Model N-Channel JFET

Semiconductor Devices

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}ValuesCorresponding *I*_{D}EquationOff

*V*_{GS}–*V*_{t0}≤ 0*I*_{D}= 0Linear

0 <

*V*_{DS}<*V*_{GS}–*V*_{t0}*I*_{D}=*β**V*_{DS}(2(*V*_{GS}–*V*_{t0}) –*V*_{DS})(1 +*λ**V*_{DS})Saturated

0 <

*V*_{GS}–*V*_{t0}≤*V*_{DS}*I*_{D}=*β*(*V*_{GS}–*V*_{t0})^{2}(1 +*λ**V*_{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}ValuesCorresponding *I*_{D}EquationOff

*V*_{GD}–*V*_{t0}≤ 0*I*_{D}= 0Linear

0 < –

*V*_{DS}<*V*_{GD}–*V*_{t0}*I*_{D}=*β**V*_{DS}(2(*V*_{GD}–*V*_{t0}) +*V*_{DS})(1 –*λ**V*_{DS})Saturated

0 <

*V*_{GD}–*V*_{t0}≤ –*V*_{DS}*I*_{D}=*β*(*V*_{GD}–*V*_{t0})^{2}(1 –*λ**V*_{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 the*IS***Saturation current**parameter value. Otherwise, the block calculatesfrom the datasheet parameters you specify.*IS**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

`Specify using equation parameters directly`

for
the *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,*d**V*_{th}/*d**T*.

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.

**Parameterization**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*.

**Gate reverse current, I_gss**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.**Saturated drain current, I_dss**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.**I_dss measurement point, [V_gs V_ds]**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.**Small-signal parameters, [g_fs g_os]**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.**Small-signal measurement point, [V_gs V_ds]**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.**Transconductance parameter**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}.**Saturation current**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.**Threshold voltage**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.**Channel-length modulation**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.**Measurement temperature**The temperature for which the datasheet parameters are quoted. 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

`0.01`

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

.

**Parameterization**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.

**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**Model junction capacitance**parameter. The default value is`4.5`

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**Model junction capacitance**parameter. The default value is`1.5`

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**Model junction capacitance**parameter. The default value is`3`

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**Model junction capacitance**parameter. The default value is`1.5`

pF.

**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. 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,*d**V*_{t0}/*d**T*. Regardless of the block parameterization method, you also have to provide values for*BEX*and for the simulation temperature,*T*_{s}.

**Gate reverse current, I_gss, at second measurement temperature**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.**Saturated drain current, I_dss, at second measurement temperature**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 measurement temperature**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, EG**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 exponent, XTI**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`

.**Gate threshold voltage temperature coefficient, dVt0/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 JFETs. 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.

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.

[2] G. Massobrio and P. Antognetti. *Semiconductor
Device Modeling with SPICE*. 2nd Edition, McGraw-Hill,
1993. Chapter 2.

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