mu'}$ are a subset of Rollett’s ${K} {-} \Delta$ stability criterion [16]. As described by Edwards and Sinsky [16], both ${\mu}$ and ${\mu'}$ are geometrically derived from the distance between the origin of the respective reflection plane, $\Gamma = {0},$ and the nearest point of the load or source stability circle, respectively, and therefore, quantify the stability margin. In addition, unconditional stability is ensured if any of ${\mu}$ or ${\mu'}$ is greater than 1.
Since efficiency represents a key parameter of PAs, their stabilization is typically ensured via appropriate IMNs. Hence, stability analysis was executed next. It was based on the setup shown in Figure 4(a), which served to extract the small-signal stability parameters ${\mu}$ and ${\mu'}$ [16] as well as load and source stability circles (see “Stability Parameters”). This way, any transformation of stability circles and relaxations due to undesired combiner losses could be taken into account during the design of the IMN.
Figure 4. The schematic used to extract small-signal stability parameters, ${\mu}$ and ${\mathit{\mu’}},$ as well as stability circles of the main amplifier branch, is illustrated in (a). Altogether with the frequency response of the designed IMN’s reflection coefficient, ${\Gamma}_{\text{IMN}}\,{(}{f}{)}$, toward the transistor’s gate, selected source stability circles are shown in (b).
Moreover, while ${\mu}$ and ${\mu'}$ display frequencies of potential instability, plotting the frequency response of an IMN’s reflection coefficient, ${\Gamma}_{\text{IMN}}{(}{f}{),}$ toward the transistor and source stability circles together in the same Smith chart, shown in Figure 4(b), allows one to identify critical areas as well as possibilities to avoid them. Given this additional piece of information, an effective insertion loss of only 0.3 dB despite the broadband stabilization of the Doherty PA was achieved using an ${R}\Vert{C} {-} {\text{element}}\,({{10.7}\,\Omega}\Vert{{4.7}\,{\text{pF}}})$ in series and two RC elements ${(}{10.7}\,\Omega,\,{22}\,{\text{pF}}{)}$ in shunt configuration. These elements are highlighted in Figure 2.
The only RF section that remained to complete the Doherty PA was the drive function. Simulations of a branchline coupler and a Wilkinson divider indicated that the latter one provides a higher isolation between its output ports, and was chosen for this reason. The desired phase shift got realized by a delay line. Moreover, the layout was extended by dedicated spots for dielectric shards, which could be added during measurements to reproducibly adjust the relative phase.
However, the completion of a Doherty PA demonstrator requires two more crucial aspects to be taken care of. First, the ability to measure the RFPA demands for coaxial interfaces that have been realized via SMA end launch connectors. Even though default footprints are typically provided, the design of a custom footprint optimized for low insertion loss is key since the impact of the output transition on output power and both efficiencies is just as severe as losses of the Doherty combiner.
The second aspect concerns the generation of gate bias voltages to be derived from a single dc supply rail. Unfortunately, GaN HEMTs typically exhibit notable variations of their threshold voltages such that a possibility to individually adjust each of them appears to be highly advisable. For this reason, two tunable gate bias drivers, similar to the ones presented in [4], were designed. Each of them consists of a single zero-drift operational amplifier driving a large capacitance, which required the use of an in-the-loop compensation for stabilization. Moreover, use of a bandgap reference grants resilience versus minor variations of the −5-V supply rail.
Following Musolff et al. [4], simulation time can be reduced significantly by substituting a two-tone HB with a single-tone HB accompanied by estimation algorithms for linearity and two-tone efficiency. The latter approach requires keeping all the PA’s memory effects as low as possible [17] since the single-tone HB results are unable to capture them. However, minimization of memory effects of all kinds aligns well with the overall design goal of sufficient linearity for the Doherty PA.
Given a numerically extracted distribution of the input power, the subsequent computation of the average input, output, and supply power based on the single-tone HB’s results and their insertion into (2) yields a good estimation of the two-tone PAE.
