Dynamic Mosfet model.

The mosfet is probably the workhorse of power electronics. Although used so extensively, the modeling of the mosfet is not that straightforward, including a lot of pitfalls. Depending on the application where the mosfet is used, also the model should be chosen carefully. In many cases the ideal mosfet modeled by an on-off resistance controlled from a block diagram is sufficient.
The dynamics can be included by adding a RC or time delay to model the delay caused by the gate charging and some wire inductance to model the overvoltage during switching.
If more detailed wave forms are required, the complete non-linear mosfet model would be more appropriate. The non-linear capacitances of the mosfet finally determine the dynamic transient response during switching.

What model is required
In the first place the static characteristic determines the static (mostly on-state) losses. If the mosfet is switching fast, the model can be approximated by a simple on-off switch.
More detailed modeling would also include the dependency on the gate voltage, where the on resistance is modeled as a non-linear function of VDS and VGS. This is required if also the driver is modeled in detail and a more accurate simulation result is expected regarding the parasitic components surrounding the mosfet.


Static transfer function
The static transfer function for the mosfet is defined as:

Ohmic Region:IDS=(KP/2) · VDS · (2 · (VGS-VTO)-VDS)
Active Region:IDS=(KP/2) · (VGS-VTO)2
The parameters VTO KP as well as Rd have to be specified for proper operation of the mosfet. First read the value of VTO from the data sheet. It is specified as the Gate threshold voltage and VGS(th) and has a typical value of 3 volts. The parameter KP is not always given, but you can calculate it from the transfer characteristic in the active region. Use the above given formula for the active region for calculating KP. Select IDS, VGS and VTO and calculate the correct value of KP. The on-state resistance is mostly given in the data sheet and its value at 25 degrees Celcius should be used. During the simulation both KP and Rd will change with temperature.


Dynamics
The gate capacitance CGS is constant in this model. The other capacitances are non-linear and are modeled by the parameters CGD, CDS, VJ, M and FC.
The capacitances are depending on the voltage across them by:


The mosfet dynamics are further influenced by the transconductance KP and the treshold value of the gate voltage VTO


Integrated reverse conducting diode
The reverse conducting diode of the mosfet is always included in the model of the mosfet. The parameters can be set such to make it a very worse diode and also the reverse recovery of the diode can be included. The dynamic model for the diode is based on partly based on spice or on measurement parameters. A great advantage compared to the original Spice model is that the dynamic diode model can also simulate reverse recovery.
The reverse diode is modeled as an ideal diode, but including reverse recovery.

The reverse recovery in the diode model is based on stored charge during the conduction interval. Dependent on the way the diode is forced to turn-off, the reverse recovery current is provided by the stored charge in the diode. This can be modeled and parameterized in various ways:

Each method predicts the reverse recovery current during turn-off. Depending on the parameters provided, the model is parameterized. Leaving the remaining parameters equal to zero, cancels them. To model the reverse recovery correctly, the step size dt for the simulation should be chosen such small, that the reverse recovery can be simulated in detail. This requires a small value of the step size dt, which leads to longer simulation times. However it will show the transients that will occur during the turn off of the diode and any unwanted effects due to a possible high reverse recovery current. Also the effects of the parasitic components surrounding the diode can be studied in more detail.

Losses and Thermal simulation
The mosfet model has a thermal connection that has to be connected to a heat sink model. The temperature rise due to the conduction, switching and reverse recovery losses is modeled on this connection. A heat sink is build from the components found in components/library/Heatsink The parameter Rth and Cth model the thermal model form junction to case. The initial temperature of the junction is modeled by the parameter Tth0. If a more detailed thermal model for the junction to case thermal path has to be build, Rth and Cth simply model the first chip-layer and the following layers are modeled by subsequent thermal models.

Overview of the parameters
The parameters for the mosfet are summarized in the following table. For the parameters that are compatible with the spice diode model the column Spice shows the spice parameter name. Parameters that do not exist in the spice model are indicated with N.A. Default values for the parameters are given.

Mosfet Static Parameters
ParameterDefaultSpiceFunction
VTO3VTOGate threshold voltage
KP6.4KPGain
RG10RGInternal Gate resistance
RD190mOhmRDInternal Drain resistance
Mosfet Dynamic Parameters
ParameterDefaultSpiceFunction
CDS730pFCDSDrain Source Capacitance maximum value
CGD50pFCGDGate Drain Capacitance maximum value
CGS2350pFCGSGate Source Capacitance constant value
FC0.5N.A.Forward bias junction fit parameter
M 0.5N.A.Grading coefficient
VJ1 N.A.Junction Potential
Mosfet Wire Parameters
ParameterDefaultSpiceFunction
LD10nHN.A.Drain wire inductance
LG5nH N.A.Gate wire inductance
LS12nHN.A.Source wire inductance
Mosfet Reverse Diode Parameters
ParameterDefaultSpiceFunction
IS10-14 ISSaturation current.
BV650VoltBVReverse breakdown "knee" voltage.
N1.5NEmission coefficient.
TT0TTForward Storage Time (Transit Time).
RS1mOhm RSOn resistance.
τrr (tau_rr)0N.A.Decay time constant of the reverse recovery current after IRR. If this value is set to zero, the diode has a snappy recovery.
IF 0N.A.Measured maximum forward current.
dIF/dt 0N.A.Measured current gradient during turn off. (Measure at the zero-crossing)
QRR 0N.A.Measured reverse recovery charge.
TRR 0N.A.Measured reverse recovery time.
Thermal Parameters
ParameterDefaultSpiceFunction
Rth1N.A.Thermal junction-case resistance.
Cth0.5mN.A.Thermal junction-case capacitance.
Tth025N.A.Initial junction temperature.

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