X-parameter measurement on a GaN HEMT device: complexity reduction study of load-pull characterization test setup

    Corresponding author: Yelin Wang, walyerwong@hotmail.com
  • Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg Ø, Denmark

Key words: X-parametersGaN HEMTpower amplifierload-pulldevice characterizationbehavioral modeling

Abstract: Characterization of power transistors is an indispensable step in the design of radio frequency and microwave power amplifiers. A full harmonic load-pull measurement setup is normally required for the accurate and comprehensive characterization of RF power transistors. The setup is usually highly complex, leading to a relatively high hardware cost and low measurement throughput. This paper presents X-parameter measurement on a gallium nitride (GaN) high-electron-mobility transistor and studies the potential of utilizing an X-parameter-based modeling technique to highly reduce the complexity of the harmonic load-pull measurement setup for transistor characterization. During the X-parameter measurement and characterization, load impedance of the device is tuned and controlled only at the fundamental frequency and is left uncontrolled at other higher harmonics. However, it proves preliminarily that the extracted X-parameters can still predict the behavior of the device with moderate to high accuracy, when the load impedance is tuned up to the third-order harmonic frequency. It means that a fundamental-only load-pull test setup is already enough even though the device is to be characterized under load tuning up to the third-order harmonic frequency, by utilizing X-parameters.

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1.   Introduction
  • The radio frequency (RF) and microwave power amplifier (PA) is an essential component in wireless transmitter systems. The design of high-quality RF and microwave PAs requires accurate and comprehensive characterization of power transistors. To accomplish the task of transistor characterization, a full-harmonic load-pull measurement setup, which contains several mechanical tuners for impedance tuning, is normally employed[1, 2, 3, 4]. To establish such a measurement setup is never a trivial task. What is more, the high-level complexity, or in turn the relatively high hardware cost and low measurement throughput, of the setup become critical, especially for high frequency and power applications[5, 6, 7]. To reduce the complexity of the harmonic load-pull measurement setup, efforts have been made in the direction of trying to decrease the fundamental load tuning points or avoid the impedance tuners for harmonic frequencies (while, of course, maintaining the characterization accuracy). In the work presented in Reference [8], a technique is proposed to achieve high density transistor characterization by interpolating a small (sparse) number of measured load tuning positions. The overall characterization time is decreased while the same measurement throughput is maintained. However, the work only deals with the fundamental, while the possibility of avoiding the harmonic tuners is out of the scope of the research. Another representative effort has been reported in Reference [9]. In that work, the load impedance at the harmonics are controlled and tuned by a tunable pre-matching circuitry instead of mechanical tuners. The hardware cost of the test setup can be lowered in this way. However, one limitation of the method lies in the fact that the pre-matching circuitry can easily become rather complicated to design when many harmonics need to be involved, and a large impedance tuning area (i.e., on the Smith chart) needs to be considered. Moreover, an accurate model of the transistor package is required as well. Another effort has been reported in Reference [10], where the authors establish a time-domain load-pull system eliminating the need of impedance tuners for the harmonics. Nevertheless, accurate models of the transistor's nonlinearity and package are indispensable in this method. Moreover, the load impedance at the harmonics have to be fixed at certain values that are predefined according to the operation 'class' of the PA to be designed.

    The similarity of the methods described above is that the impedance tuners for harmonics can be avoided at the price of some extra designing (i.e., the pre-matching circuitry) and modeling (i.e., the transistor nonlinearity) work. $X$-parameters, developed as an extension to $S$-parameters, provide another possibility to deal with the issue[11]. Unlike the classic $S$-parameters, which only consider the device's small-signal linear behavior, $X$-parameters capture the device's behavior under large-signal operating points (LSOPs) and linearize nonlinear behavior around the LSOPs[11]. Recent studies have shown that $X$-parameter-based modeling is a powerful modeling technique to characterize and model transistors, PAs and other RF and microwave circuits[12, 13, 14, 15, 16, 17]. Specifically, for transistor characterization, the $X$-parameter-based modeling technique has the potential of reducing the complexity of the load-pull measurement setup by avoiding harmonic tuners without any extra designing and modeling work as described above. This work presents $X$-parameter measurement and characterization of a gallium nitride (GaN) high-electron-mobility transistor (HEMT) which is available commercially. During the device characterization, the load impedance is controlled and tuned at only the fundamental but left uncontrolled at higher harmonics. By analyzing the simulations on the extracted $X$-parameter model of the device, it is preliminarily proven that the behavior of the device under load impedance tuning up to the third-order harmonic can still be precisely characterized by the $X$-parameter model. It indicates that by utilizing $X$-parameters, a fundamental-only load-pull measurement setup is already enough, even if the device (in this work) is to be characterized under load tuning up to the third-order harmonic frequency.