By contrast, the algorithm computing intermodulation distortion (IMD) levels, inspired by [12, p. 245] and used to estimate the PA’s linearity, is more complicated. Deviating from Cripps’ approach, the algorithm makes use of a phasor-based representation of the two-tone signal ${V}_{\text{in}}(\text{t})$ \begin{align*}{V}_{\text{in}}{(}{t}{)} & = {A}\cdot{e}^{{j}{(}{\omega}_{0}{-}{\omega}_{m}{)}{t}} + {A}\cdot{e}^{{j}{(}{\omega}_{0} + {\omega}_{m}{)}{t}} \\ & = {2}{A}\cos{(}{\omega}_{m}{t}{)}\cdot{e}^{\text{j}{\omega}_{0}\text{t}}\mathop=\limits^{\text{def}}{V}_{{\text{in}},\,{\text{env}}}{(}{t}{)}\cdot{e}^{\text{j}{\omega}_{0}\text{t}} \tag{3} \end{align*} defining the input envelope signal ${V}_{{\text{in}},\,{\text{env}}}(\text{t})$ as well as the angular tone spacing $\Delta{\omega} = {\omega}_{2}{-}{\omega}_{1} = {2}{\omega}_{m}{.}$ This is consistent with the common assumption for AM-PM and is therefore advantageous over the use of real-valued time signals.
Within the estimation algorithm, the PA’s distortive impact is described via a nonlinear mapping, ${g}{:}{V}_{\text{in}}\in{\mathbb{R}}\rightarrow{V}_{\text{out}}\in{\mathbb{C}},$ which is equivalent to the information given by the gain and the AM-PM resulting from a single-tone HB simulation in the case of a fixed system impedance ${Z}_{0} = {50}\,\Omega{.}$ Because of the real-valued nature of ${V}_{{\text{in}},\,{\text{env}}}(\text{t}),$ it is important to ensure ${V}_{\text{in}}\in{\mathbb{R}}$ via simultaneous phase rotations of both ${V}_{\text{in}}$ and ${V}_{\text{out}}{.}$ Furthermore, it is beneficial to mirror the voltage mapping according to an odd symmetry since ${V}_{{\text{in}},\,{\text{env}}}(\text{t})$ also features negative values. Additionally, a signed ${V}_{\text{in}} {-} {\text{axis}}$ prevents interpolation issues that might occur due to insufficient voltage amplitudes.
The application of the nonlinear mapping on ${V}_{{\text{in}},\,{\text{env}}}(\text{t})$ maintains the signal’s periodic nature such that ${V}_{{\text{out}},\,{\text{env}}}(\text{t})$ can be represented by a Fourier series [12, p. 245]: \[{V}_{{\text{out}},\,{\text{env}}}{(}{t}{)} = {g}\left({V}_{{\text{in}},\,{\text{env}}}{(}{t}{)}\right) = \mathop{\sum}\limits_{k}{{\mu}_{k}}\cdot{e}^{\text{jk}{\omega}_{m}\text{t}}{.} \tag{4} \]
In addition, Cripps mentions [12] the possibility to reconstruct the RF signal via a multiplication of ${V}_{{\text{out}},\,{\text{env}}}(\text{t})$ with ${e}^{\text{j}{\omega}_{0}\text{t}},$ which might be helpful for a general understanding. However, for the analysis of various tone powers as well as IMD levels, it is sufficient to determine the coefficients ${\mu}_{k}$ of the output envelope signal via a fast Fourier transform (FFT) \begin{align*}{V}_{{\text{out}},\,{\text{env}}}{(}{\omega}{)} & = {\text{FFT}}\left\{{V}_{{\text{out}},\,{\text{env}}}{(}{t}{)}\right\} \\ & = \mathop{\sum}\limits_{k}{{\mu}_{k}}\,{\cdot}\,{\delta}{(}{\omega}{-}{k}\cdot{\omega}_{m}{)} \tag{5} \end{align*} where ${\delta}$ denotes the Dirac distribution.
Figure 6 shows a direct comparison of measured and estimated IMD traces to illustrate the algorithm’s accuracy, which is moderate. The IMD estimation is based on the nonlinear mapping defined by the gain and AM-PM displayed in Figure 5, which originate from single-tone measurements. For the analysis, an FFT size of 32 was used to keep both the computational effort as well as aliasing effects low.
Figure 5. The measured single-tone gain and AM-PM of the Doherty PA demonstrator at 3.6 GHz.
Even though a higher accuracy would be desirable, one should keep in mind the low computational effort to obtain the IMD estimates and the fact that only a single-tone measurement or single-tone HB simulation, respectively, were necessary. Since the algorithm presented was the only metric used to estimate the PA’s linearity during the design, the authors’ opportunity to write this article demonstrates the overall potential of the algorithm to considerably speed up the design at the expense of slightly reduced accuracy, which nevertheless yields high linearity. Further optimizations can be carried out subsequently, either by more accurate simulations or by manually tuning the PA in the lab.
