IMPROVED MESFET CHARACTERISATION FOR ANALOG CIRCUIT DESIGN AND ANKYSIS

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2 IMPROVED MESFET CHARACTERISATION FOR ANALOG CIRCUIT DESIGN AND ANKYSIS Anthony E. Parker and David J. Skellern School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney Australia 2109 ABSTRACT The third derivative of MESFET drain current behavior is useful for device characterisation. It provides information necessary to devise a model to predict large-signal dynamic behavior with accuracy over an extended range of operating conditions. Extra parameters are proposed to define behavior in sub-threshold and triode operating regions. A continuously differentiable form that models third-order behavior correctly describes these regions. The result is an accurate large-signal model suitable for design and analysis of distortion and intermodulation in analog circuits. INTRODUCTION Circuit design and analysis are performed with the aid of device models. The models use a set of parameters as constants in equations that describe the electrical behavior of the devices. Characterisation of device behavior is usually accomplished by defining the model parameters to fit the results of electrical measurement. It is desirable to have a minimum set of parameters in a simple mathematical equation with each parameter being derivable from an associated measured property of device operation. For example, the pinch-off voltage parameter is associated with the gate-source potential that turns off the drain current. Basic MESFET models, which do provide simple mathematical descriptions using a small number of parameters, are included in various versions of SPICE (1-3). Values for the first-order parameters to suit particular operating conditions are obtained from characterisation based on standard measurements. Additional parameters are necessary to describe second-order behavior and extend accuracy to a wider range of operating conditions. For example, the pinch-off parameter, which is constant in the first-order model, actually varies with drainsource potential. An additional parameter, 7, defines this behavior in the model proposed by McCamant et al. (4). This paper proposes a further extension to the MESFET parameter set to model an even wider range of operating conditions and to accurately describe the third-order detail of a device. The resulting model provides a more accurate description of the triode and sub-threshold regions of operation. Comparison with measured third-order intermodulation shows that correct description of these extreme regions is necessary to model thirdorder behavior in the normal saturation region. This improves the prediction of intermodulation and distortion performance of analog circuit designs. THIRD-ORDER INTERMODULATION The level of third-order intermodulation is an important figure of merit in analog systems because the intermodulation products can fall in-band. For effective design evaluation it is necessary to accurately model the non-linearity that produces intermodulation. A MESFET fed with an input ui will produce an output U, proportional to its transconductance, g, and load resistance, RL: vo = VigmRL (1) When fed with two equal-power tones at frequencies fi and fz, transconductance non-linearity can produce a third-order intermodulation product at a frequency (2fi-fz). The power level of this product, PI,, is related to the output power of one of the tones, PO, by the third-order intercept defined as ZP3 =:PO -;PI, (5). A Taylor expansion of Eq. 1 reveals that the third-order intercept is given by In a common-source configuration, the transconductance of a MESFET is the derivative of drain current with respect to gate potential. Thus Eq. 2 implies that the third derivative of drain current must be correctly characterised to predict third-order intermodulation. A model suitable for this purpose is presented in the section following a description of existing models. Model parameters defining the sub-threshold and triode operating regions are implemented in a manner consistent with the results of intermodulation measurements. EXISTING MESFET MODELS Equation 3 is the generally accepted MESFET description proposed by McCamant et al. (4). Drain-source current, Ids, is described in terms of gate-source potential, Vas, and drain-source potential, V,. The six parameters in the description, B, Q, V, a, 6 and 7, characterise the device. The triode region of operation is GaAs IC Symposium - 225

3 16 0 \ I Fig. 1. Comparison of the third derivative of drain current in the saturation region described by the models given in Eqs 3 to 7. The parameters S and 7 have been set to zero. The new model (Eqs 5-7) is able to describe the zennwssing point. 04- I Fig. 2. Measured third-order intercept point of a typical 1 x 300 pm GaAs MESFET in common-source configuration. The test was performed with two tones at 100 and 110 MHz, a 3 V drain bias and 50 R source and load impedance. The data is referenced to the gate input (i.e. intercept level at the output divided by the gain). defined by a and is related to the saturation region by the hyperbolic tangent function?. Z, = PV," tanh( ayh) v, = v, -v, + yv& Equation 3 introduces an effective gate potential term, V, defined as the voltage above pinch-off between the gate and source terminals. In the sub-threshold region, where V, < 0, current is set to zero. The value of the exponent parameter, Q, dominates the third derivative of drain current. Typically Q has a value between 2 and 3, so the third derivative of drain current with respect to gate potential follows an inverse power law in the saturation region. The description proposed by Statz et al. (3), Eq. 4, fixes Q to a value of 2, but uses an additional parameter, b. Ids0 = - tanh(av,) 1+ bv, With the parameters available in Eqs 3 and 4, it is possible to characterise a device so that the models closely agree in their prediction of first- and second-order characteristics at particular operating points. However, the two models predict vastly different third-order behavior as shown in Fig. 1. The model parameters given for Eqs 3 and 4 in Fig. 1 are chosen to match dc characteristics and transconductance. Despite this match, the third derivatives of drain current differ. Our new model resolves this disparity by including a description of sub-threshold drain current. f The model is commonly implemented with a polynomial approximation of the hyperbolic tangent function. (3) (4) PROPOSED MESFET MODEL Fig. 2 shows the measured third-order intercept referenced to the gate terminal of a typical n-channel MESFET. The results show a discontinuity, with the intercept level rising sharply at a drain current of about 2 mk Equation 2 shows that this occurs when the second derivative of g, or equivalently the third derivative of drain current, passes through zero. Sub-threshold Region The low-current side of the discontinuity includes the subthreshold region where drain current reduces exponentially as the device pinches off. Since the behavior is exponential the third derivative in this region is positive. The high-current side of the discontinuity, or zero-crossing, therefore must have a negative third derivative. The total description of this behavior requires a smooth transition from a function of exponential form to another with a negative third derivative. MOSFET models use an exponential function of gate potential to describe current in a sub-threshold region, which is defined as having a gate potential less than a critical value (6). However in these models the derivatives are not necessarily continuous over the transition from the sub-threshold region to the high-current region. An alternative approach is to add a description of subthreshold current to the high-current equation by redefining the effective gate potential as The use of Eq. 5 provides a smooth and continuously differentiable transition between the high-current and subthreshold regions. As V,, is reduced the effective gate potential, V, reduces exponentially towards zero. The new sub-threshold voltage parameter, VIt, defines the rate of exponential decrease. A GaAs IC Symposium

4 model using this definition of V, will not abruptly pinch off. Instead, when V, < Vlt, the model will adopt an exponential subthreshold behavior. When V, is greater than V,,, which is typically 0.1 V, the original model's description of the high-current region is not significantly altered because V, = V,, - V,, + UV,. Saturation Region A good description of the high-current region in FET devices, which is used in Eq. 3, is a power law (7). However Fig. 1 shows that this incorrectly predicts a positive third derivative of drain current with respect to gate voltage. Equation 4 correctly predicts a negative derivative, but the hyperbolic tangent function is unsatisfactory in the triode region. An alternative is a modified power law: When VIi,,&d = min(vd,, V,), Eq. 6 is a general power-law description of the triode region that saturates when vd, = V,. The maximum value of VIimikd can be restricted to describe the early saturation phenomenon in short-channel MESFETs. In general, the description of the drain current in the saturation region depends on the maximum value of Vlimild as a function of V,. A simple function is shown in Eq. 7, which uses a parameter, K, to define the early saturation phenomenon. 1; I& [ d l Fig. 3. Measured and modeled gain of the MESFET described in Fig. 2. The measured data, squares, is predicted by both the model proposed by McCamant et al. (4), dotted line, and the new model, solid line. The two new parameters, Mt and 5 define the value of drainsource potential at which early saturation occurs. The definition uses the effective gate potential, V, and total channel-depletion potential, which is the difference between the gate-junction potential and the threshold potential parameter, V,. Equation 9 provides the flexibility necessary to fit the measured intermodulation measurements. The proposed definition of the effective drain-source potential uses a new parameter, P, which is effectively the exponent of the power law in the triode region: 60 (7) Small values of V, in Eq. 7 allow saturation at Vdr = V, whereas Vli~kd is restricted to K when V, is large. Fig. 1 shows the third derivative of Eq. 6, using Eqs 5 and 7, with parameters selected to give dc characteristics and transconductance close to that of the other two models shown. This new equation gives a smooth transition between normal and subthreshold regions with the expected zero-crossing point. This is the same trend found from s-parameter measurements (8). Triode &Pion As with a similar scheme used to model velocity saturation in MOSFETs (9), Eqs 6 and 7 produce a non-differentiable transition between the triode and saturation regions. The solution is to replace Eq. 7 with a function that smoothly limits V,imid: This function sets V&,,i&d equal to the effective drain-source potential, Vb,, but limits its maximum value asymptotically to V,. The drain current in the saturation region depends on V,,, which can be described in terms of V,: v, VI01 = 1+vg/(qvg+5(% -%,) (9) The independent control of the triode region exponent allows better fitting of the model to measured device characteristics (10). If P is equal to Q then Vht is simply equal to V,. Threshold Modulation and Freauenw DeDendence The term fl& in Eqs 3 and 5 describes pinch-off potential modulation by the drain voltage. The extent of this effect depends on the frequency of drain voltage variation