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. I t provides information
necessary to devise a model to predict large-signal dynamic
behavior with accuracy over a n 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 a n accurate large-signal
model suitable for design a n d analysis of distortion a n d
intermodulation in analog circuits.
INTRODUCTION
Circuit design and analysis are performed with the aid of
device models. The models use a set of parameters a s constants in
equations t h a t 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.
I t is desirable to have a minimum set of parameters in a
simple mathematical equation with each parameter being
derivable from a n 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 t h e 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 a n 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 t h a t 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 a n 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 t h a t produces
intermodulation.
A MESFET fed with an input ui will produce an output U,
proportional to its transconductance, g
, and load resistance, R L :
(1)
vo = V i g m R L
When fed with two equal-power tones at frequencies fi and
fz, transconductance non-linearity can produce a third-order
intermodulation product a t a frequency (2fi-fz). The power level of
this product, PI,, is related to the output power of one of the
tones, P O , by t h e third-order intercept defined a s
ZP3 =:PO -;PI, ( 5 ) . A Taylor expansion of Eq. 1 reveals t h a t
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 t h a t 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 t h e 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, I d s , 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
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0
I
\
040
0.2
0.1
0.3
0.4
0.5
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.
defined by a and is related to the saturation region by the
hyperbolic tangent function?.
,Z
= PV," tanh( ayh)
(3)
v, = v, -v, + yv&
Equation 3 introduces an effective gate potential term, V,,
defined a s 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,
(4)
With the parameters available in Eqs 3 and 4, i t is possible
to characterise a device so that the models closely agree in their
prediction of first- and second-order characteristics a t particular
operating points. However, the two models predict vastly different
third-order behavior a s 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
approximationof the hyperbolic tangent function.
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20
I
30
40
0.6
Fig. 2. Measured third-orderintercept 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).
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 a t a
drain current of about 2 m k Equation 2 shows that this occurs
when the second derivative of g, or equivalently the third
derivative of drain current, passes through zero.
Sub-thresholdRegion
The low-current side of the discontinuity includes the subthreshold region where drain current reduces exponentially a s 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 a n exponential function of gate
potential to describe current in a sub-threshold region, which is
defined a s 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 a s
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
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 i s a general power-law
description of the triode region that saturates when v d , = V,. The
maximum value of VIimikd can be restricted to describe the early
saturation phenomenon in short-channel MESFETs. In general,
the description of t h e drain current in the saturation region
depends on the maximum value of Vlimilda s a function of V,. A
simple function is shown in Eq. 7, which uses a parameter, K,to
define the early saturation phenomenon.
1;
5
40
20
60
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 a t 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 parameter, @b, and the threshold potential parameter,
V,. Equation 9 provides t h e flexibility necessary to fit t h e
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:
(7)
Small values of V , in Eq. 7 allow saturation a t Vdr = V,
whereas V l i ~ k dis restricted to K when V, is large.
Fig. 1shows the third derivative of Eq. 6, using Eqs 5 and 7,
with parameters selected to give dc characteristics a n d
transconductance close to t h a t 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, V b , , 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,:
VI01 =
v,
1 + v g / ( q v g + 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 f l & 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 a t low frequencies ( 1 1 ) .
This can be described by ac and de parameters, 70cand 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 y d e to
dominate a t low frequency, where V , = V h , and yw to dominate a t
high frequencies, where Vopis constant. The pinch-off modulation
terms presented so far use linear scale factors with no units. I t
has been proposed t h a t 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
allows good fitting to dc
characteristics of a MESFET without requiring the independent
control of triode region given by Eq. 10. However, a s described in
the next section, third-order behavior dictates the use of the linear
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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.
30
3
E
m
z
20
II
40
20
-10
1
I,
[ d l
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 a t 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, 8-11. 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 a t 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 h a s 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
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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.
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