    The paper is organized as follows: Section 2 describes the fundamentals of load-dependent $X$-parameters briefly and analyzes the potential of $X$-parameters in reducing the complexity of the load-pull measurement setup. Section 3 elaborates the $X$-parameter measurement and characterization of the transistor studied in this work by using a non-linear vector network analyzer (NVNA) based on an Agilent PNA-X. The extracted $X$-parameter model of the transistor is validated in Section 4 with emphasis on investigating complexity reduction of the load-pull test setup by avoiding load tuners at harmonics. In Section~5, further optimization of the load-pull test setup by reducing the number of the fundamental load tuning points is revealed based on some preliminary measurement and simulation results. Finally, the paper is concluded in Section~6.

2.   Basics of load-dependent $\boldsymbol{X}$-parameters
  • The theory and mathematical deduction of $X$-parameters are presented in Reference [11]. $X$-parameters are the parameters of a poly-harmonic distortion model and the basic equation of $X$-parameters can be written as Reference [11]:
    \begin{split} b_{mk}{}& =X^F_{mk}(|a_{11}|, \varGamma_{\rm L}, V_{\rm B})\, P^k \nonumber \\& + \sum_{(m, n) \neq (1, 1)}X^S_{mk, nl}(|a_{11}|, \varGamma_{\rm L}, V_{\rm B})\, P^{k-l}\, a_{nl} \\& + \sum_{(m, n) \neq (1, 1)}X^T_{mk, nl}(|a_{11}|, \varGamma_{\rm L}, V_{\rm B})\, P^{k+l}\, a^*_{nl}, \\ \end{split}
    where $b$ and $a$ represent the outgoing and incident waves; their indices ($m$ or $n$) and ($k$ or $l$) are the port and harmonic index, respectively. $a_{11}$ is the large-signal fundamental wave incident at port 1 (i.e., the input port or gate terminal) of the device under test (DUT); $P={\rm e}^{j\varphi(a_{11})}$ represents the phase of $a_{11}$. $a_{nl}$ is the parameter extraction tone incident at port $n$ at the $l^{\rm th}$-order harmonic and it has a fairly small amplitude compared to $a_{11}$; $a^*_{nl}$ is the complex conjugate of $a_{nl}$. $\varGamma_{\rm L}$ and $V_{\rm B}$ represent the reflection coefficients at load (in turn, load impedances) and DC biasing condition, respectively. $a_{11}$, $\varGamma_{\rm L}$ and $V_{\rm B}$ jointly determine the LSOPs of the DUT. $X^F_{mk}(\cdot)$, $X^S_{mk, nl}(\cdot)$, $X^T_{mk, nl}(\cdot)$ $\in$ ${C}$ are $X$-parameters, dependent on the LSOPs of the DUT.

    During $X$-parameter extraction, the DUT is excited by $a_{11}$ with certain selected settings of $\varGamma_{\rm L}$ and $V_{\rm B}$. The parameter extraction tones $a_{nl}$ are injected to the ports of the DUT. This kind of tone injection is in fact simulating the process of active load-pull characterization. It means that the extracted $X$-parameters capture the behavior of the DUT not only under those selected LSOPs, but also under impedance mismatch around those LSOPs to some extent. This mechanism is illustrated simply in Figure 1. The figure plots an example of the fundamental load impedance tuning points as black dots. To make the illustration simple but generic, harmonic loads are assumed to be at certain values and unchanged. Take the tuning point '$X$' as an example. The $X$-parameters extracted at '$X$' can certainly characterize the DUT's behavior at '$X$' (F-type $X$-parameters $X^F_{mk}(\cdot)$ functioning). What is more, they are also able to account for a certain area of load mismatch around '$X$' as the shadowed area ($S$- and $T$-type $X$-parameters $X^S_{mk, nl}(\cdot)$ and $X^T_{mk, nl}(\cdot)$ functioning). The size of the shadowed area depends mainly on the measurement settings (e.g., power of $a_{nl}$) and the DUT's sensitivity to load mismatch from '$X$' (e.g., in terms of changes in power and efficiency).

