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Model N-Channel JFET
The N-Channel JFET block uses the Shichman and Hodges equations to represent an N-Channel JFET using a model with the following structure:
G is the transistor gate, D is the transistor drain, and S is the transistor source. The drain current, I_{D}, depends on the region of operation and whether the transistor is operating in normal or inverse mode.
In normal mode (V_{DS} ≥ 0), the block provides the following relationship between the drain current I_{D} and the drain-source voltage V_{DS}.
Region | Applicable Range of V_{GS} and V_{DS} Values | Corresponding I_{D} Equation |
---|---|---|
Off | V_{GS} – V_{t0} ≤ 0 | I_{D} = 0 |
Linear | 0 < V_{DS} < V_{GS} – V_{t0} | I_{D} = βV_{DS}(2(V_{GS} – V_{t0}) – V_{DS})(1 + λV_{DS}) |
Saturated | 0 < V_{GS} – V_{t0} ≤ V_{DS} | I_{D} = β (V_{GS} – V_{t0})^{2} (1 + λV_{DS}) |
In inverse mode (V_{DS} < 0), the block provides the following relationship between the drain current I_{D} and the drain-source voltage V_{DS}.
Region | Applicable Range of V_{GS} and V_{DS} Values | Corresponding I_{D} Equation |
---|---|---|
Off | V_{GS} – V_{t0} ≤ 0 | I_{D} = 0 |
Linear | 0 < –V_{DS} < V_{GS} – V_{t0} | I_{D} = βV_{DS}(2(V_{GD} – V_{t0}) + V_{DS})(1 – λV_{DS}) |
Saturated | 0 < V_{GS} – V_{t0} ≤ –V_{DS} | I_{D} = β (V_{GD} – V_{t0})^{2} (1 – λV_{DS}) |
In the preceding equations:
V_{GS} is the gate-source voltage.
V_{GD} is the gate-drain voltage.
V_{t0} is the threshold voltage. If you select Specify using equation parameters directly for the Parameterization parameter, V_{t0} is the Threshold voltage parameter value. Otherwise, the block calculates V_{t0} from the datasheet parameters you specify.
β is the transconductance parameter. If you select Specify using equation parameters directly for the Parameterization parameter, β is the Transconductance parameter parameter value. Otherwise, the block calculates β from the datasheet parameters you specify.
λ is the channel-length modulation parameter. If you select Specify using equation parameters directly for the Parameterization parameter, λ is the Channel-length modulation parameter value. Otherwise, the block calculates λ from the datasheet parameters you specify.
The currents in each of the diodes satisfy the exponential diode equation
$${I}_{GD}=IS\cdot \left({e}^{\frac{q{V}_{GD}}{k{T}_{m1}}}-1\right)$$
$${I}_{GS}=IS\cdot \left({e}^{\frac{q{V}_{GS}}{k{T}_{m1}}}-1\right)$$
where:
IS is the saturation current. If you select Specify using equation parameters directly for the Parameterization parameter, IS is the Saturation current parameter value. Otherwise, the block calculates IS from the datasheet parameters you specify.
q is the elementary charge on an electron (1.602176e–19 Coulombs).
k is the Boltzmann constant (1.3806503e–23 J/K).
T_{m1} is the measurement temperature. The value comes from the Measurement temperature parameter.
The block models gate junction capacitance as a fixed gate-drain capacitance C_{GD} and a fixed gate-source capacitance C_{GS}. If you select Specify using equation parameters directly for the Parameterization parameter, 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:
C_{GD} = Crss
C_{GS} = 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 measurement temperature value, T_{m1}, is replaced with the simulation temperature, T_{s}. The transconductance, β, and the threshold voltage, V_{t0}, become a function of temperature according to the following equations:
$${\beta}_{Ts}={\beta}_{Tm1}{\left(\frac{{T}_{s}}{{T}_{m1}}\right)}^{BEX}$$
V_{t0s} = V_{t01} + 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.
β_{Tm1} is JFET transconductance at the measurement temperature.
β_{Ts} is JFET transconductance at the simulation temperature. This is the transconductance value used in the JFET equations when temperature dependence is modeled.
V_{t01} is the threshold voltage at measurement temperature.
V_{t0s} is the threshold voltage at simulation temperature. This is the threshold voltage value used in the JFET 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 JFETS, 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 the saturated drain current, I_dss. 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 I_dss 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 fixed drain-source voltage plotted at more than one temperature, then you can also use Simulink^{®} Design Optimization™ software to help tune the values for α and BEX.
In addition, the saturation current term, IS, in the gate-drain and gate-source current equations depends on temperature
$$I{S}_{Ts}=I{S}_{Tm1}\cdot {({T}_{s}/{T}_{m1})}^{XTI}\cdot \mathrm{exp}\left(-\frac{EG}{k{T}_{s}}(1-{T}_{s}/{T}_{m1})\right)$$
where:
IS_{Tm1} is the saturation current at the measurement temperature.
