Engee documentation

PNP Bipolar Transistor

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NPN/PNP bipolar transistor with usage of extended Ebers-Moll equations.

blockType: AcausalElectricPowerSystems.Semiconductors.BJT

npn bipolar transistor

NPN Bipolar Transistor

Path in the library:

/Physical Modeling/Electrical/Semiconductors & Converters/NPN Bipolar Transistor

pnp bipolar transistor

PNP Bipolar Transistor

Path in the library:

/Physical Modeling/Electrical/Semiconductors & Converters/PNP Bipolar Transistor

Description

The PNP Bipolar Transistor and PNP Bipolar Transistor blocks use 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:

  • Earley effect.

  • Additional base, collector, and emitter resistors.

  • Additional fixed base-emitter and base-collector capacitances.

The collector and base currents are:

For PNP transistor β ,

ββ .

For NPN-transistor β ,

ββ ,

where

  • - are the base and collector currents (positive when flowing into the transistor);

  • - saturation current;

  • - base-emitter voltage and base-collector voltage respectively;

  • β - ideal maximum forward current gain ;

  • β - ideal maximum reverse current gain ;

  • - direct Earley voltage ;

  • - elementary charge of an electron (1.602176e-19 Cl);

  • - Boltzmann constant (1.3806503e-23 J/K).

  • - temperature of the transistor, determined by the value of the parameters Measurement temperature.

You can specify the behaviour of the transistor using datasheet parameters, which the block converts into equations describing the transistor, or you can set the equation parameters directly.

For an NPN transistor, if or , then the corresponding exponential values in the equations are replaced by и . For a PNP transistor, if or , then the corresponding exponential values in the equations are replaced with and . и respectively. This avoids the numerical problems associated with the gradient of the exponential function with a steep slope for large values of .

Similarly for an NPN transistor, if. or , then the corresponding exponential values in the equations are replaced by и . For a PNP transistor, if or , then the corresponding exponential values in the equations are replaced by и

Additionally, the base-emitter and base-collector junction capacitances can be set to fixed values. The base, collector and emitter connection resistances can also be set.

Capacitance and charge modelling

You model capacitance and charge using the parameters Base-collector junction capacitance and Base-emitter junction capacitance. You can also set the reverse recovery charge and its dynamics using the parameters Total forward transit time and Total reverse transit time. The equation that determines the base-collector charge:

,

where

  • - is the value of parameters Total reverse transit time;

  • - collector-emitter current;

  • - parameter value Base-collector junction capacitance;

  • - base-collector voltage.

The equation that determines the base-collector charge and capacitor current:

.

The equation that determines the base-emitter charge:

,

where

  • - is the value of parameters Total forward transit time;

  • - collector current;

  • - parameter value Base-emitter junction capacitance;

  • - base-emitter voltage.

The equation that determines the base-emitter charge and capacitor current:

.

Modelling the 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 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 β and β become a function of temperature according to the following equations:

,

ββ ,

ββ ,

where

  • - is the temperature at which the parameters of the transistor are set, determined by the value of the parameter Measurement temperature;

  • - is the simulation temperature;

  • - saturation current at the measurement temperature;

  • - saturation current at simulation temperature. It is this saturation current value that is used in the bipolar transistor equations when modelling the temperature dependence.

  • β and β are the forward and reverse gain factors at the measurement temperature;

  • β and β - forward and reverse gain factors at simulation temperature. These are the values used in the bipolar transistor equations when modelling temperature dependence;

  • - width of the forbidden zone for this type of semiconductor, measured in joules. For silicon, a value of 1.11 eV (electronvolts) is usually taken, where 1 eV is equal to 1.602e-19 Joules;

  • - is the temperature exponent of the saturation current;

  • - temperature coefficient of forward and reverse gain;

  • - Boltzmann constant (1.3806503e-23 J/K).

The corresponding values of 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

Conserving

# B — base contact
electricity

Details

An electrical port associated with the base contact of a transistor.

Program usage name

base

# C — collector contact
electricity

Details

An electrical port associated with the collector contact of a transistor.

Program usage name

collector

# E — emitter contact
electricity

Details

An electrical port associated with the emitter contact of a transistor.

Program usage name

emitter

Parameters

Main

# Transistor type — transistor type
NPN | PNP

Details

Selecting the transistor type - NPN or PNP.

Values

NPN | PNP
Default value

—
Program usage name

type
Evaluatable

No

# Parameterization — block parameterization
Specify from a datasheet | Specify from equation parameters directly

Details

Select one of the following block parameterization methods:

  • Specify from a datasheet - provide parameters that the block converts into equations that describe the transistor. The block calculates the direct Earley voltage as , where is the value of the parameter Collector current at which h-parameters are defined, and is the value of the parameter Output admittance, h_oe. The block sets to the small signal value Forward current transfer ratio, h_fe. The block calculates the saturation current from the set value of Voltage Vbe and Current Ib for voltage Vbe, when is 0. This method is used by default.

