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Chapter 8
(only) by Rdrive
and Cgd . Finally, in T3, the current starts falling toward zero. The
gate voltage falls exponentially (as an RC circuit)—down to Vt , at which moment, the
end of subinterval T3 is declared. The transition is now complete as far as the switch
is concerned. But after that, during T4, the RC exponential discharge continues down
to 10% of the initial gate drive amplitude. As before, driver dissipation occurs over
T1 T2 T3 T4, whereas crossover occurs during T2 T3.
8.9 Gate Charge Factors
A more recent way of describing the parasitic capacitor-based effects in a MOSFET is
in terms of gate charge factors . In Figure 8.15 , we show how these charge factors, Qgs ,
Qgd , and Qg , are defined. On the right column of the table in the figure, we have given
VdriveVsat
g
Io
Vt +
T1 = −Tg ln
Vgs = (Vdrive Vsat) × e + Vsat
Neither Id nor Vd change here because Vgs is still high enough and so the MOSFET is fully conducting.
Since logic level thresholds are steadily getting lower, we can no longer afford to ignore the saturation drop across the pull-
down transistor of the driver stage. We call this Vsat (typically 0.2 V).
Vgs falls exponentially. The equation given here satisfies the required boundary conditions.
(Gate Drive)
Vgs (Gate Voltage)
Id (Drain Current)
Vd (Drain Voltage)
Interval
T1
Tg Rdrive × Cg
Cg = Cgd + Cgs
TURN-OFF
time
time
time
time
Vdrive
Vdrive
Vsat
Vin
lo
Vt + lo/g
T1
t
Tg
Vsat
Vd = Vin
Id = 0
Figure 8.11 : First interval of turn-off
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267Conduction and Switching Losses
the relationships between the gate charge factors and the capacitances, assuming the latter
are constants. Gate char
ge factors represent a more accurate way of proceeding, since the
interelectrode capacitances are such strong functions of the applied voltage. However, our
entire analysis of the turn-on and turn-off intervals so far has been implicitly based on the
assumption that the interelectrode capacitances are constants. A possible way out of this,
one that also helps reduce the error in our switching loss estimates, is detailed in Figure
8.16 , using the Si4442DY (from Vishay) as an example.
Basically, we are using the gate charge factors to tell us what the effective capacitances
are (and the voltage swings from 0 to Vin ). We see that the effective input capacitance
( Ciss ), for example, is about 50% greater than the single-point Ciss value that we would
Vsat
If t T1, Vd 0, and if t T1T2, Vd Vin, so
Vgs is fixed at Vt Io/g (Miller region). So current through Cgs is zero.
However, Drain voltage is changing. Thus that injects a charging current Cgd * d(Vd)/dt through Cgd into the gate.
But there is a current flowing out of the gate described by (Vsat Vgs)/Rdrive. Therefore this must equal the Cgd charging current.
Equating terms, we get the d(Vd)/dt ,and so we get the equation for Vd.
During turn-off, the Drain current cannot change unless the switching node (and thus in effect Vd too) goes completely to Vin,
and thereby forward biases the diode (ignoring its forward drop), allowing it to start sharing some or all of the Drain current Id.
(t T1)
Cgd × Rdrive
Vin × Cgd × Rdrive
Vsat
g
Io
Vgs Vt +
Vt + Io/g
Io
t1 t2
t1
(Gate Drive)
Vgs (Gate Voltage)
Id (Drain Current)
Vd (Drain Voltage)
g
Io
Vt
Vsat
g
Io
Vt
Vin
Vd
T2 =
TURN-OFF
time
time
time
time
Vdrive
Vdrive
Interval
T2
Id lo
Tg Rdrive × Cg
Cg = Cgd + Cgs
Figure 8.12 : Second interval of turn-off

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