because trapped charges, which reduce y, have time to form at low frequencies (11). This can be described by ac and de parameters, 70c and Ydc, and a running average of the drain-source potential, Vop, which is effectively the operating point of the FET. Altering the pinch-off modulation term allows yde to dominate at low frequency, where V, = Vh, and yw to dominate at high frequencies, where Vop is constant. The pinch-off modulation terms presented so far use linear scale factors with no units. It has been proposed that the modulation effect is proportional to -and the modulation parameter should have units V I R (12). The choice of a linear or non-linear modulation term has a significant influence on the predicted harmonic generation (11). The non-linear term, of the form 6 allows good fitting to dc characteristics of a MESFET without requiring the independent control of triode region given by Eq. 10. However, as described in the next section, third-order behavior dictates the use of the linear GaAs IC Symposium - 227

5 E m 20 z II I, [dl Fig. 4. Measured and modeled third-order intercept of the MESFET described in Fig. 2. The measured data, squares, is closely followed by the new model, solid line. The model proposed by McCamant et al. (4), dotted line, departs from the measurements at high currents and does not predict a discontinuity. Refer to the text for a description of the curve labeled A. form. COMPARISON WITH MEASUREMENT Figs 3 and 4 show measured gain and third-order intercept of a typical 1 pm x 300 pm n-channel MESFET at a drain bias of 3 V. The measurements were made using tones at 100 and 110 MHz with 50 Cl source and load impedances. Figs 3 and 4 also show simulations with the model proposed by McCamant et al. (41, based on Eq. 3, and the new model, based on Eqs 5, 6, The parameters of the two sets models were chosen so that they both follow the measured dc characteristics of the MESFET and the measured gain shown in Fig. 3. The new model gives a significantly improved prediction of the third-order intercept in the region at high drain current. The new model predicts the discontinuity in the third-order intercept because the addition of sub-threshold conduction gives a zero-crossing point in the third derivative. The sign of the third derivative is important because it affects the phase of third-order intermodulation and related harmonics. A model that predicts correct phase is vital for design of analog circuits that use cancellation techniques to reduce distortion. The independent description of the triode region allows simultaneous fitting of dc, gain and third-order characteristics. It does not appear possible to reduce the number of parameters in the new model and still obtain an adequate fit to the measured data. For example, curve A in Fig. 4 is representative of simplifying the triode region model either by eliminating Mg from Eq. 9 or using a hyperbolic tangent function. Curve A is also representative of using a non-linear pinch-off modulation term in Eq. 11 and setting P = Q in Eq. 10. In all cases the dc and gain characteristics can be modeled but there are insufficient parameters to fit the third-order intercept curve. CONCLUSION An improved MESFET model has been devised with information acquired from third-order intermodulation measurements. The inclusion of sub-threshold current and an independent triode region description extends the accuracy of the model to a wider range of operating conditions. The associated parameters are necessary to allow correct characterisation of device behavior. The new model allows significantly improved prediction of intermodulation and distortion performance vital to analog circuit design. This gives a better device description for assessing highperformance microwave and analog circuits in communications, signal processing, analog-digital interfaces and switching applications. ACKNOWLEDGMENTS The authors thank Allen Podell, Ed Stoneham and Mike Heimlich of Pacific Monolithics, Inc., Sunnyvale, CA., for provision of and permission to publish intermodulation measurements and modeling results. This work is funded by Macquarie University, the Australian Telecommunications and Electronics Research Board (ATERB), the Australian Research Council (ARC), and the Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) Division of Radiophysics. REFERENCES (1) W.R. Curtice, A MESFET Model for Use in the Design of GaAs Integrated Circuits, IEEE Trans. MTT, Vol. 28, No. 5, pp : May (2) W.R. Curtice and M. Ettenberg, A Non-linear GaAs FET Model for use in the Design of Output Circuits of Power Amplifiers, IEEE Trans. MTT, Vol. 36, No. 2, pp : Dec (3)H. Statz, P. Newman, W. Smith, R.A. Puce1 and H.A. Haus, GaAs FET Device and Circuit Simulation in SPICE, IEEE Trans. Electron Devices, Vol. 34, No. 2, pp : Feb (4)A.J. McCamant, G.D. McCormack and D.H. Smith, An Improved GaAs MESFET Model for SPICE, IEEE Trans. MTT, Vol. 38, No. 6, pp : June (5) S.A. Maas, Microwave Mixers, Artech House, pp : (6) P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE, McGraw-Hill, pp : (7) I. Richer and R.D. Middlebrook, Power-law Nature of Field- Effect Transistor Experimental Characteristics, Proc. IEEE, Vol. 51, NO. 8, pp : Aug (8) S.A. Maas and D. Neilson, Modeling GaAs MESFETs for Intermodulation Analysis, Microwave Journal, pp : May (9) P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE, McGraw-Hill, pp : (10) A.E. Parker and D.J. Skellern, work to be published. (11) A.E. Parker and D.J. Skellern, GaAs Device Modelling for Design and Applications, IEEE Int. Sym. on Circuits and Systems: Singapore, pp : June 11-14, (12) C.D. Hartgring, An Accurate JFETMESFET Model for Circuit Analysis, Solid-state Electronics, Pergamon Press, Vol. 25, NO. 3, pp : GaAs IC Symposium