IS_{Ts} is the saturation current at the simulation temperature. This is the saturation current value used in the bipolar transistor equations when temperature dependence is modeled.
EG is the energy gap.
k is the Boltzmann constant (1.3806503e–23 J/K).
XTI is the saturation current temperature exponent.
Similar to α, you have two ways of specifying EG and XTI:
If you parameterize the block from a datasheet, you have to specify the gate reverse current, I_gss, at a second measurement temperature. The block then calculates the value for EG based on this data and assuming a p-n junction nominal value of 3 for XTI.
If you parameterize by specifying equation parameters, you have to provide the values for EG and XTI directly. This option gives you most flexibility to match device behavior, for example, if you have a graph of I_gss as a function of temperature. With this data you can use Simulink Design Optimization software to help tune the values for EG and XTI.
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.
The model is based on the following assumptions:
This block does not allow you to specify initial conditions on the junction capacitances. If you select the Start simulation from steady state option in the Solver Configuration block, the block solves the initial voltages to be consistent with the calculated steady state. Otherwise, voltages are zero at the start of the simulation.
You may need to use nonzero ohmic resistance and junction capacitance values to prevent numerical simulation issues, but the simulation may run faster with these values set to zero.
The block does not account for temperature-dependent effects on the junction capacitances.
When you specify I_dss 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 I_dss value on the Main tab. Inconsistent values for I_dss at the higher temperature will result in unphysical values for α and unrepresentative simulation results.
You may need to tune the value of BEX to replicate the I_{D}-V_{GS} relationship (if available) for a given device. The value of BEX affects whether the I_{D}-V_{GS} curves for different temperatures cross each other, or not, for the ranges of I_{D} and V_{GS} considered.
Select one of the following methods for block parameterization:
Specify from a datasheet — Provide parameters that the block converts to equations that describe the transistor. This is the default method.
Specify using equation parameters directly — Provide equation parameters β, IS, V_{t0}, and λ.
The reverse current that flows in the diode when the drain and source are short-circuited and a large negative gate-source voltage is applied. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is -1 nA.
The current that flows when a large positive drain-source voltage is applied for a specified gate-source voltage. For a depletion-mode device, this gate-source voltage may be zero, in which case I_dss may be referred to as the zero-gate voltage drain current. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 3 mA.
A vector of the values of V_{GS} and V_{DS} at which I_dss is measured. Normally V_{GS} is zero. V_{DS} should be greater than zero. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is [ 0 15 ] V.
A vector of the values of g_fs and g_os. g_fs is the forward transfer conductance, that is, the conductance for a fixed drain-source voltage. g_os is the output conductance, that is, the conductance for a fixed gate-source voltage. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is [ 3e+03 10 ] uS.
A vector of the values of V_{GS} and V_{DS} at which g_fs and g_os are measured. V_{DS} should be greater than zero. For depletion-mode devices, V_{GS} is typically zero. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is [ 0 15 ] V.
The derivative of drain current with respect to gate voltage. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 1e-04 A/V^{2}.
The magnitude of the current that the ideal diode equation approaches asymptotically for very large reverse bias levels. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 1e-14 A.
The gate-source voltage above which the transistor produces a nonzero drain current. For an enhancement device, Vt0 should be positive. For a depletion mode device, Vt0 should be negative. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is -2 V.
The channel-length modulation. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 0 1/V.
The temperature for which the datasheet parameters are quoted. 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 0.01 Ω. The value must be greater than or equal to 0.
Select one of the following methods for block 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 Model junction capacitance parameter. The default value is 4.5 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 Model junction capacitance parameter. The default value is 1.5 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 Model junction capacitance parameter. The default value is 3 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 Model junction capacitance parameter. The default value is 1.5 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. You also have to provide a set of additional parameters depending on the block parameterization method. If you parameterize the block from a datasheet, you have to provide values for I_gss and I_dss at second measurement temperature. If you parameterize by directly specifying equation parameters, you have to provide the values for EG, XTI, and the gate threshold voltage temperature coefficient, dV_{t0}/dT. Regardless of the block parameterization method, you also have to provide values for BEX and for the simulation temperature, T_{s}.
The value of the gate reverse current, I_gss, at the 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 -200 nA.
The value of the saturated drain current, I_dss, at the second measurement temperature, and when the I_dss measurement point is the same as defined by the I_dss measurement point, [V_gs V_ds] parameter on the Main tab. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter on the Main tab. The default value is 2.5 mA.
Second temperature T_{m2} at which Gate reverse current, I_gss, at second measurement temperature and Saturated drain current, I_dss, at second measurement temperature are 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.
Energy gap value. 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 1.11 eV.
Saturation current temperature coefficient value. 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 3.
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 JFETs. 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.
[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.
[2] G. Massobrio and P. Antognetti. Semiconductor Device Modeling with SPICE. 2nd Edition, McGraw-Hill, 1993. Chapter 2.