NPN Bipolar Transistor
NPN / PNP bipolar transistor using extended Ebers-Moll equations.
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Description
The Bipolar Transistor block uses a variant of the Ebers-Moll equations to represent a bipolar transistor. The Ebers-Moll equations are based on two exponential diodes and two current controlled current sources. The block uses the following enhancements to this model:
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Earley effect.
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Additional base, collector, and emitter resistors.
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Additional fixed base-emitter and base-collector capacitances.
The collector and base currents are:
For PNP transistor
For NPN transistor
where:
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- base and collector currents (positive when flowing into the transistor).
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- saturation current.
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- base-emitter voltage and base-collector voltage respectively.
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- ideal maximum forward current gain .
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- ideal maximum reverse current gain .
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- Earley forward voltage .
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- The elementary charge of an electron (`1.602176e-19 Coulomb).
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- Boltzmann constant (`1.3806503e-23 J/K).
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- Transistor temperature, determined by the value of the Measurement temperature parameter.
Modelling of temperature dependence
By default, the temperature dependence is not modelled and the device is simulated at the temperature for which the block parameters are set. It is optionally possible to enable the simulation of the temperature dependence of the static behaviour of the transistor during the simulation. The temperature dependence of the junction capacitances is not modelled, as this has a much smaller effect.
When the temperature dependence is taken into account, the governing equations of the transistor remain the same. The measurement temperature value, , is replaced by the simulation temperature, . The saturation current, , and the forward and reverse gain coefficients and become a function of temperature according to the following equations:
Where:
- The temperature at which the transistor parameters are set, determined by the value of the Measurement temperature parameter.
- simulation temperature.
- saturation current at the measurement temperature.
- saturation current at the simulation temperature. It is this value of saturation current that is used in the bipolar transistor equations when modelling the temperature dependence.
and are the forward and reverse gain factors at the measurement temperature.
and - forward and reverse gain factors at simulation temperature. These are the values used in the bipolar transistor equations when modelling temperature dependence.
- energy gap for a given type of semiconductor, measured in joules. For silicon, a value of 1.11 eV (electronvolts) is usually adopted, where 1 eV is equal to 1.602e-19 Joules.
- temperature exponent of the saturation current.
- temperature coefficient of forward and reverse gain.
The respective values and depend on the type of transistor and the semiconductor material used. In practice, the values , and need to be adjusted to simulate the exact behaviour of a particular transistor. Some manufacturers specify them in the SPICE Netlist (component connection list), where these values can be referred to. Otherwise, it is possible to determine the values , and , using the data specified in the data sheet, at a higher temperature . For this purpose, the block has a parameterization option according to the technical data sheet.
Ports
Non-directional
B - base contact
electricity
An electrical port associated with the base contact of a transistor.
C is the collector contact
electricity
The electrical port associated with the collector contact of a transistor.
E is the emitter contact
electricity
The electrical port associated with the emitter contact of a transistor.
Parameters
Main
Transistor type - transistor type
NPN (by default) | PNP
Selects whether the transistor type is NPN or PNP.
parameterization - block parameterization
Specify from a datasheet (by default) | `Specify using equation parameters directly `
Select one of the following methods for block parameterization:
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Specify from a datasheet- provide parameters that the block converts into equations that describe the transistor. The block calculates the forward Earley voltage as , where is the collector current at which the h-parameter value is determined and is the value of the complex conductance parameter. The block sets to the small-signal value of the direct current transfer coefficient . The block calculates the saturation current for the set value of voltage and the appropriate current for the voltage value when is0. This method is used by default. -
Specify using equation parameters directly- provide equation parameters , and .
Forward current transfer ratio hfe - forward current transfer ratio
100 (By default)
Small signal current gain ratio.
Dependencies
This parameter is only used when the Specify from a datasheet option is selected for the Parameterization parameter.
Output admittance h_oe - complex conductance
50e-6 1/ohm (by default).
The derivative of collector current versus collector-emitter voltage for a fixed base current.
Dependencies
This parameter is only used when Specify from a datasheet is selected for parameterization.
Collector current at which h-parameters are defined - collector current at which h-parameters are defined
1 mA (by default).
The h-parameters depend on the operating point and are defined for a given value of collector current.
Dependencies
This parameter is only used when Specify from a datasheet is selected for the Parameterization parameter.
Collector-emitter voltage at which h-parameters are defined - collector-emitter voltage at which h-parameters are defined
5 V (By default).
h-parameters depend on the operating point and are defined for a given value of collector-emitter voltage.
Dependencies
This parameter is only used when the Specify from a datasheet option is selected for the Parameterization parameter.
Voltage V_be - base-emitter voltage
0.55 V (by default).
Base-emitter voltage at base current . The data pair ] should be given for the case where the transistor is in the normal active region, i.e. not in the saturated region.
Dependencies
This parameter is only used when the Specify from a datasheet option is selected for the Parameterization parameter.
Current Ib for voltage Vbe - current Ib for voltage Vbe
0.5 mA (By default)
Base current when the base-emitter voltage is equal to . The data pair ] should be given for the case when the transistor is in the normal active region, i.e., not in the saturated region.