Contemporary RFPA design methodology fully relies on accurate models of transistors, taking into account self-heating, nonlinear capacitances, and nonlinear transconductive behavior, such as the ASM GaN model [18] used by Infineon. Due to the complexity of these models, they are commonly handled via nonlinear circuit simulators like ADS. Typically, these software tools provide capabilities to compute EM results and to include further modeling libraries.
However, based on this reality, one should by no means conclude that the analytic PA theory was obsolete. In contrast, it remains an extremely powerful tool to recognize and understand the root causes of several phenomena, which is essential to use today’s simulative capabilities in a target-oriented way. Accordingly, the tuners discussed in the following section provide an example of how the theory may be used to achieve better design goals that are likely to reduce the number of iterations required for a satisfying PA design.
Figure 7(a) illustrates the internal structure of the IMN tuners, which are included in Figure 3. Each of them features three outer ports: the multiharmonically tuned port to be connected to the transistor’s gate; the biasing port used to set the gate voltage; and the second RF port receiving the exciting RF signal.
Instead of a broadband bias tee, a frequency multiplexer is directly connected to the transistor’s gate. This is advantageous as it allows competing objectives to be resolved when choosing inductance and capacitance values for the RF choke and the dc block. In the case of a classic bias tee, the ability to ideally tune the impedances at the fundamental frequency and the higher harmonics presented to the transistor’s gate demands for high values of both inductance and capacitance. Such a choice, however, does not allow one to approximate a final bias network’s transient behavior, which appears as bias memory in the case of modulated signals. Therefore, the results of multitone simulations utilizing an RF choke and a dc block are misleading. An alternative resolving this issue is shown in Figure 7(a). Apart from emulating the baseband response of a shorted quarter wavelength (qw) transmission line (TL) based on Cripps’ considerations [12, pp. 343–354], the lowpass branch of the frequency multiplexer is used to bias the transistor’s gate. There is no impact on branches for the other frequencies.
While higher harmonics are terminated via reflection coefficients, adjusting the fundamental frequency requires a transmissive tuning network. Figure 7(b) shows two possibilities to realize a lossless two-port tuner capable of reaching any passive impedance at their tuned port given a matched termination at their second one. The upper example served to derive the general relations of a lossless and reciprocal two-port tuner, which are given in (6). Except for an additional phase indicated by the matched TL, all scattering parameters can be calculated from the desired reflection coefficient ${s}_{{11},\,{\text{tuned}}}{:}$ \begin{align*}{s}_{11} & = {s}_{{11},\,{\text{tuned}}} \\ {z}_{{s}_{11}} & = \frac{{1} + {s}_{11}}{{1}{-}{s}_{11}} \\ {s}_{12} & = {s}_{21} = {2}\cdot\frac{\sqrt{\Re{\{}{z}_{{s}_{11}}{\}}}}{{z}_{{s}_{11}} + {1}} \\ {s}_{22} & = \frac{{1}{-}{z}_{{s}_{11}}^{\ast}}{{1} + {z}_{{s}_{11}}}{.} \tag{6} \end{align*}
During the design process, iterative load and source pull tuning using ADS revealed a distinct tendency of the $\left|{{s}_{11}{(}{f}_{0}{)}}\right|$ target to approach the unit circle of the Smith chart, which is characteristic for GaN HEMTs.
Because of the unitarity identity of lossless networks [19, pp. 181–183], the transmission parameter ${s}_{21}{(}{f}_{0}{)}$ vanishes in the extreme case of $\left|{{s}_{11}{(}{f}_{0}{)}}\right| = {1}{.}$ In reality, unavoidable losses of an IMN counteract this trend and therefore shift the optimum reflection magnitude toward lower values. To imitate this behavior, and inspired by the aforementioned unitarity identity, a power sum ${p}_{\text{sum}}$ \begin{align*}{p}_{\text{sum}} = {\left|{{s}_{11}}\right|}^{2} + {\left|{{s}_{21}}\right|}^{2}\begin{cases}\begin{array}{ll}{ = {1},}&{\text{lossless}}\,{\text{case}}\\{{<}{1},}&{\text{lossy}}\,{\text{case}}\end{array}\end{cases} \tag{7} \end{align*} is defined that is utilized to compute the effective losses ${\ell}_{{\text{eff}},\,{\text{dB}}}$ \begin{align*}{\ell}_{{\text{eff}},\,{\text{dB}}} & = {-}{20}\cdot{\log}_{10}\left[{\frac{\left|{{s}_{{21},\,{\text{lossy}}}}\right|}{\left|{{s}_{{21},\,{\text{ideal}}}}\right|}}\right]{\text{dB}} \\ & = {-}{20}\cdot{\log}_{10}\left[{\frac{\sqrt{{p}_{\text{sum}}{-}{\left|{{s}_{11}}\right|}^{2}}}{\sqrt{{1}{-}{\left|{{s}_{11}}\right|}^{2}}}}\right]{\text{dB}} \tag{8} \end{align*} of the IMN as a function of $\left|{{s}_{11}}\right|{.}$ Within the tuner shown in Figure 7(a), the rightmost two-port implements the described penalty function that counteracts increasing ${s}_{11}$-magnitudes, and thus, completes the IMN tuner. For example, with a power sum of 0.975, an increase of $\left|{{s}_{11}}\right|$ from 0.8 to 0.9 causes a monotonic increase of the effective losses from 0.3 to 0.6 dB.