  • Specify from equation parameters directly - provide equation parameters , and .

Values

Specify from a datasheet | Specify from equation parameters directly
Default value

Specify from a datasheet
Program usage name

parameterization
Evaluatable

No

# Forward current transfer ratio, BF — forward current ratio

Details

The ideal maximum forward current gain.

Dependencies

To use this parameter, set the parameters Parameterization to . Specify from equation parameters directly.

Default value

100.0
Program usage name

beta_f
Evaluatable

Yes

# Saturation current, IS — saturation current
A | MA | kA | mA | nA | pA | uA

Details

The saturation current of a transistor.

Dependencies

To use this parameter, set the parameters Parameterization to . Specify from equation parameters directly.

Units

A | MA | kA | mA | nA | pA | uA
Default value

1e-14 A
Program usage name

I_sat
Evaluatable

Yes

# Forward Early voltage, VAF — direct Earley voltage
V | MV | kV | mV

Details

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

To use this parameter, set the Parameterization parameters to Specify from equation parameters directly.

Units

V | MV | kV | mV
Default value

200.0 V
Program usage name

V_A
Evaluatable

Yes

# Forward current transfer ratio, h_fe — forward current ratio

Details

The current gain of a small signal.

Dependencies

To use this parameter, set the Parameterization parameters to . Specify from a datasheet.

Default value

100.0
Program usage name

h_fe
Evaluatable

Yes

# Output admittance, h_oe — complex conductivity
S | mS | nS | uS | 1/Ohm

Details

The derivative of collector current versus collector-emitter voltage for a fixed base current.

Dependencies

To use this parameter, set the parameter Parameterization to . Specify from a datasheet.

Units

S | mS | nS | uS | 1/Ohm
Default value

5e-05 1/Ohm
Program usage name

h_oe
Evaluatable

Yes

# Collector current at which h-parameters are defined — collector current, at which h parameters are determined
A | MA | kA | mA | nA | pA | uA

Details

The h-parameters depend on the operating point and are determined for a given collector current value.

Dependencies

To use this parameter, set the parameters Parameterization to . Specify from a datasheet.

Units

A | MA | kA | mA | nA | pA | uA
Default value

—
Program usage name

I_c_h
Evaluatable

Yes

# Collector-emitter voltage at which h-parameters are defined — collector-emitter voltage, at which h parameters are determined
V | MV | kV | mV

Details

The h-parameters depend on the operating point and are determined for a given collector-emitter voltage.

Dependencies

To use this parameter, set the parameters Parameterization to . Specify from a datasheet.

Units

V | MV | kV | mV
Default value

—
Program usage name

V_ce_h
Evaluatable

Yes

# Voltage Vbe — base-emitter voltage
V | MV | kV | mV

Details

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

To use this parameter, set the parameter Parameterization to the value of Specify from a datasheet.

Units

V | MV | kV | mV
Default value

—
Program usage name

V_be
Evaluatable

Yes

# Current Ib for voltage Vbe — current Ib for voltage Vbe
A | MA | kA | mA | nA | pA | uA

Details

Base current when the base-emitter voltage is . 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

To use this parameter, set the parameter Parameterization to the value of Specify from a datasheet.

Units

A | MA | kA | mA | nA | pA | uA
Default value

—
Program usage name

I_be
Evaluatable

Yes

# Reverse current transfer ratio, BR — reverse current gain

Details

The ideal maximum reverse current gain. This value is often not listed on manufacturers' datasheets 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.

Default value

1.0
Program usage name

beta_r
Evaluatable

Yes

# Measurement temperature — measuring temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The temperature , at which and , or are measured.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

25.0 degC
Program usage name

T_measurement
Evaluatable

Yes

Ohmic Resistance

# Collector resistance, RC — collector resistance
Ohm | GOhm | MOhm | kOhm | mOhm

Details

Resistance at the collector.

Units

Ohm | GOhm | MOhm | kOhm | mOhm
Default value

0.01 Ohm
Program usage name

R_c
Evaluatable

Yes

# Emitter resistance, RE — emitter resistance
Ohm | GOhm | MOhm | kOhm | mOhm

Details

Resistance at the emitter.

Units

Ohm | GOhm | MOhm | kOhm | mOhm
Default value

1e-4 Ohm
Program usage name

R_e
Evaluatable

Yes

# Zero bias base resistance, RB — base resistance at zero offset
Ohm | GOhm | MOhm | kOhm | mOhm

Details

Resistance at the base at zero offset.