    The property of $X$-parameters described above becomes more interesting when considering the load tuning at harmonics. Assume that a fundamental-only load-pull system is used to characterize a transistor utilizing $X$-parameters. In the measurement, the fundamental load can be tuned as desired (e.g., as in Figure 1). However, the harmonic loads are falling to some uncontrolled positions on the Smith chart. These uncontrolled positions depend mainly on the operating frequency, fundamental load tuning positions and mechanics of the passive tuner (more details are described later in the text). If the DUT is very insensitive to the changes in the harmonic loads, the extracted $S/T$-type $X$-parameters at harmonics may account for the impedance mismatch over the entire Smith chart from those uncontrolled positions. It means that the DUT can still be comprehensively characterized (at both fundamental and harmonics) even using a fundamental-only load-pull system. In this way, the measurement setup for device characterization can be significantly simplified. Following this concept, this work conducts $X$-parameter measurement and characterization on a commercial GaN HEMT device. Based on the simulations on the extracted $X$-parameter model, the possibility in reducing the complexity of the load-pull setup is explored for this device.

3.   Device characterization
  • The DUT is a Cree CGH40010F 10 W RF GaN HEMT power transistor suitable for applications up to 6 GHz. The typical output power, power gain and drain efficiency of the device are rated at 12.5 W, 14.5 dB and 65 %, respectively[18]. Figure 2 shows the simplified block diagram describing the measurement setup to characterize the transistor under test and extract the load dependent $X$-parameters of it.

    As the core of the measurement setup, an Agilent PNA-X Microwave Network Analyzer is configured to nonlinear vector network analyzer (NVNA) mode to enable large-signal and $X$-parameter measurement. It controls all the hardware involved in this measurement setup (through GPIB/LAN) as well as the entire $X$-parameter measurement and extraction process. Two comb generators are used in cooperation with the PNA-X to provide accurate phase references (for fundamental as well as harmonics) for cross-frequency phase calibration and $X$-parameter measurement, respectively. During the measurement, the transistor is biased in deep class-AB operation mode by two DC power analyzers. To facilitate accurate efficiency measurement, the drain current is sensed by a current probe and measured by a digital multimeter. Passive impedance tuners from Maury Microwave are set and controlled by the Automated Test System (ATS) installed directly on the PNA-X/NVNA platform.

    The standard of PNA-X port power is typically rated at 30 dBm, but the maximum output power of the transistor under test is about 43 dBm. To satisfy the DUT's power requirement as well as protect the hardware, a high-power test set is employed, as illustrated in the shadowed area in Figure 2, and two broadband linear pre-amplifiers are used in the measurement. In order to meet the linearity requirement of PNA-X internal receivers (i.e., R1, A, R3 and C in Figure 3) and guarantee high measurement reliability, it requires that the power at the inputs of the PNA-X internal receivers should not exceed $-20$ dBm at peak value[19]. Based on this reliability requirement as well as the DUT's power specification, the PNA-X power budget can be figured out, which is illustrated in Figure 3. Parameter extraction tones (represented as ET in Figure 3) 20 dBm below the fundamental tones at the source port of the PNA-X (Port 1 in Figure 3) are assumed in the calculation.

    The transistor under test is biased in deep class-AB operation mode during the measurement: the gate and drain terminals are biased at $-3.1$ and 28 V, respectively. The measurement is performed under pulsed continuous wave (CW) condition and the operating frequency of the device is at 2.1 GHz. The mechanical tuner sweeps the fundamental load impedance within a selected area in the Smith chart such that the reflection coefficient at the fundamental frequency moves in a way as shown in Figure 4. The real and imaginary part of the reflection coefficient are swept from $-0.5$ to $-0.2$ and from 0.2 to 0.5 in steps of 0.1, respectively. $X$-parameters of the device are extracted up to the third-order harmonic with well controlled fundamental load tuning (as shown in Figure 4) and uncontrolled load impedance at the second and third-order harmonics, as mentioned previously. The extracted $X$-parameters are then imported into ADS and fitted to the poly-harmonic distortion model (namely, the XnP component) for further simulations and validation.

4.   $\boldsymbol{X}$-parameter model validation
  • The objective of validating the extracted $X$-parameter model is to investigate the potential of $X$-parameters in reducing the measurement complexity (by avoiding harmonic load tuners) in transistor characterization. In particular, for the DUT in this work, the load impedance is tuned as desired only at the fundamental, albeit the goal is to characterize the device with load tuning up to the third-order harmonic. From this perspective, the emphasis of the validation will be put on trying to prove that the extracted $X$-parameter model, which is based on fundamental-only load-pull characterization, is still able to accurately predict the behavior of the device under load tuning up to the third-order harmonic.

