Jan Verspecht bvba Gertrudeveld 15 1840 Steenhuffel Belgium email:
[email protected] web: http://www.janverspecht.com
Easy and Accurate Empirical Transistor Model Parameter Estimation from Vectorial Large-Signal Measurements
D. Schreurs, J. Verspecht, S. Vandenberghe, G. Carchon. K. van der Zanden, B. Nauwelaers
Presented at the IEEE Microwave Theory and Techniques Symposium 1999
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EASY AND ACCURATE EMPIRICAL TRANSISTOR MODEL PARAMETER ESTIMATION FROM VECTORIAL LARGE-SIGNAL MEASUREMENTS D. Schreurs, J. Verspecht , S. Vandenberghe, G. Carchon, K. van der Zanden, and B. Nauwelaers K.U.Leuven, div. ESAT-TELEMIC, Kard. Mercierlaan 94, B-3001 Heverlee, Belgium HP-NMDG, VUB-ELEC, Pleinlaan 2, B-1050 Brussel, Belgium IMEC, Div. MCP/NMC, Kapeldreef 75, B-3001 Heverlee, Belgium ABSTRACT The standard empirical non-linear model parameter estimation is often cumbersome as several measurement systems are involved. We show that the model generation complexity can be reduced tremendously by only using full two-port vectorial large-signal measurements. Furthermore realistic operating conditions can easily be included in the optimisation procedure, as we illustrate on GaAs PHEMTs.
NON-LINEAR MODEL PARAMETER ESTIMATION PROCEDURE The non-linear models of microwave and millimetre wave devices are commonly described in terms of state-functions. The non-linear quasistatic model of a HEMT, represented in Figure 1, consists of four state-functions, namely a charge and current source at both gate-source and drainsource terminals. The quasi-static assumption is valid for the frequencies used in the experiments presented in the next Section.
INTRODUCTION In recent years, the development of different vectorial large-signal prototype measurement systems, e.g., [1,2,3], has world-wide initiated researchers to investigate the implications of the additional measurement information on the ease and accuracy of non-linear model extraction. In general, we can distinguish two main approaches. The first category studies methods to efficiently extract the device’s non-linear state-functions directly from these measurements [4]. The goal of the second category is to utilise the vectorial large-signal measurements to enhance the existing non-linear models. In this work, we focus to the second approach and present an easy but accurate procedure to estimate the parameters of empirical functions representing the device’s state-functions. We will first outline the procedure and subsequently illustrate its properties by experimental HEMT results.
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Figure 1: Intrinsic quasi-static non-linear model of a HEMT.
These state-functions can be represented by look-up tables or by empirical functions. The latter is often preferred by foundries, since the data to be transfered to the customer is only a limited number of model parameters. The classic procedure to determine these parameters is to optimise the empirical functions towards the DC measured state-functions, e.g., Ids , and/or the S-parameter measurement based state-functions, e.g., Cgs or the corresponding large-signal Qgs . An extension proposed by Bandler et al. [5] is the consis-
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tent optimisation towards all available measurements, such as DC, multi-bias S -parameter and large-signal magnitude spectral data. An obvious way to incorporate the additional phase information of vectorial large-signal measurements could be to add the measured phase of the spectral components of the terminal currents and voltages to the optimisation procedure. The drawback is that special optimisation software is required to ensure the consistency, because this method is not straightforwardly implementable in standard available microwave circuit simulators, like e.g., HP MDS. The reason is that it is not possible to optimise simultaneously towards DC, Sparameter and harmonic-balance simulations. We have elaborated a non-linear model parameter estimation procedure based on only vectorial large-signal measurements. These measurements return both the amplitude and the phase values of the spectral components of the travelling voltage waves and hence contain all the necessary information. Therefore, we can conclude that it is sufficient to fit the model parameters towards only vectorial large-signal measurements. The advantage of our approach is that only one type of measurements, i.e., vectorial large-signal measurements, and only one type of simulation, i.e., harmonic-balance analysis, are needed. It is even possible to include “DC” or “S-parameter”-like information, by choosing the appropriate operating conditions, e.g., low input power, when performing the vectorial large-signal measurements. We have developed this procedure on the Nonlinear Network Measurement System (NNMS) [3] linked to HP MDS. The advantage of the NNMS compared to Microwave Transition Analyzer (MTA) based results [2] is the enhanced phase calibration and the straightforward way to measure simultaneously the instantaneous currents and voltages at both device ports. The latter implies that the empirical expressions for all the charge and current source state-functions can be optimised at once.
The first step of the procedure is to perform a number of NNMS measurements, called “experiments”. It is possible to sweep any degree of freedom, like input power, excitation frequency, DC bias, load impedance, . . . but, as we will discuss in the next Section, one could focus on particular experiments depending on the application. The program that controls the instruments according to the different experiment definitions has been written in Mathematica. The measurement data are stored in Citifile format, which is compatible with MDS. To allow any kind of excitation settings, we take as independent variables the experiment number and the frequencies. We however save explicitly the excitation data in order to perform automatically the harmonic-balance simulations at exactly the operating conditions at which the vectorial large-signal measurements were performed. Subsequently, the parameters of the empirical non-linear model are estimated during one optimisation process in which all the experiments are combined. The optimisation goals are expressed in terms of minimising the difference between the measured and simulated spectral components where we consider all the significant harmonics and, if present, intermodulation products. We have implemented this estimation process in MDS by making use of the built-in optimisation tools. A benefit of this proposed parameter estimation procedure is to have direct information about the non-linear behaviour of the intrinsic capacitors, as the detour via small-signal measurements and extractions in the classical approach complicates the procedure and may hence introduce additional errors. The proposed procedure is also advantageous for the often limited capability of an empirical function. The choice of a particular empirical expression is often a compromise between simplicity and accuracy. Therefore the empirical non-linear model often reaches the necessary accuracy only at some bias points, while the fit is worse in the
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EXPERIMENTAL RESULTS To demonstrate the developed parameter estimation procedure, we present the results of the empirical Chalmers model applied to a 0.2 m gatelength and 100 m gatewidth GaAs pseudomorphic HEMT (PHEMT). The empirical expression for the drain-source current Ids is based on [6] and the expressions for the intrinsic biasdependent capacitances are taken from [7]. The device is operated in class B while the input power is swept between -20.4 dBm and -3.4 dBm. All the model parameters are simultaneously optimised towards these vectorial large-signal measurements. Figure 2 compares on the top graph the measured and simulated time domain waveform of the gate-source current Igs (t) as a function of the time domain waveform of the gatesource voltage Vgs (t) and on the bottom graph the measured and simulated Ids (t) time domain waveform as a function of the Vgs (t) time domain waveform at a high input power. This Figure clearly indicates a very good agreement and hence high model accuracy.