Units

Ohm | GOhm | MOhm | kOhm | mOhm
Default value

1.0 Ohm
Program usage name

R_b
Evaluatable

Yes

Capacitance

# Base-collector junction capacitance — base-collector junction capacitance
F | mF | nF | pF | uF

Details

Parasitic capacitance at the base-collector junction.

Units

F | mF | nF | pF | uF
Default value

5.0 pF
Program usage name

C_bc
Evaluatable

Yes

# Base-emitter junction capacitance — base-emitter junction capacitance
F | mF | nF | pF | uF

Details

Parasitic capacitance at the base-emitter junction.

Units

F | mF | nF | pF | uF
Default value

5.0 pF
Program usage name

C_be
Evaluatable

Yes

# Total forward transit time — total forward travel time
d | s | hr | ms | ns | us | min

Details

Represents the average transit time of non-basic carriers through the base region from emitter to collector and is often denoted by the parameters TF.

Units

d | s | hr | ms | ns | us | min
Default value

0.0 us
Program usage name

forward_transit_time
Evaluatable

Yes

# Total reverse transit time — total return time
d | s | hr | ms | ns | us | min

Details

Represents the average transit time of non-basic carriers through the base region from collector to emitter and is often denoted by the parameters .

Units

d | s | hr | ms | ns | us | min
Default value

0.0 us
Program usage name

reverse_transit_time
Evaluatable

Yes

Temperature Dependence

# Model Temperature Dependence — temperature dependence modelling

Details

If the checkbox is unchecked (by default), the temperature dependence is not modelled and the parameters are used at the temperature , set by the parameter Measurement temperature.

If you select this check box, you must also specify a set of additional parameters depending on the method of parameterising 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 measuring temperature. If you parameterise the block by specifying the parameters of the equation directly, you must specify the values for , and .

Default value

false (switched off)
Program usage name

temperature_dependence
Evaluatable

No

# Forward current transfer ratio, h_fe, at second measurement temperature — forward current transfer coefficient, hfe, at the second measurement temperature

Details

The small-signal current gain factor at the second measurement temperature. It should be specified at the same collector-emitter voltages and collector current as for the parameters Forward current transfer ratio, h_fe.

Dependencies

To use this parameter, set the parameters Parameterization to Specify from a datasheet.

Default value

125.0
Program usage name

h_fe_T2
Evaluatable

Yes

# Voltage Vbe at second measurement temperature — voltage Vbe at the second measurement temperature
V | MV | kV | mV

Details

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

To use this parameter, set the parameters Parameterization to the value of Specify from a datasheet.

Units

V | MV | kV | mV
Default value

—
Program usage name

V_be_T2
Evaluatable

Yes

# Current Ib for voltage Vbe at second measurement temperature — current Ib for voltage Vbe at the second measurement temperature
A | MA | kA | mA | nA | pA | uA

Details

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

To use this parameter, set the parameter Parameterization to the value of Specify from a datasheet.

Units

A | MA | kA | mA | nA | pA | uA
Default value

—
Program usage name

I_be_T2
Evaluatable

Yes

# Second measurement temperature — second measurement temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The second temperature , at which и . are measured.

Dependencies

To use this parameter, set the parameters Parameterization to Specify from a datasheet.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

125.0 degC
Program usage name

T2
Evaluatable

Yes

# Current gain temperature coefficient, XTB — temperature current gain

Details

The value of the temperature current gain.

Dependencies

To use this parameter, set the parameters Parameterization to . Specify from equation parameters directly.

Default value

0.0
Program usage name

XTB
Evaluatable

Yes

# Energy gap, EG — forbidden band width
Btu_IT | J | MJ | MWh | Wh | eV | kJ | kWh | mJ | mWh

Details

The value of the forbidden zone width.

Dependencies

To use this parameter, set the Parameterization parameters to . Specify from equation parameters directly.

Units

Btu_IT | J | MJ | MWh | Wh | eV | kJ | kWh | mJ | mWh
Default value

1.11 eV
Program usage name

E_g
Evaluatable

Yes

# Saturation current temperature exponent, XTI — temperature exponent of saturation current

Details

The value of the temperature exponent of the saturation current.

Dependencies

To use this parameter, set the parameters Parameterization to . Specify from equation parameters directly.

Default value

3.0
Program usage name

XTI
Evaluatable

Yes

# Device simulation temperature — device modelling temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The temperature , at which the device is simulated.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

25.0 degC
Program usage name

T_device
Evaluatable

Yes

Literature

  1. G. Massobrio and P. Antognetti. Semiconductor Device Modeling with SPICE . 2nd Edition, McGraw-Hill, 1993.

  2. H. Ahmed and P.J. Spreadbury. Analogue and digital electronics for engineers. 2nd Edition, Cambridge UniversityPress, 1984.

Examples