The internal structure of the tuner utilized to emulate the Doherty combiner is illustrated in Figure 8(a). It consists of several TLs and two output matching network (OMN) tuners, which are identical to the IMN tuners just described except for the missing tuning of the fundamental and the penalty attenuator. Signals at the fundamental frequency therefore pass each of the OMNs unchanged such that the corresponding termination is exclusively realized via the Doherty combiner being connected to the load and the other HEMT. The theoretical background of the selected combination of TLs is explained in the following.
A modified model for the Doherty combiner commonly used to analytically explain the mechanism of active load modulation is shown in Figure 8(b). Cripps’ original schematic [12, p. 293] has been extended by a quarter wavelength TL to transform the ${50}\Omega$ load to the desired impedance at the junction point and two offset lines with an electrical length of ${\lambda}{/}{2}$ [14, pp. 99–105]. In the case of a single-frequency analysis, none of the ${\lambda}{/}{2}$ TLs affects the load modulation since any reflection coefficient draws a complete circle in the Smith chart.
Representation of the main and peak transistors via ideal current sources is, however, inaccurate since transistors exhibit parasitic drain-source capacitances, as shown in Figure 8(c). Moreover, the bonding wires connecting the HEMTs’ drain pads with an output network realized on PCB are represented by inductors ${L}_{\text{bond}}{.}$ Similar to the matching approach absorbing device parasitics discussed by Cripps [12, p. 98], additional series inductances and shunt capacitances may lead to equivalent TLs, which had been the major reason to include the offset lines in Figure 8(b).
Generally, the lowpass ${\pi} {-} {\text{network}}$ absorbing the parasitics is likely to transform the impedance in addition to the quarter wavelength impedance inversion TL. For an effective goal identification, it is preferable to employ a model for the Doherty combiner with a minimal number of degrees of freedom. Therefore, three lossless two-port tuners are connected to obtain a comprehensive model for a three-port tuner, as shown in Figure 8(d). The three shunt reactances ${jB}_{1},\,{jB}_{2},$ and ${jB}_{3}$ can be combined to jB, reducing the count of variables from nine to seven. In addition, the matched offset TL with an electrical length of ${\varphi}_{3}$ is obsolete in this particular case since the load exhibits the same impedance as the TL.
Moreover, from a mathematical point of view, one of the three transformation ratios ${n}_{1},\,{n}_{2},$ and ${n}_{3}$ can be chosen arbitrarily, such that five real-valued degrees of freedom remain for the Doherty combiner. Nevertheless, the final tuner illustrated in Figure 8(a) maintains all three of them via quarter wavelength TLs featuring line impedances of ${Z}_{\text{inv}},\,{Z}_{\text{out}},$ and ${Z}_{\text{Pk}}$. The use of a shorted TL has been preferred over an open one because of its behavior for an electrical length of 90° to transit continually between the inductive and the capacitive region in the Smith chart.
Although the derived tuning circuit allows one to identify a sound initial design goal for the Doherty combiner, its lossless property has both an upside and a downside. It is beneficial because an attempt to fit the tuner automatically yields a low-loss implementation. On the other hand, the absence of unavoidable losses means that there is no indication on how they should be distributed among the scattering parameters. For this reason, an HB-based reoptimization of the implemented combiner is required.
Figure 9 visualizes a block diagram of the setup used to characterize the PA demonstrator. Its principal instrument is an Agilent PNA-X N5244A vector network analyzer (VNA) equipped with the ability to internally generate a two-tone signal. A GPIB link between the VNA and the Agilent DC Power Analyzer N6705B supplying the PA under test transfers corresponding data such that the resulting PAE can be computed directly by the VNA.
