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Model N-Channel MOSFET using Shichman-Hodges equation

The N-Channel MOSFET block uses the Shichman and Hodges equations [1] for an insulated-gate field-effect transistor to represent an N-Channel MOSFET.

The drain-source current, *I*_{DS},
depends on the region of operation:

In the off region (

*V*_{GS}<*V*_{th}) the drain-source current is:In the linear region (0 <

*V*_{DS}<*V*_{GS}–*V*_{th}) the drain-source current is:In the saturated region (0 <

*V*_{GS}–*V*_{th}<*V*_{DS}) the drain-source current is:

In the preceding equations:

*K*is the transistor gain.*V*_{DS}is the positive drain-source voltage.*V*_{GS}is the gate-source voltage.*V*_{th}is the threshold voltage.*λ*is the channel modulation.

The block models gate junction capacitance as a fixed gate-source
capacitance *C*_{GS} and either
a fixed or a nonlinear gate-drain capacitance *C*_{GD}.

If you select `Specify using equation parameters
directly` for the **Parameterization** parameter
in the **Junction Capacitance** tab, you specify
the **Gate-drain junction capacitance** and **Gate-source
junction capacitance** parameters directly. Otherwise, the
block derives them from the **Input capacitance, Ciss** and **Reverse
transfer capacitance, Crss** parameter values. The two parameterizations
are related as follows:

*C*_{GD}=*Crss**C*_{GS}=*Ciss*–*Crss*

If you select the `Gate-drain charge function is
nonlinear` option for the **Charge-voltage linearity** parameter,
then the gate-drain charge relationship is defined by the piecewise-linear
function shown in the following figure.

For instructions on how to map a time response to device capacitance values, see the N-Channel IGBT block reference page. However, this mapping is only approximate because the Miller voltage typically varies more from the threshold voltage than in the case for the IGBT.

The default behavior is that dependence on temperature is not modeled, and the device is simulated at the temperature for which you provide block parameters. You can optionally include modeling the dependence of the transistor static behavior on temperature during simulation. Temperature dependence of the junction capacitances is not modeled, this being a much smaller effect.

When including temperature dependence, the transistor defining
equations remain the same. The gain, *K*, and the
threshold voltage, *V*_{th},
become a function of temperature according to the following equations:

*V*_{ths} = *V*_{th1} + *α* ( *T*_{s} – *T*_{m1})

where:

*T*_{m1}is the temperature at which the transistor parameters are specified, as defined by the**Measurement temperature**parameter value.*T*_{s}is the simulation temperature.*K*_{Tm1}is the transistor gain at the measurement temperature.*K*_{Ts}is the transistor gain at the simulation temperature. This is the transistor gain value used in the MOSFET equations when temperature dependence is modeled.*V*_{th1}is the threshold voltage at the measurement temperature.*V*_{ths}is the threshold voltage at the simulation temperature. This is the threshold voltage value used in the MOSFET equations when temperature dependence is modeled.*BEX*is the mobility temperature exponent. A typical value of*BEX*is -1.5.*α*is the gate threshold voltage temperature coefficient,*d**V*_{th}/*d**T*.

For most MOSFETS, you can use the default value of `-1.5` for *BEX*.
Some datasheets quote the value for *α*, but
most typically they provide the temperature dependence for drain-source
on resistance, *R _{DS}(on)*.
Depending on the block parameterization method, you have two ways
of specifying

If you parameterize the block from a datasheet, you have to provide

*R*at a second measurement temperature. The block then calculates the value for_{DS}(on)*α*based on this data.If you parameterize by specifying equation parameters, you have to provide the value for

*α*directly.

If you have more data comprising drain current as a function
of gate-source voltage for more than one temperature, then you can
also use Simulink^{®} Design Optimization™ software to help tune the
values for *α* and *BEX*.

The block has an optional thermal port, hidden by default. To
expose the thermal port, right-click the block in your model, and
then from the context menu select **Simscape block choices** > **Show
thermal port**. This action displays the thermal port
H on the block icon, and adds the **Thermal port** tab
to the block dialog box.

