Model N-Channel MOSFET using Shichman-Hodges equation
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, I_{DS}, depends on the region of operation:
In the off region (V_{GS} < V_{th}) the drain-source current is:
$${I}_{DS}=0$$
In the linear region (0 < V_{DS} < V_{GS} –V_{th}) the drain-source current is:
$${I}_{DS}=K\left(({V}_{GS}-{V}_{th}){V}_{DS}-{V}_{DS}{}^{2}/2\right)\left(1+\lambda \left|{V}_{DS}\right|\right)$$
In the saturated region (0 < V_{GS} –V_{th} < V_{DS}) the drain-source current is:
$${I}_{DS}=(K/2){({V}_{GS}-{V}_{th})}^{2}\left(1+\lambda \left|{V}_{DS}\right|\right)$$
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 junction capacitances either by fixed capacitance values, or by tabulated values as a function of the drain-source voltage. In either case, you can either directly specify the gate-source and gate-drain junction capacitance values, or let the block derive them from the input and reverse transfer capacitance values. Therefore, the Parameterization options for charge model on the Junction Capacitance tab are:
Specify fixed input, reverse transfer
and output capacitance
— Provide fixed parameter
values from datasheet and let the block convert the input and reverse
transfer capacitance values to junction capacitance values, as described
below. This is the default method.
Specify fixed gate-source, gate-drain
and drain-source capacitance
— Provide fixed
values for junction capacitance parameters directly.
Specify tabulated input, reverse transfer
and output capacitance
— Provide tabulated capacitance
and drain-source voltage values based on datasheet plots. The block
converts the input and reverse transfer capacitance values to junction
capacitance values, as described below.
Specify tabulated gate-source, gate-drain
and drain-source capacitance
— Provide tabulated
values for junction capacitances and drain-source voltage.
Use one of the tabulated capacitance options (Specify
tabulated input, reverse transfer and output capacitance
or Specify
tabulated gate-source, gate-drain and drain-source capacitance
)
when the datasheet provides a plot of junction capacitances as a function
of drain-source voltage. Using tabulated capacitance values will give
more accurate dynamic characteristics, and avoids the need to iteratively
tune parameters to fit the dynamics.
If you use the Specify fixed gate-source, gate-drain
and drain-source capacitance
or Specify
tabulated gate-source, gate-drain and drain-source capacitance
option,
the Junction Capacitance tab lets you specify
the Gate-drain junction capacitance, Gate-source
junction capacitance, and Drain-source junction
capacitance parameter values (fixed or tabulated) directly.
Otherwise, the block derives them from the Input capacitance,
Ciss, Reverse transfer capacitance, Crss,
and Output capacitance, Coss parameter values.
These two parameterization methods are related as follows:
C_{GD} = Crss
C_{GS} = Ciss – Crss
C_{DS} = Coss – Crss
The two fixed capacitance options (Specify fixed
input, reverse transfer and output capacitance
or Specify
fixed gate-source, gate-drain and drain-source capacitance
)
let you model 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 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.
Note: Because this block implementation includes a charge model, you must model the impedance of the circuit driving the gate to obtain representative turn-on and turn-off dynamics. Therefore, if you are simplifying the gate drive circuit by representing it as a controlled voltage source, you must include a suitable series resistor between the voltage source and the gate. |
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:
$${K}_{Ts}={K}_{Tm1}{\left(\frac{{T}_{s}}{{T}_{m1}}\right)}^{BEX}$$
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, dV_{th}/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, R_{DS}(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 R_{DS}(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 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_{DS}(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 R_{DS}(on) value. Inconsistent values for R_{DS}(on) at the higher temperature will result in unphysical values for α and unrepresentative simulation results. Typically R_{DS}(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, 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_{DS}(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. R_{DS}(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. 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.
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.
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 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.
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_{DS}(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 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.
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 fixed input, reverse transfer
and output capacitance
— Provide fixed parameter
values from datasheet and let the block convert the input, output,
and reverse transfer capacitance values to junction capacitance values,
as described in Charge Model. This
is the default method.
Specify fixed gate-source, gate-drain
and drain-source capacitance
— Provide fixed
values for junction capacitance parameters directly.
Specify tabulated input, reverse transfer
and output capacitance
— Provide tabulated capacitance
and drain-source voltage values based on datasheet plots. The block
converts the input, output, and reverse transfer capacitance values
to junction capacitance values, as described in Charge Model.
Specify tabulated gate-source, gate-drain
and drain-source capacitance
— Provide tabulated
values for junction capacitances and drain-source voltage.
The gate-source capacitance with the drain shorted to the source. This parameter is visible only for the following two values for the Parameterization parameter:
If you select Specify fixed input, reverse
transfer and output capacitance
, the default value is 350
pF.
If you select Specify tabulated input,
reverse transfer and output capacitance
, the default
value is [720 700 590 470 390 310]
pF.
The drain-gate capacitance with the source connected to ground. This parameter is visible only for the following two values for the Parameterization parameter:
If you select Specify fixed input, reverse
transfer and output capacitance
, the default value is 80
pF.
If you select Specify tabulated input,
reverse transfer and output capacitance
, the default
value is [450 400 300 190 95 55]
pF.
The drain-source capacitance with the gate and source shorted. This parameter is visible only for the following two values for the Parameterization parameter:
If you select Specify fixed input, reverse
transfer and output capacitance
, the default value is 0
pF.
If you select Specify tabulated input,
reverse transfer and output capacitance
, the default
value is [900 810 690 420 270 170]
pF.
The value of the capacitance placed between the gate and the source. This parameter is visible only for the following two values for the Parameterization parameter:
If you select Specify fixed gate-source,
gate-drain and drain-source capacitance
, the default
value is 270
pF.
If you select Specify tabulated gate-source,
gate-drain and drain-source capacitance
, the default
value is [270 300 290 280 295 255]
pF.
The value of the capacitance placed between the gate and the drain. This parameter is visible only for the following two values for the Parameterization parameter:
If you select Specify fixed gate-source,
gate-drain and drain-source capacitance
, the default
value is 80
pF.
If you select Specify tabulated gate-source,
gate-drain and drain-source capacitance
, the default
value is [450 400 300 190 95 55]
pF.
The value of the capacitance placed between the drain and the source. This parameter is visible only for the following two values for the Parameterization parameter:
If you select Specify fixed gate-source,
gate-drain and drain-source capacitance
, the default
value is 0
pF.
If you select Specify tabulated gate-source,
gate-drain and drain-source capacitance
, the default
value is [450 410 390 230 175 115]
pF.
The drain-source voltages corresponding to the tabulated capacitance
values. This parameter is visible only for tabulated capacitance models
(Specify tabulated input, reverse transfer and output
capacitance
or Specify tabulated gate-source,
gate-drain and output capacitance
). The default value
is [0.1 0.3 1 3 10 30]
V.
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.
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.
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.
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_{DS}(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 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.
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 T_{s} at
which the device is simulated. The default value is 25
°C.
The block has the following ports:
G
Electrical conserving port associated with the transistor gate terminal
D
Electrical conserving port associated with the transistor drain terminal
S
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.