Identification technique of FET model based on vector nonlinear measurements G. Avolio, D. Schreurs, A. Raffo, G. Crupi, I. Angelov, G. Vannini and B. Nauwelaers A new modelling approach which exploits only vector nonlinear measurements is described. The parameters of the I-V and Q-V non- linear constitutive functions are identified by combining low- and high-frequency large-signal measurements with a numerical optimis- ation routine. Low-frequency dispersion manifesting in the I-V charac- teristics is also correctly accounted for. As a case study a gallium nitride HEMT on silicon carbide substrate is considered and very good agreement between measurements and simulation is achieved. Introduction: Nonlinear models for active devices are essential for the accurate prediction of the performance of high-frequency circuits, such as power amplifiers. The latter constitutes one of the most critical blocks in the transceiver chain since high power is required in the micro- wave frequency range while preserving power efficiency. To satisfy power requirements, new semiconductor technologies have been inves- tigated in the last decades and, particularly, wideband gap materials such as gallium nitride (GaN) constitute the most suitable candidates in the high-power and high-frequency applications arena. In parallel, the vector calibrated nonlinear measurement system has been developed in the last decade, thus allowing one to identify nonlinear models from experiments under realistic operating conditions. With reference to a field effect transistor (FET) circuit topology (see Fig. 1), measurement based techniques can be exploited to identify the linear and nonlinear parts of the network in Fig. 1. For instance, multi-bias scattering (S-) parameter measurements are widely employed to derive nonlinear models [1, 2]. Nevertheless this approach, which is accurate for the determination of the parasitic elements and the nonlinear charge sources, yields inaccurate results when low-frequency (LF) dispersion is significant [3]. LF dispersion, which is originated by the presence of defects in the materials and thermal effects, mainly affects the non- linear behaviour of the drain-source current generator [4]. To properly account for LF dispersion, either pulsed I-V measurements or low-fre- quency vector nonlinear measurements [4] constitute valid techniques to characterise and model the nonlinear current source. In [5, 6], high- frequency nonlinear measurements are exploited to identify both the I-V and Q-V nonlinear functions. However, the procedures in [5, 6] do not account for LF dispersion. V G C p1 C p2 V GS R G L G L D L S R S I D R D V D V DS C DS I DS I G Q GD Q GS Fig. 1 High-frequency nonlinear model of FET in common source configuration At low frequencies circuit simplifies to drain-source current generator and drain and source parasitic resistances In this Letter, the parameters for both the I-V and Q-V nonlinear func- tions are derived by vector nonlinear measurements along with a numerical optimisation routine and a harmonic balance (HB) solver. Compared to other approaches [5, 6], low-frequency vector nonlinear measurements are exploited in combination with high-frequency non- linear measurements and, also, the value of the parasitic elements is optimised. Specifically, the values of R S and R D are optimised within the LF optimisation, whereas R G and the reactive parasitics are opti- mised within the HF optimisation. This way, we can benefit from the proper selection of the frequency range to provide larger influence and sensitivity of the parasitic elements and accuracy of the model fit. Model identification: The proposed approach exploits two sets of vector large-signal measurements performed with an enhanced large-signal network analyser which enables vector calibrated nonlinear measure- ments in the 10 kHz – 24 MHz and 600 MHz – 50 GHz bandwidths [7]. Load-pull experiments were performed at a fixed bias point, V GS0 ¼ 22 V and V DS0 ¼ 20 V (class-A operation), and at two different fre- quencies, 2 MHz and 4 GHz. The low frequency value is properly chosen above the cutoff frequency of the LF dispersion, as experimen- tally investigated in [4]. Such an approximation, which is valid for the considered case, has to be verified depending on the device under test. In fact, traps and thermal dynamics might manifest time constants over a broader frequency range. The high frequency value is selected to be sufficiently high to boost the contribution of the charge sources and low enough to neglect non-quasi-static (NQS) effects which, never- theless, could be straightforwardly included in the model. Under these assumptions, numerical optimisation is performed to determine the par- ameters of the nonlinear I-V and Q-V functions which are described in this Letter by Angelov’s semi-empirical nonlinear expressions, which account also for thermal dependence [8]: I ds = IPK0 * (1 + tanh(c)) * tanh(a * V ds ) * (1 + l * V ds ) (1) c = P1 * (V gs - V pkm )+ P2 * (V gs - V pkm ) 2 + P3 * (V gs - V pkm ) 3 (2) a = a R + a * S (1 + tanh(c)) (3) Q gs = CGSPI * V gs + CGS0 * ((phi1 + Lc1 - QGS0) *(1 - tanh(phi2))/P11) (4) where l accounts for the slope of the output characteristics in the satur- ation region, IPK0 and V pkm are the current and the voltage at the maximum transconductance, a R and a S define the slope in the linear region, and P1, P2, P3 are fitting parameters. Regarding the charge source, CGSPI and CGS0 are the values of the gate-source capacitance, P11 is a fitting coefficient, and phi1, phi2, Lc1, QGS0 are nonlinear functions of the intrinsic voltages. A similar expression as (2) can be written for the Q gd source. The expressions in (1)–(4) are purely algebraic which is consistent with the frequency independence of both current and charge sources. Additionally, the current source parameters in (1)–(3) strongly depend on the quiescent condition which actually determines the electrical state of the traps. Differently, the parameters of the nonlinear charge sources are assumed dispersionless, which is a reasonable approxi- mation in many practical cases [4]. Consequently, when the quiescent point is changed, current source parameters have to be extracted for the new quiescent operating condition. Nevertheless, the design of power amplifiers is commonly carried out at a fixed bias condition and, thus, the technique presented in this Letter is suitable for this case. In light of these considerations, the numerical optimisation is per- formed in two steps. First, the current source parameters are estimated by simplifying the circuit into only the current source and the drain and source resistive parasitic elements, and by exploiting the LF measure- ments set. Next, optimisation of the complete circuit is performed fixing the known parasitics and current source parameters. After this step, the parameters of the charge sources, the value of the constant drain-source capacitance, and of the remaining parasitics are obtained by exploiting the HF measurements set. Model validation: The simulation of the LF and HF equivalent circuits, after the optimisation routines, is compared with the measurements in Figs 2 and 3. Good agreement is observed, confirming that the adopted nonlinear functions can predict the experiments under different loading and power condtions with a small number of model parameters. Additionally, the extracted model is validated with another set of non- linear measurements performed at 2 GHz and with the bias point fixed to V GS0 ¼ 22 V and V DS0 ¼ 20 V. The input power is swept and the output is terminated with 50 V. The comparison between the model prediction and experiments is illustrated in Fig. 4 where the output power at the fundamental and the harmonic frequencies is shown. Good agreement is achieved also in this case, thus proving the validity of the proposed model extraction procedure. ELECTRONICS LETTERS 24th November 2011 Vol. 47 No. 24