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 V_DS and V_GS. 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 V_TO K_P as well as R_d have to be specified for proper operation of the mosfet. First read the value of V_TO from the data sheet. It is specified as the Gate threshold voltage and V_GS(th) and has a typical value of 3 volts. The parameter K_P 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 K_P. Select I_DS, V_GS and V_TO and calculate the correct value of K_P. 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 K_P and R_d will change with temperature.

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

• C_GD
  V_GD <= FC · V_J C_GD(V_GD) = C_GD · (1-(V_GD / V_J) )^m
  V_GD > FC · V_J C_GD(V_GD) = C_GD · (1-(FC · V_J / V_J) )^m


• C_DS
  V_DS <= FC · V_J C_DS(V_DS) = C_DS · (1-(V_DS / V_J) )^m
  V_DS > FC · V_J C_DS(V_DS) = C_DS · (1-(FC · V_J / V_J) )^m


• C_GS
  C_GS(V_GS) = C_GS

The mosfet dynamics are further influenced by the transconductance K_P and the treshold value of the gate voltage V_TO

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:

• Spice parameter based
• Physical parameter based
• Measured data based

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.

• Spice parameter based The original spice parameters are not that bad. The only problem is the model, that was originally designed for small signal diodes. However the parameter TT, modeling the transit time, can be used to model the reverse recovery behavior.
  The parameter TT can approximately be chosen as TT=40ns for a diode with a blocking voltage of 100V, to TT=4us for a diode capable of blocking 1000Volt. If TT is set to zero the transit time is approximated from the reverse breakdown voltage BV.
• Physical parameter based The forward storage time in the diode is modeled by the parameter TT, modeling the transit time. The parameter is the same as in the original spice specification, so it can be used to model the reverse recovery behavior.
  The parameter TT can approximately be chosen as TT=40ns for a diode with a blocking voltage of 100V, to TT=4us for a diode capable of blocking 1000Volt. If TT is set to zero the transit time is approximated from the reverse breakdown voltage BV.
  The time constant with which the reverse recovery is ending is specified by the parameter τ_rr. If τ_rr (tau_rr)=0, the diode snaps off very fast. A value greater than zero defines the time constant by which the reverse recovery current decays from I_RR towards zero.
• Measured data based If measured data is available, the parameters I_F, dI_F/dt, Q_RR and T_RR can be specified.
  

  IF	The maximum forward current during the conduction of the diode. During conduction the total amount of charge is depending on this value.
  dIF/dt	The gradient of the diode current during turn of, measured at the zero crossing of the diode current. This value is depending on the load circuit connected to the diode and the parasitic inductance in series with the diode.
  QRR	The reverse recovered charge is taken from the specification in the data sheet and is specified for a typical forward current IF and turn off gradient dIF/dt of the forward current
  TRR	The reverse recovery time is taken from the specification in the data sheet and is specified for a typical forward current IF and turn off gradient dIF/dt of the forward current

  In the datasheet the parameters Q_RR and T_RR are specified for a typical measurement, where I_F and dI_F/dt are the test circuit conditions.

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 R_th and C_th model the thermal model form junction to case. The initial temperature of the junction is modeled by the parameter T_th0. If a more detailed thermal model for the junction to case thermal path has to be build, R_th and C_th 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

Parameter	Default	Spice	Function
VTO	3	VTO	Gate threshold voltage
KP	6.4	KP	Gain
RG	10	RG	Internal Gate resistance
RD	190mOhm	RD	Internal Drain resistance

Mosfet Dynamic Parameters

Parameter	Default	Spice	Function
CDS	730pF	CDS	Drain Source Capacitance maximum value
CGD	50pF	CGD	Gate Drain Capacitance maximum value
CGS	2350pF	CGS	Gate Source Capacitance constant value
FC	0.5	N.A.	Forward bias junction fit parameter
M	0.5	N.A.	Grading coefficient
VJ	1	N.A.	Junction Potential

Mosfet Wire Parameters

Parameter	Default	Spice	Function
LD	10nH	N.A.	Drain wire inductance
LG	5nH	N.A.	Gate wire inductance
LS	12nH	N.A.	Source wire inductance

Mosfet Reverse Diode Parameters

Parameter	Default	Spice	Function
IS	10-14	IS	Saturation current.
BV	650Volt	BV	Reverse breakdown "knee" voltage.
N	1.5	N	Emission coefficient.
TT	0	TT	Forward Storage Time (Transit Time).
RS	1mOhm	RS	On resistance.
τrr (tau_rr)	0	N.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	0	N.A.	Measured maximum forward current.
dIF/dt	0	N.A.	Measured current gradient during turn off. (Measure at the zero-crossing)
QRR	0	N.A.	Measured reverse recovery charge.
TRR	0	N.A.	Measured reverse recovery time.

Thermal Parameters

Parameter	Default	Spice	Function
Rth	1	N.A.	Thermal junction-case resistance.
Cth	0.5m	N.A.	Thermal junction-case capacitance.
Tth0	25	N.A.	Initial junction temperature.