Use the thermal port to simulate the effects of generated heat
and device temperature. For more information on using thermal ports
and on the **Thermal port** tab parameters, see Simulating Thermal Effects in Semiconductors.

When modeling temperature dependence, consider the following:

The block does not account for temperature-dependent effects on the junction capacitances.

When you specify

*R*at a second measurement temperature, it must be quoted for the same working point (that is, the same drain current and gate-source voltage) as for the other_{DS}(on)*R*value. Inconsistent values for_{DS}(on)*R*at the higher temperature will result in unphysical values for_{DS}(on)*α*and unrepresentative simulation results. Typically*R*increases by a factor of about 1.5 for a hundred degree increase in temperature._{DS}(on)You may need to tune the values of

*BEX*and threshold voltage,*V*_{th}, to replicate the*V*_{DS}-*V*_{GS}relationship (if available) for a given device. Increasing*V*_{th}moves the*V*_{DS}-*V*_{GS}plots to the right. The value of*BEX*affects whether the*V*_{DS}-*V*_{GS}curves for different temperatures cross each other, or not, for the ranges of*V*_{DS}and*V*_{GS}considered. Therefore, an inappropriate value can result in the different temperature curves appearing to be reordered. Quoting*R*values for higher currents, preferably close to the current at which it will operate in your circuit, will reduce sensitivity to the precise value of_{DS}(on)*BEX*.

**Parameterization**Select one of the following methods for block parameterization:

`Specify from a datasheet`— Provide the drain-source on resistance and the corresponding drain current and gate-source voltage. The block calculates the transistor gain for the Shichman and Hodges equations from this information. This is the default method.`Specify using equation parameters directly`— Provide the transistor gain.

**Drain-source on resistance, R_DS(on)**The ratio of the drain-source voltage to the drain current for specified values of drain current and gate-source voltage.

*R*should have a positive value. This parameter is only visible when you select_{DS}(on)`Specify from a datasheet`for the**Parameterization**parameter. The default value is`0.025`Ω.**Drain current, Ids, for R_DS(on)**The drain current the block uses to calculate the value of the drain-source resistance.

*I*_{DS}should have a positive value. This parameter is only visible when you select`Specify from a datasheet`for the**Parameterization**parameter. The default value is`6`A.**Gate-source voltage, Vgs, for R_DS(on)**The gate-source voltage the block uses to calculate the value of the drain-source resistance.

*V*_{GS}should have a positive value. This parameter is only visible when you select`Specify from a datasheet`for the**Parameterization**parameter. The default value is`10`V.**Gain, K**Positive constant gain coefficient for the Shichman and Hodges equations. This parameter is only visible when you select

`Specify using equation parameters directly`for the**Parameterization**parameter. The default value is`5`A/V^{2}.**Gate-source threshold voltage, Vth**Gate-source threshold voltage

*V*_{th}in the Shichman and Hodges equations. For an enhancement device,*V*_{th}should be positive. For a depletion mode device,*V*_{th}should be negative. The default value is`1.7`V.**Channel modulation, L**The channel-length modulation, usually denoted by the mathematical symbol

*λ*. When in the saturated region, it is the rate of change of drain current with drain-source voltage. The effect on drain current is typically small, and the effect is neglected if calculating transistor gain*K*from drain-source on-resistance,*R*. A typical value is 0.02, but the effect can be ignored in most circuit simulations. However, in some circuits a small nonzero value may help numerical convergence. The default value is_{DS}(on)`0`1/V.**Measurement temperature**Temperature

*T*_{m1}at which**Drain-source on resistance, R_DS(on)**is measured. This parameter is only visible when you select`Model temperature dependence`for the**Parameterization**parameter on the**Temperature Dependence**tab. The default value is`25`C.

**Source ohmic resistance**The transistor source resistance. The default value is

`1e-4`Ω. The value must be greater than or equal to`0`.**Drain ohmic resistance**The transistor drain resistance. The default value is

`0.001`Ω. The value must be greater than or equal to`0`.

**Parameterization**Select one of the following methods for capacitance parameterization:

`Specify from a datasheet`— Provide parameters that the block converts to junction capacitance values. This is the default method.`Specify using equation parameters directly`— Provide junction capacitance parameters directly.