  • 4.1.   Load impedance settings

  • Before going to the validation, it is worthwhile to look deeply into the load impedance settings of the device during the characterization and $X$-parameter measurement. These impedance settings are those at which the $X$-parameters of the device are extracted. Except for the (controlled) tuning positions of the fundamental load, Figure 4 also plots the positions of the uncontrolled second and third-order harmonic load. For a passive tuner, the reflection coefficient (impedance) is determined by the position of the slug (deciding the magnitude) relative to the tuner slabline (deciding the phase). The slug is typically broadband so that the reflection magnitude does not change much from fundamental to the (second and third-order) harmonics. However, the reflection phase will rotate along the slabline at the harmonics. In other words, the uncontrolled harmonic loads are actually somehow related to the fundamental load, given a certain operating frequency and a particular passive tuner. This mechanism is clearly interpreted in Figure 4. In particular, the figure highlights one of the fundamental load tuning points and the corresponding uncontrolled positions of the harmonic loads, as illustrated by the three circles with a cross (namely, the No. 1 load tuning position as marked in Figure 4).

  • 4.2.   Validation of the effect of $\boldsymbol{S/T}$-type $\boldsymbol{X}$-parameters

  • Figure 5 shows one of the examples of the validation results. In this measurement, the fundamental load is fixed at one of the tuning positions that are used in the device characterization and $X$-parameter measurement (as marked by the black cross in Figure 5). The load at the second-order harmonic is fixed at the position which is corresponding to the load used for the fundamental (as marked by the blue cross in Figure 5). The load at the third-order harmonic is set in such a way that the load reflection coefficient ($\Gamma_3$) moves around on the edge of the Smith chart, as illustrated by the red crosses in Figure 5(a). Measurement and simulation are performed on the real device and the extracted $X$-parameter model of the device using the same load condition described above. The available input power (Pavs) is 30 dBm. The measured and simulated power delivered to the load (Pdel) and power-added-efficiency (PAE) versus the phase of $\Gamma_3$ are compared in Figure 5(b). It can be seen that the simulated Pdel and PAE curves track the measurement very well and the maximum difference between the simulation and measurement is about 0.6 dB and 1.8 %-point for Pdel and PAE, respectively. Remember that during the device characterization and $X$-parameter measurement, the load at the second and third-order harmonics are left uncontrolled (but dependent on the fundamental load). Specifically for the third-order harmonic, if the fundamental load is at the black cross, the corresponding load at the third-order harmonic will be at a specific position as marked by the gray cross in Figure 5(a). From this perspective, the result shown in Figure 5 indicates that the extracted $X$-parameter model of the device is able to accurately predict the behavior of the real device under load tuning at the third-order harmonic, even though those load tuning positions (even at the edge of the Smith chart) are not used during $X$-parameter model extraction. This in turn validates the effect of the $S$- and $T$-type $X$-parameters (of the third-order harmonic) discussed before. Figure 6 shows another example of the validation result using a similar method, where another set of load at the fundamental and second-order harmonic is used, and Pavs is equal to 19 dBm instead. Good match between the measurement and simulation can be observed again. The maximum difference between the measured and simulated Pdel and PAE is about 0.3 dB and 1.2 %-point, respectively. Measurements and simulations using other fundamental load positions give similar matching in the results.

    Figure 5 and 6 validate the effect of the $S$- and $T$-type $X$-parameters at the third-order harmonic. A similar validation can also be conducted for the second-order harmonic. Examples of the validation results are shown in Figure 7 and 8. In these measurements and simulations, loads at the fundamental and third-order harmonic are fixed at certain load tuning positions that are used in the device characterization and $X$-parameter measurement, while the load at the second-order harmonic is swept such that $\Gamma_2$ moves around on the edge of the Smith chart. Pavs is equal to 23 and 14 dBm for Figure 7 and 8, respectively. Good matching between the measurements and simulations is achieved again. The corresponding measured and simulated curves have similar shapes. The maximum difference between the measured and simulated Pdel and PAE are about 0.6 dB and 1.9 %-point for Figure 7, and 0.1 dB and 1.0 %-point for Figure 8, respectively.

