N-Channel JFET

N-Channel junction field-effect transistor

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Libraries:
Simscape / Electrical / Semiconductors & Converters

Description

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 VGS and VDS Values	Corresponding ID Equation
  Off	VGS – Vt0 ≤ 0	ID = 0
  Linear	0 < VDS < VGS – Vt0	ID = βVDS(2(VGS – Vt0) – VDS)(1 + λVDS)
  Saturated	0 < VGS – Vt0 ≤ VDS	ID = β (VGS – Vt0)2 (1 + λVDS)

• 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 VGS and VDS Values	Corresponding ID Equation
  Off	VGD – Vt0 ≤ 0	ID = 0
  Linear	0 < –VDS < VGD – Vt0	ID = βVDS(2(VGD – Vt0) + VDS)(1 – λVDS)
  Saturated	0 < VGD – Vt0 ≤ –VDS	ID = β (VGD – Vt0)2 (1 – λVDS)

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

Modeling Temperature Dependence

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

$$I{S}_{Ts}=I{S}_{Tm1}\cdot {(T_s/T_{m1})}^{XTI}\cdot \exp \left(-\frac{EG}{k{T}_s}(1-T_s/T_{m1})\right)$$

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 gate diode 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.

Thermal Port

You can expose the thermal port to model the effects of generated heat and device temperature. To expose the thermal port, set the Modeling option parameter to either:

• No thermal port — The block does not contain a thermal port and does not simulate heat generation in the device.

• Show thermal port — The block contains a thermal port that allows you to model the heat that conduction losses generate. For numerical efficiency, the thermal state does not affect the electrical behavior of the block.

For more information on using thermal ports and on the Thermal Port parameters, see Simulating Thermal Effects in Semiconductors.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Use nominal values to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources. One of these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Plot Basic I-V Characteristics

You can plot the basic I-V characteristics of the N-Channel JFET block without building a complete model. Use the plots to explore the impact of your parameter choices on device characteristics. If you parameterize the block from a datasheet, you can compare your plots to the datasheet to check that you parameterized the block correctly. If you have a complete working model but do not know which manufactured part to use, you can compare your plots to datasheets to help you decide.

To enable this option, set the Modeling option parameter of the N-Channel JFET block to No thermal port. To plot the basic characteristics, right-click the block and select Electrical > Basic characteristics from the context menu. For more information about the Basic characteristics option, see Plot Basic I-V Characteristics of Semiconductor Blocks.

Examples

JFET Amplifier and Frequency Response Analysis

An audio amplifier circuit based on an N-channel JFET. The desired operating point is taken to be Vds=5V, Id=2mA and Vgs=-2V. The manufacturer datasheet gives the JFET forward transfer conductance and output conductance values as 3mS and 50uS. These values are used to populate the mask of the N-Channel JFET block.

• Open Model

Assumptions and Limitations

• 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.

Ports

Conserving

G — Gate terminal

electrical

Electrical conserving port associated with the transistor gate terminal.

D — Drain terminal

electrical

Electrical conserving port associated with the transistor drain terminal.

S — Source terminal

electrical

Electrical conserving port associated with the transistor source terminal.

H — Thermal port

thermal

Thermal conserving port.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Parameters

Modeling option — Whether to enable thermal port

No thermal port (default) | Show thermal port

Whether to enable the thermal port of the block and model the effects of generated heat and device temperature.

Main

Parameterization — Block parameterization

Specify from a datasheet (default) | Specify using equation parameters directly

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 — Gate reverse current

-1 nA (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter.

Saturated drain current, I_dss — Saturated drain current

3 mA (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter.

I_dss measurement point, [V_gs V_ds] — I_dss measurement point

[0, 15] V (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter.

Small-signal parameters, [g_fs g_os] — Small-signal parameters

[3000, 10] uSuS (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter.

Small-signal measurement point, [V_gs V_ds] — Small-signal measurement point

[0, 15] V (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter.

Transconductance parameter — Transconductance parameter

6.2e-4 AV2 (default)

The derivative of drain current with respect to gate voltage.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter.

Saturation current — Saturation current

5e-10 A (default)

The magnitude of the current that the ideal diode equation approaches asymptotically for very large reverse bias levels.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter.

Threshold voltage — Threshold voltage

-2.3 V (default)

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.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter.

Channel-length modulation — Channel-length modulation

0.003 1/V (default)

The channel-length modulation.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter.

Measurement temperature — Measurement temperature

25 degC (default)

The temperature for which the datasheet parameters are quoted.

Ohmic Resistance

Source ohmic resistance — Source ohmic resistance

0.0001 Ohm (default) | nonnegative scalar

The transistor source resistance.

Drain ohmic resistance — Drain ohmic resistance

0.01 Ohm (default) | nonnegative scalar

The transistor drain resistance.

Junction Capacitance

Parameterization — Junction capacitance parameterization

Specify from a datasheet (default) | Specify using equation parameters directly

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 — Input capacitance

4.5 pF (default)

The gate-source capacitance with the drain shorted to the source.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter in the Junction Capacitance tab.

Reverse transfer capacitance, Crss — Reverse transfer capacitance

1.5 pF (default)

The drain-gate capacitance with the source connected to ground.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter in the Junction Capacitance tab.

Gate-source junction capacitance — Gate-source junction capacitance

3 pF (default)

The value of the capacitance placed between the gate and the source.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter in the Junction Capacitance tab.

Gate-drain junction capacitance — Gate-drain junction capacitance

1.5 pF (default)

The value of the capacitance placed between the gate and the drain.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter in the Junction Capacitance tab.

Temperature Dependance

Parameterization — Temperature dependence parameterization

None — Simulate at parameter measurement temperature (default) | Model temperature dependence

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.

Gate reverse current, I_gss, at second measurement temperature — Gate reverse current at second measurement temperature

-200 nA (default)

The value of the gate reverse current, I_gss, at the second measurement temperature.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter on the Main tab.

Saturated drain current, I_dss, at second measurement temperature — Saturated drain current at second measurement temperature

2.5 mA (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter on the Main tab.

Second measurement temperature — Second measurement temperature

125 degC (default)

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.

Dependencies

This parameter is visible only when you select Specify from a datasheet for the Parameterization parameter on the Main tab.

Energy gap, EG — Energy gap

1.11 eV (default)

Energy gap value.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter on the Main tab.

Saturation current temperature exponent, XTI — Saturation current temperature exponent

3 (default)

Saturation current temperature coefficient value.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter on the Main tab.

Gate threshold voltage temperature coefficient, dVt0/dT — Gate threshold voltage temperature coefficient

-2 mV/K (default)

The rate of change of gate threshold voltage with temperature.

Dependencies

This parameter is visible only when you select Specify using equation parameters directly for the Parameterization parameter on the Main tab.

Mobility temperature exponent, BEX — Mobility temperature exponent

-1.5 (default)

Mobility temperature coefficient value. You can use the default value for most JFETs. See the Assumptions and Limitations section for additional considerations.

Device simulation temperature — Device simulation temperature

25 degC (default)

Temperature T_s at which the device is simulated.

References

[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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2008a

R2019b: Thermal network simlog paths

From R2019b forward, it is possible to model the thermal network of this block either internally or externally.

As a result, the simlog paths corresponding to the thermal network have changed. If you have a script that programmatically access the simlog, you have to manually update it to reflect these changes.