277
Compact MOSFET Models for RF Applications
In the 40/60 partitioning scheme, D xpart varies from 0.5 at V d  = 0 to 0.4 in the
saturation region, and S xpart varies from 0.5 to 0.6 [33,48]. However, since the
0.4/0.6 scheme covers a wide range of voltage and the error introduced by
using a constant D xpart  = 0.4 and S xpart  = 0.6 is less than 5%, these values can be
adopted to simplify the model.
In the QS approach, it is assumed that
dQ t
dt
dQ t
dt
dQ
dV
dV
dt
i
iq
iq
( )
( )
=
=
(7.42)
where:
Q iq (t) is the equilibrium, or QS, channel charge under the instantaneous
bias at any time t
The assumption of equilibrium at all times gives an error in calculating the
NQS currents. To account for the NQS current, a new state variable Q def is
introduced to keep track of the amount of deficit (or surplus) channel charge
relative to the QS charge at a given time.
Q t Q t Q t
def
i q
i
( )
( )
( )
=
_
(7.43)
and
dQ t
dt
dQ t
dt
dQ t
dt
def
iq
i
( )
( )
( )
=
−
(7.44)
Q def is allowed to decay exponentially to zero after a step change in bias with
a bias-dependent NQS relaxation time, τ. Thus, the charging current can be
approximated by
dQ t
dt
dQ t
i
def
( )
( )
≅
τ
(7.45)
Q def (t) can be calculated from Equation 7.44, and a subcircuit, shown in
Figure  7.6, has been introduced to obtain the solution. The subcircuit is a
direct translation from Equation 7.44. The node voltage gives the value of
Q def (t). The total charging current is given by the current going through the
resistor of value τ. With this approach, only one additional node is needed
and the topology of the original transistor model is not affected.
The value of the channel relaxation time constant τ is composed of the terms
related to the diffusion and drift currents (calculated from the RC Elmore
equivalent circuit discussed earlier). The components of τ are given by
τ
µ
diffusion
eff
kT
L
v
=
(
)
/4
2
(7.46)