    The validation results shown in Figure 5-8 consider sweeping the phase of either $\Gamma_3$ or $\Gamma_2$. Can the similar good matching also be achieved if the magnitude of $\Gamma_3$ or $\Gamma_2$ is swept? The answer to this question may in fact be found from the results illustrated in Figure 5-8. In these figures, the magnitude of $\Gamma_3$ or $\Gamma_2$ is fixed on the edge of the Smith chart, namely, 1. Under this extreme condition of the magnitude of $\Gamma_3$ or $\Gamma_2$, good matching is already achieved. It can be imagined that the matching will certainly become better when the magnitude of $\Gamma_3$ or $\Gamma_2$ is fixed to another value that is less than 1. To verify this rough conclusion, Figure 9(b) plots the validation result when the magnitude of $\Gamma_2$ is swept from 0 to 1, as illustrated in Figure 9(a). The load setting for the fundamental and third-order harmonic, and the input power setting are the same as those in Figure 7. The phase of $\Gamma_2$ is fixed to be at 210$^\circ$. As expected, the matching becomes better as the magnitude decreases from 1 (namely, moves from the edge to the center of the Smith chart).

    Figure 5-8 show some examples of the validation results. In those figures, the simulations based on the extracted $X$-parameter model of the device can track the experimental measurements on the real device with reasonable accuracy. To have an overall picture on the modeling accuracy of the extracted $X$-parameter model of the device in terms of validating the effect of the $S$- and $T$-type $X$-parameters, Figures 10 and 11 plot the maximum difference between the measured and simulated Pdel and PAE as a function of Pavs and the No. of the (fundamental) load tuning positions (i.e., No. 1-16 as illustrated in Figure 4) in 3D style. The harmonic load is swept in the same ways as in Figure 5 and 6, and Figure 7 and 8, respectively. Available input power Pavs is swept from 10 to 33 dBm in steps of 1 dB. From Figure 10, it can be seen that the maximum differences between the measured and simulated Pdel and PAE are lower than 1.2 dB and 2.2 %-point respectively, over the entire tuning area of the fundamental load and whole sweeping range of Pavs. For those measurements and simulations, $\Gamma_3$ is swept on and around the edge of the Smith chart while the loads at the fundamental and second-order harmonic are fixed at the tuning positions used in the transistor characterization and $X$-parameters extraction. Similarly, from Figure 11, it is seen that the maximum differences between the measured and simulated Pdel and PAE are lower than 1.4 dB and 5.5 %-point respectively, while $\Gamma_2$ is swept around the edge of the Smith chart instead.

    From the figures, it can be observed that the maximum difference occurs at high Pavs (i.e., 33 dBm) used in the measurements and simulations. This is because the device is driven hard into saturation with those high Pavs so that it shows strong nonlinearities and its performance becomes quite sensitive to the changes in load. Take the results in Figure 11 as an example. In the $X$-parameter model simulations, the second-order harmonic load is swept at the positions that are far away from those used in the device characterization and $X$-parameter model extraction (recall Figure 4). With low Pavs, the device behaves linearly and is relatively insensitive to the changes in load. Attributed to the extracted $S$- and $T$-type $X$-parameters of the second-order harmonic with low Pavs, the $X$-parameter model can still predict the behavior of the real device under this large load mismatch with appreciable accuracy (i.e., with Pavs lower than 15 dBm, the difference in Pdel and PAE is lower than 0.4 dB and 1.0 %-point, respectively). On the other hand, when saturated, the device becomes sensitive to load mismatch and the modeling accuracy of the extracted $X$-parameter model is deteriorated (i.e., with highest Pavs, the difference in Pdel and PAE reaches about 1.4 dB and 5.3 %-point, respectively). In other words, the extracted $S$- and $T$-type $X$-parameters of the second-order harmonic under high Pavs cannot completely account for such large load mismatch from the load positions used in the model extraction. Constant extrapolation is used for the model to produce part of the simulation results.

