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Semiconductor Devices
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, IDS, depends on the region of operation:
In the off region (VGS < Vth) the drain-source current is:
In the linear region (0 < VDS < VGS –Vth) the drain-source current is:
In the saturated region (0 < VGS –Vth < VDS) the drain-source current is:
In the preceding equations:
K is the transistor gain.
VDS is the positive drain-source voltage.
VGS is the gate-source voltage.
Vth is the threshold voltage.
λ is the channel modulation.
The block models gate junction capacitance as a fixed gate-drain capacitance CGD and a fixed gate-source capacitance CGS. If you select Specify using equation parameters directly for the Parameterization parameter in the Junction Capacitance tab, you specify these values directly using the Gate-drain junction capacitance and Gate-source junction capacitance parameters. Otherwise, the block derives them from the Input capacitance Ciss and Reverse transfer capacitance Crss parameter values. The two parameterizations are related as follows:
CGD = Crss
CGS = Ciss – Crss
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, Vth, become a function of temperature according to the following equations:
Vths = Vth1 + α ( Ts – Tm1)
where:
Tm1 is the temperature at which the transistor parameters are specified, as defined by the Measurement temperature parameter value.
Ts is the simulation temperature.
KTm1 is the transistor gain at the measurement temperature.
KTs is the transistor gain at the simulation temperature. This is the transistor gain value used in the MOSFET equations when temperature dependence is modeled.
Vth1 is the threshold voltage at the measurement temperature.
Vths 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, dVth/dT.
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, RDS(on). Depending on the block parameterization method, you have two ways of specifying α:
If you parameterize the block from a datasheet, you have to provide RDS(on) at a second measurement temperature. The block then calculates the value for 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 on the block in your model, 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 RDS(on) 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 RDS(on) value. Inconsistent values for RDS(on) at the higher temperature will result in unphysical values for α and unrepresentative simulation results. Typically RDS(on) increases by a factor of about 1.5 for a hundred degree increase in temperature.
You may need to tune the values of BEX and threshold voltage, Vth, to replicate the VDS-VGS relationship (if available) for a given device. Increasing Vth moves the VDS-VGS plots to the right. The value of BEX affects whether the VDS-VGS curves for different temperatures cross each other, or not, for the ranges of VDS and VGS considered. Therefore, an inappropriate value can result in the different temperature curves appearing to be reordered. Quoting RDS(on) 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 BEX.
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.
The ratio of the drain-source voltage to the drain current for specified values of drain current and gate-source voltage. RDS(on) 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 0.025 Ω.
The drain current the block uses to calculate the value of the drain-source resistance. IDS 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.
The gate-source voltage the block uses to calculate the value of the drain-source resistance. VGS 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.
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/V2.
Gate-source threshold voltage Vth in the Shichman and Hodges equations. For an enhancement device, Vth should be positive. For a depletion mode device, Vth should be negative. The default value is 1.7 V.
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, RDS(on). 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 0 1/V.
Temperature Tm1 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.
The transistor source resistance. The default value is 1e-4 Ω. The value must be greater than or equal to 0.
The transistor drain resistance. The default value is 0.001 Ω. The value must be greater than or equal to 0.
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.
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.
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.
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.
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.
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, Ts, a value for BEX, and a value for the measurement temperature Tm1 (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 RDS(on) at a second measurement temperature, and the block will calculate α based on that. If you parameterize by specifying equation parameters, you have to provide the value for α directly.
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 temperature Tm2 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.
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 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.
Temperature Ts at which the device is simulated. The default value is 25 C.
The block has the following ports:
Electrical conserving port associated with the transistor gate terminal.
Electrical conserving port associated with the transistor drain terminal.
Electrical conserving port associated with the transistor source terminal.
[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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