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other bias regions. In this case, it is difficult for the user to know which bias points should be accurately modelled for a particular largesignal application. For most applications, the class of operation (A, AB, . . . ) and hence the DC bias is known, but there is less knowledge about the instantaneous terminal voltages that could be reached during operation and precisely at these values the non-linear model should be accurate. Therefore we propose to perform vectorial largesignal measurements at that class of operation, so that the empirical non-linear model can directly be optimised at the terminal voltages that are typical for that particular operating condition. This procedure will be illustrated on GaAs PHEMTs in the next Section. It is however important to note that the proposed method is general in the sense that it can be applied to any empirical non-linear transistor model.
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Figure 2: Measured (x) and simulated ( ) Igs (t) versus Vgs(t) (top) and Ids (t) versus Vgs (t) (bottom) of a GaAs PHEMT (VgsDC = -0.5 V, VdsDC = 1.5 V, f0 = 3.6 GHz, Pin = -3.4 dBm).
The important advantage of this new approach is the ease of the model parameter estimation as only one measurement system, the NNMS, and only one simulator with an optimiser, MDS, are involved. Furthermore, realistic operating conditions can easily be included in the optimisation procedure. An illustration are loadpull measurements. These are seldom added to the optimisation process in the classical approach due to the need of complex hardware like e.g., a VNA extended with a loadpull system. It is however convenient to perform active or passive fundamental loadpull measurements on the NNMS as this measurement system allows the injection of an incident a2 travelling voltage wave. Figure 3 shows the measured Ids (t) as a function of Vgs (t) at a certain load ,L . This measurement
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is compared on the top graph with the simulated Ids (t) when using a model that was only optimised towards NNMS measurements in a 50
load. The bottom graph shows the improvement in model accuracy when several loadpull experiments are added to the optimisation procedure. 25
ACKNOWLEDGEMENTS The authors acknowledge Hewlett-Packard for the donation of the Nonlinear Network Measurement System. This work was supported by ESA, IWT and the Belgian program on interuniversity attraction poles (IUAP-IV/2). D. Schreurs is supported by the Fund for Scientific ResearchVlaanderen as a post-doctoral researcher.
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[1] F. van Raay and G. Kompa, “A New On-Wafer Large-Signal Waveform Measurement System with 40 GHz Harmonic Bandwidth”, in IEEE MTT-S Int. Microwave Symp. Digest, 1992, pp. 1435–1438. [2] J. Leckey, J. Stewart, A. Patterson, and M. Kelly, “Nonlinear MESFET Parameter Estimation using Harmonic Amplitude and Phase Measurements”, in IEEE MTT-S Int. Microwave Symp. Digest, 1994, pp. 1563–1566. [3] J. Verspecht, P. Debie, A. Barel, and L. Martens, “Accurate On Wafer Measurement Of Phase And Amplitude Of The Spectral Components Of Incident And Scattered Voltage Waves At The Signal Ports Of A Nonlinear Microwave Device”, in IEEE MTT-S Int. Microwave Symp. Digest, 1995, pp. 1029–1032. [4] D. Schreurs, “Extraction of non-linear device models from large-signal waveform measurements”, in IEEE MTT-S Workshop: New Developments in Time Domain Methods for Non-linear Design, June 1998, pp. 28–52. [5] J. Bandler, Q. Zhang, S. Ye, and S. Chen, “Efficient Large-Signal FET Parameter Extraction Using Harmonics”, IEEE Trans. Microwave Theory Techn., vol. 37, no. 12, pp. 2099–2108, 1989. [6] I. Angelov, H. Zirath, and N. Rorsman, “Validation of a Nonlinear Transistor Model by Power Spectrum Characteristics of HEMT’s and MESFET’s”, IEEE Trans. Microwave Theory Techn., vol. 43, no. 5, pp. 1046–1052, 1995. [7] I. Angelov, H. Zirath, and N. Rorsman, “A New Empirical Nonlinear Model for HEMT and MESFET Devices”, IEEE Trans. Microwave Theory Techn., vol. 40, no. 12, pp. 2258–2266, 1992.
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Figure 3: Measured (x) and simulated ( ) Ids (t) without (top) and with (bottom) including loadpull measurement information in the optimisation versus Vgs (t) of a GaAs PHEMT (VgsDC = -0.5 V, VdsDC = 1.5 V, f0 = 3.6 GHz, Pin = -3.9 dBm, ,L = 0.26 6 62).
CONCLUSIONS We have shown that only full two-port vectorial large-signal measurements are sufficient to estimate accurately the parameters of empirical non-linear transistor models. The developed quasi-automatic procedure has been successfully demonstrated on GaAs PHEMTs.
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