  • 4.3.   More discussion and results

  • Comparing Figure 10 and Figure 11, it can be observed that the difference between the measurement and simulation in Figure 11 is generally larger than that in Figure 10, especially for PAE. It means the extracted $S$- and $T$-type $X$-parameters at the second-order harmonic can account for a smaller load mismatch area (from those loads used in the $X$-parameter extraction) than the case of the third-order harmonic. Recalling the description of $S$- and $T$-type $X$-parameters in Section~2, this observation can be explained. As described, the $S$- and $T$-type $X$-parameters are extracted based on the injection of parameter extraction tones $a_{nl}$ to the ports of the DUT during the $X$-parameter measurement. This kind of tone injection is similar to active load-pulling around the LSOPs. How much area of load mismatch from the LSOPs can the $S$- and $T$-type $X$-parameters account for? Represented by the magnitude of the reflection coefficient related to the LSOPs, the area can be approximated by following equations:
    \begin{align} |\Gamma|_{{\rm mismatch}, i}=\sqrt{10^{\frac{P_{{\rm ET}, i}-P_{{\rm OUT}, i}}{10}}}, \label{eq:2} \end{align}(1)
    where $i$ is the harmonic index (i.e., equals to 2 and 3 in this work), $P_{{\rm ET}, i}$ and $P_{{\rm OUT}, i}$ represent the power of parameter extraction tone injected at the load $a_{2i}$ and output power of the DUT at the $i^{\rm th}$-order harmonic under the LSOPs, respectively. During the $X$-parameter measurement in the work, $P_{{\rm ET}, i}$ is set always as 20 dB lower than the output power at the fundamental frequency $P_{\rm OUT, Fund.}$. Equation~(2) indicates that the higher $P_{{\rm OUT}, i}$ is, the lower $|\Gamma_{{\rm mismatch}, i}|$ is (in other words, the area of load mismatch that the $S$- and $T$-type $X$-parameters can account for is smaller). Figure 12 plots the measured output power of the DUT at the fundamental, second and third-order harmonics versus Pavs under one of the load settings shown in Figure 4. It can be seen when Pavs is low to medium (linear region), $P_{\rm OUT, 3}$ is always 34 dB lower than $P_{\rm OUT, Fund.}$. When the device is saturated, the difference between $P_{\rm OUT, 3}$ and $P_{\rm OUT, Fund.}$ is smaller than 20 dB. For the case of the second-order harmonic, the situation is similar. However, $P_{\rm OUT, 2}$ is generally always larger than $P_{\rm OUT, 3}$ in the whole range of Pavs. Another observation is that the difference between the output power at harmonics and fundamental becomes smaller and smaller as Pavs swept from low to high. Applying the information contained in Figure 12 to Equation~(2), it can be explained why the modeling accuracy and capability of the $S$- and $T$-type $X$-parameters at the second-order harmonic is lower than those at the third-order harmonic, as observed from Figure 10 and Figure 11.

    Above text shows and discusses the validation results at only one frequency (2.1 GHz). The validity of the concept also needs to be investigated at other operating frequencies. Similar to Figures 10 and Figures 10, 11-16 plot the overall accuracy of the extracted $X$-parameter models of the device at 1.8 and 2.7 GHz, respectively. The method used in analyzing and plotting the results is the same as that used in the discussion above. From Figures 13-16, it can be seen that the modeling accuracy of the $X$-parameter models of the device extracted at 1.8 and 2.7 GHz is also acceptable. At 1.8 GHz, the maximum differences between the measured and simulated Pdel and PAE are lower than 0.8 dB and 1.5 %-point, and 1.0 dB and 2.3 %-point, while $\Gamma_3$ and $\Gamma_2$ is swept around the edge of the Smith chart, respectively, as illustrated in Figures 13 and 14. At 2.7 GHz, the corresponding numbers become 1.4 dB and 2.7 %-point, and 1.9 dB and 6.9 %-point, respectively, as shown in Figures 15 and 16.

  • 4.4.   Model validation summary

  • Based on the results presented above, some preliminary conclusions can be drawn. The transistor under test is characterized by using a fundamental-only load-pull measurement, where only the fundamental load is controlled and tuned while other harmonic loads are left uncontrolled. Based on this kind of measurement, an $X$-parameter model is extracted for the DUT. Model validation results show that the extracted $X$-parameter model can still predict the behavior of the real device under load tuning at the third-order harmonic over the entire Smith chart with good enough accuracy in terms of Pdel and PAE. It indicates that by utilizing the $X$-parameter technique, the load tuner for the third-order harmonic can be avoided in the load-pull test setup in order to characterize the DUT under load tuning up to the third-order harmonic. Similarly, the results presented also reveal the potential of avoiding the load tuner for the second-order harmonic. Compared to the case of the third-order harmonic, the extracted $X$-parameter model characterizes the behavior of the real device under load tuning at the second-order harmonic over the entire Smith chart with lower accuracy, especially when the device is driven hard into saturation. However, for those applications where the transistor is expected to be operating only in its linear region, the modeling accuracy of the $X$-parameter model is still appreciable and the tuner for the second-order harmonic may also be avoided. Avoidance of the harmonic load tuners can significantly simplify the load-pull test setup for transistor characterization and dramatically improve the overall measurement throughput.