**Input capacitance, Ciss**The gate-source capacitance with the drain shorted to the source. This parameter is only visible when you select

`Specify from a datasheet`for the**Parameterization**parameter. The default value is`350`pF.**Reverse transfer capacitance, Crss**The drain-gate capacitance with the source connected to ground. This parameter is only visible when you select

`Specify from a datasheet`for the**Parameterization**parameter. The default value is`80`pF.**Gate-source junction capacitance**The value of the capacitance placed between the gate and the source. This parameter is only visible when you select

`Specify using equation parameters directly`for the**Parameterization**parameter. The default value is`270`pF.**Gate-drain junction capacitance**The value of the capacitance placed between the gate and the drain. This parameter is only visible when you select

`Specify using equation parameters directly`for the**Parameterization**parameter. The default value is`80`pF.**Output capacitance, Coss**The output capacitance applied across the drain-source ports. The default value is

`0`pF.**Charge-voltage linearity**Select whether gate-drain capacitance is fixed or nonlinear:

`Gate-drain capacitance is constant`— The capacitance value is constant and defined according to the selected parameterization option, either directly or derived from a datasheet. This is the default method.`Gate-drain charge function is nonlinear`— The gate-drain charge relationship is defined according to the piecewise-nonlinear function described in Charge Model. Two additional parameters appear to let you define the gate-drain charge function.

**Gate-drain oxide capacitance**The gate-drain capacitance when the device is on and the drain-gate voltage is small. This parameter is only visible when you select

`Gate-drain charge function is nonlinear`for the**Charge-voltage linearity**parameter. The default value is`200`pF.**Drain-gate voltage at which oxide capacitance becomes active**The drain-gate voltage at which the drain-gate capacitance switches between off-state (

*C*_{GD}) and on-state (*C*_{ox}) capacitance values. This parameter is only visible when you select`Gate-drain charge function is nonlinear`for the**Charge-voltage linearity**parameter. The default value is`-0.5`V.

**Parameterization**Select one of the following methods for temperature dependence parameterization:

`None — Simulate at parameter measurement temperature`— Temperature dependence is not modeled. This is the default method.`Model temperature dependence`— Model temperature-dependent effects. Provide a value for simulation temperature,*T*_{s}, a value for*BEX*, and a value for the measurement temperature*T*_{m1}(using the**Measurement temperature**parameter on the**Main**tab). You also have to provide a value for*α*using one of two methods, depending on the value of the**Parameterization**parameter on the**Main**tab. If you parameterize the block from a datasheet, you have to provide*R*at a second measurement temperature, and the block will calculate_{DS}(on)*α*based on that. If you parameterize by specifying equation parameters, you have to provide the value for*α*directly.

**Drain-source on resistance, R_DS(on), at second measurement temperature**The ratio of the drain-source voltage to the drain current for specified values of drain current and gate-source voltage at second measurement temperature. This parameter is only visible when you select

`Specify from a datasheet`for the**Parameterization**parameter on the**Main**tab. It must be quoted for the same working point (drain current and gate-source voltage) as the**Drain-source on resistance, R_DS(on)**parameter on the**Main**tab. The default value is`0.037`Ω.**Second measurement temperature**Second temperature

*T*_{m2}at which**Drain-source on resistance, R_DS(on), at second measurement temperature**is measured. This parameter is only visible when you select`Specify from a datasheet`for the**Parameterization**parameter on the**Main**tab. The default value is`125`C.**Gate threshold voltage temperature coefficient, dVth/dT**The rate of change of gate threshold voltage with temperature. This parameter is only visible when you select

`Specify using equation parameters directly`for the**Parameterization**parameter on the**Main**tab. The default value is`-6`mV/K.**Mobility temperature exponent, BEX**Mobility temperature coefficient value. You can use the default value for most MOSFETs. See the Basic Assumptions and Limitations section for additional considerations. The default value is

`-1.5`.**Device simulation temperature**Temperature

*T*_{s}at which the device is simulated. The default value is`25`C.

[1] H. Shichman and D. A. Hodges. "Modeling and simulation of insulated-gate field-effect transistor switching circuits." IEEE J. Solid State Circuits, SC-3, 1968.

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