The full characterization of the PA under test requires input power levels of about 30 dBm, which is out of the VNA’s power range. Therefore, the network analyzer’s output signal, directly accessible via the SOURCE OUT connector associated with port 1, is preamplified by an Amplifier Research (AR) 50G1S6. Consequently, the measurement of both the power waves incoming to and reflected by the PA under test requires an external dual-directional coupler inserted after an isolator improving the source match seen by the Doherty PA. However, a 20-dB source attenuator was necessary to partially compensate for the preamplifier’s lowest possible gain of 37 dB to obtain an adequate power sweep range for the measurements.
As recommended by Keysight Technologies to ensure linear operation [20], the power levels at the VNA’s receivers were kept below −20 dBm using suitable attenuators. In addition, accurate measurements require careful calibration of the setup. Therefore, the power calibration was performed at 20 dBm to achieve a high signal-to-noise ratio for the receivers, in particular for receiver B. Since 20 dBm is close to the maximum power rating of the utilized Rohde & Schwarz NRP-Z21 power meter, it has been protected with a 20-dB attenuator, which had been characterized previously and was taken into account via a loss table. Similarly, the power handling capability of the mechanical calkit used for an enhanced response calibration has been extended. It is worth emphasizing that precise information regarding the power meter’s loss table as well as the defined thru standard used is key to accurately determine both efficiencies. Underestimating the RF output power, say by only 0.1 dB, would result in a measured drain efficiency of 63.5% for an actual value of 65%.
Altogether with simulated traces, the measurement results for a single-tone and a two-tone excitation of the Doherty PA are shown in Figures 10 and 11. In Figure 11, the average output power for which the C/I ratio fell below 30 dB for the first time, extracted from Figure 6, is marked by a dotted line. Taking into account minor deviations due to different setups and calibrations, the corresponding average PAE of 62.4% confirms the value of 61.9%, which was measured at IMS2022.
Figure 6. A comparison of measured IMD levels and estimated ones based on the measured traces shown in Figure 5. The worst-case IMD levels measured for a tone spacing of 20 MHz at 3.6 GHz are displayed.
Figure 7. (a) A block diagram of the utilized multiharmonic (Multiharm.) tuner used to emulate an IMN. (b) Two circuit options to realize a lossless and reciprocal two-port tuner and their associated equations for ${Z} = {z}_{{s}_{11}}\cdot{Z}_{0}$ and Y.
Figure 8. Different tuners and models for the Doherty combiner. (a) Tuning circuit emulating a lossless Doherty combiner including biasing and harmonics. (b) Modified model used to explain the mechanism of active load modulation [12, p. 293]. (c) Combiner model absorbing transistors’ parasitics. (d) General combiner model consisting of three lossless and reciprocal two-port tuners.
Figure 9. A block diagram of the two-tone measurement setup.
Figure 10. Single-tone measurement and simulation results at 3.6 GHz.
Figure 11. Two-tone measurement and simulation results for a tone spacing of 20 MHz at 3.6 GHz.
In general, the measurement results agree well with the simulated data, even though there are some adjustments that were not retransferred to ADS. For example, the drive function, the IMNs, and the Doherty combiner have been modified in the lab, which is clearly visible in Figure 2. Moreover, the decision to use a gold-plated brass block significantly reduces the conductivity in the immediate vicinity of the two transistors since the skin depth exceeds the thickness of the gold plating. Finally, four screws near the RF traces were necessary to prevent the PCB from bending upward at the interfaces to the GaN devices.
This article presented the Doherty PA that won the 2022 HEPA-SDC. It is based on Infineon’s latest RF GaN-on-Si HEMTs and achieved a FOM of 85.3, the fourth highest value among the winning HEPA demonstrators since 2012, which exclusively used Wolfspeed’s GaN-on-SiC transistors. Even though the authors do not believe they have reached the performance limit of GaN-on-Si, the achieved FOM is only 2.3 points below the best performance within the HEPA-SDC [9]. The applied narrowband design approach and the associated simulation setup were described in detail. Due to their generality, both can also be used to extract design goals for wideband PA designs, given a suitable variable management and additional goals regarding the PA’s frequency response. Furthermore, a computationally efficient algorithm to estimate the PA’s two-tone linearity based on single-tone data has been introduced. While it was moderately accurate in the narrowband case and thus useful for the HEPA-SDC, the algorithm’s utility for wideband designs might be limited since its accuracy is likely to degrade further with increasing tone spacing or bandwidth, respectively.
The authors would like to thank Infineon Technologies AG for providing the RF GaN-on-Si HEMTs and the associated compact models and for supporting and funding this project. In addition, the authors thank Modelithics, Inc. for providing access to the Modelithics models under the University License Program.
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Digital Object Identifier 10.1109/MMM.2022.3226547