5.   Possibility of further optimization
  • Previous analysis has focused mainly on discussing the possibility of avoiding harmonic load tuners in the load-pull measurement setup by utilizing the $S$- and $T$-type $X$-parameters at harmonics. From another angle, it is still possible to further optimize the measurement setup by reducing the number of fundamental load tuning points utilizing $X$-parameters. The magic is again the usefulness of the $S$- and $T$-type $X$-parameters, but at the fundamental.

    As the cases of the second and third-order harmonics, $S$- and $T$-type $X$-parameters are also extracted for the fundamental frequency. At each fundamental load tuning point, the extracted $X$-parameters are capable of characterizing the behavior of the device not only at the exact tuning point, but also under load mismatch over the point to some extent. The situation is illustrated in Figure 17. Fundamental load tuning point No.1 is considered (recall Figure 4). To figure out approximately how much load mismatch over point No. 1 the $X$-parameters can account for, the following measurements and simulations can be conducted step by step:

    (1) Create an $X$-parameter model of the DUT with only a fixed fundamental load impedance at point No. 1.

    (2) Perform fundamental load-pull measurements and simulations on the real device and created $X$-parameter model, where the load is tuned in the vicinity of point No. 1, i.e., a circular area with point No. 1 as the center.

    (3) Compare the measurement and simulation results, i.e., Pdel and PAE. If they are identical, increase the load tuning area in step 2, i.e., increase the radius of the circular area.

    (4) Repeat steps 2 and 3, until the difference between the measurement and simulation is to the edge of the acceptable levels, i.e., assuming that the maximum acceptable difference between the measured and simulated Pdel and PAE is 0.5 dBm and 0.5 %-point, respectively.

    (5) The final load tuning area used in step 4 is the approximate load mismatch area that the created $X$-parameter model can account for at load tuning point No. 1.

    Following the procedure, the rough load mismatch area that $X$-parameters can account for is plotted as a shadowed circular for the load tuning point No. 1, as shown in Figure 17. It can be observed that the load tuning points Nos. 2 and 5 (recall Figure 4) both fall in the shadowed area. It can be preliminarily concluded that fundamental load tuning points Nos. 2 and 5 may probably be removed during the device characterization and $X$-parameter measurement, while the accuracy of the characterization keeps at the same level as in the case where they are included. Reduction in the number of fundamental load tuning points means that a relatively higher measurement throughput can be achieved. In other words, the characterization time is decreased while the same amount of useful information of the DUT's behavior under load mismatch can be obtained. This obviously further decreases the complexity and hardware cost of the load-pull measurement setup. The concept is only preliminarily tested for the load tuning point No. 1 in this work. Similar measurements and simulations can be conducted for other tuning points to have an overall picture of the issue.

6.   Conclusion
  • This paper presents $X$-parameter-based characterization of a GaN HEMT device and studies the potential of the $X$-parameter-based modeling technique in decreasing the complexity of the load-pull measurement setup. A load-dependent $X$-parameter model of the device is created based on fundamental-only load-pull measurement on the device, where only the fundamental load is controlled and tuned at the desired positions while other harmonic loads are left uncontrolled. By comparing measurements and simulations, it is validated that the created $X$-parameter model is still able to predict the behavior of the device under the second and third-order harmonic load tuning over the entire Smith chart with reasonable accuracy. The validated modeling accuracy indicates the potential of avoiding harmonic load tuners in the load-pull test setup to characterize the transistor under study, by utilizing the $X$-parameter technique. What is more, the paper also discusses the potential of $X$-parameters in decreasing the number of fundamental load tuning points, which pulls up the measurement throughput and reduces the complexity of the test setup furthermore. Since all the measurements and simulations presented are conducted on the specific transistor studied in this work, for another device, one may end up with different conclusions. However, regarding the concept forwarded in this paper, one can still see its generality and value in the research topic.

    Acknowledgment The author would also like to thank Agilent Technologies for the instrument support.

Figure (17)  Table (2) Reference (19) Relative (20)

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