Dependencies
This parameter is only used when the Specify from a datasheet option is selected for the Parameterization parameter.
Forward current transfer ratio BF - forward current transfer ratio
100 (By default).
Ideal maximum forward current transfer ratio.
Dependencies
This parameter is only used when Specify using equation parameters directly is selected for the Parameterization parameter.
Saturation current IS - saturation current
1e-14 A (By default).
Transistor saturation current.
Dependencies
This parameter is only used when Specify using equation parameters directly is selected for the Parameterization parameter.
Forward Early voltage VAF - forward Earley voltage
200 V (by default).
In the standard Ebers-Moll equations, the gradient of the versus curve is zero in the normal active region. The additional direct Earley voltage increases this gradient. When extrapolating the linear region, the intercept on the axis is equal to − .
Dependencies
This parameter is only used when Specify using equation parameters directly is selected for the Parameterization parameter.
Reverse current transfer ratio BR - reverse current transfer ratio
1 (By default).
The ideal maximum reverse current gain. This value is often omitted from manufacturers' data sheets because it is not essential when the transistor is biased to operate in the normal active region. If the value is unknown and the transistor should not operate in the inverse region, use the default value of 1.
Measurement temperature - measurement temperature
25 °C (By default).
Temperature , at which and , or are measured.
Ohmic resistance
Collector resistance RC - collector resistance
`0.01 ohm (by default)
Collector resistance.
Emitter resistance RE - emitter resistance
1e-4 ohms (by default).
Emitter resistance.
Zero bias base resistance RB - base resistance at zero bias
`1 ohm (by default).
Resistance on the base at zero offset.
Capacitive
Base-collector junction capacitance - base-collector junction capacitance
`5 pF (by default).
The parasitic capacitance at the base-collector junction.
Base-emitter junction capacitance - base-emitter junction capacitance
`5 pF (by default).
Parasitic capacitance at the base-emitter junction.
Total forward transit time - total forward transit time
0 (By default)
Represents the average transit time of non-basic carriers through the base region from emitter to collector and is often denoted by the parameter TF.
Total reverse transit time - total reverse transit time
`0 (By default)
It represents the average time for non-basic carriers to pass through the base region from collector to emitter and is often denoted by the parameter TR.
Temperature dependence
Model temperature dependence - modelling of temperature dependence
off (by default) | on
Whether the temperature dependence is modelled.
If the checkbox is unchecked (by default), the temperature dependence is not modelled and the parameter values at the temperature set by the Measurement temperature parameter are used.
If you select this check box, you must also specify a set of additional parameters depending on the method used to parameterise the block. If you parameterise the block from the data sheet, you must specify the values for the second data pair ] and at the second measurement temperature. If you parameterise the block by specifying the equation parameters directly, you must specify the values for , and .
Forward current transfer ratio, hfe, at second measurement temperature - forward current transfer ratio, hfe, at second measurement temperature
125 (By default)
The small signal current gain factor at the second measurement temperature. It must be specified at the same collector-emitter voltage and collector current as for the Forward current transfer ratio parameter on the Main tab.
Dependencies
This parameter is only visible if `Specify from a datasheet' is selected for the Parameterization parameter on the Main tab.
Voltage Vbe at second measurement temperature - voltage Vbe at second measurement temperature
0.45 V (by default)
Base-emitter voltage when the base current is , and the temperature is set to the second measurement temperature. The data pair should be specified for the case when the transistor is in the normal active region, i.e., not in the saturation region.
Dependencies
This parameter is only visible if Specify from a datasheet is selected for the Parameterization parameter on the Main tab.
Current Ib for voltage Vbe at second measurement temperature - current Ib for voltage Vbe at second measurement temperature
0.5 mA (By default)
Base current when the base-emitter voltage is , and the temperature is set to the second measurement temperature. The data pair should be given for the case when the transistor is in the normal active region, that is, not in the saturation region.
Dependencies
This parameter is only visible if Specify from a datasheet is selected for the Parameterization parameter on the Main tab.
Second measurement temperature - second measurement temperature
125 °C (By default).
The second temperature , at which are measured.
Dependencies
This parameter is only visible if Specify from a datasheet is selected for the Parameterization parameter on the Main tab.
Current gain temperature coefficient, XTB - current gain temperature coefficient
0 (By default).
Current gain temperature coefficient value.
Dependencies
This parameter is only visible if Specify using equation parameters directly is selected for the Parameterization parameter on the Main tab.
Energy gap, EG - energy gap
1.11 eV (by default).
Value of energy gap.
Dependencies
This parameter is visible only if `Specify using equation parameters directly' is selected for the Parameterization parameter on the Main tab.
Saturation current temperature exponent, XTI - saturation current temperature exponent
3 (By default).
Value of saturation current temperature exponent.
Dependencies
This parameter is only visible if `Specify using equation parameters directly' is selected for the Parameterization parameter on the Main tab.
Device simulation temperature - device simulation temperature
25 °C (By default).
Temperature , at which the device is simulated.