NPN Bipolar Transistor

NPN bipolar transistor using enhanced Ebers-Moll equations

Libraries:
Simscape / Electrical / Semiconductors & Converters

Description

The NPN Bipolar Transistor block uses a variant of the Ebers-Moll equations to represent an NPN bipolar transistor. The Ebers-Moll equations are based on two exponential diodes plus two current-controlled current sources. The NPN Bipolar Transistor block provides the following enhancements to that model:

Early voltage effect
Optional base, collector, and emitter resistances.
Optional fixed base-emitter and base-collector capacitances.

The collector and base currents are:

$\begin{array}{l} I_{C} = I S [(e^{q V_{B E} / (k T_{m 1})} - e^{q V_{B C} / (k T_{m 1})}) (1 - \frac{V_{B C}}{V_{A}}) - \frac{1}{β_{R}} (e^{q V_{B C} / (k T_{m 1})} - 1)] \\ I_{B} = I S [\frac{1}{β_{F}} (e^{q V_{B E} / (k T_{m 1})} - 1) + \frac{1}{β_{R}} (e^{q V_{B C} / (k T_{m 1})} - 1)] \end{array}$

Where:

I_B and I_C are base and collector currents, defined as positive into the device.
IS is the saturation current.
V_BE is the base-emitter voltage and V_BC is the base-collector voltage.
β_F is the ideal maximum forward current gain BF
β_R is the ideal maximum reverse current gain BR
V_A is the forward Early voltage VAF
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 transistor temperature, as defined by the Measurement temperature parameter value.

You can specify the transistor behavior using datasheet parameters that the block uses to calculate the parameters for these equations, or you can specify the equation parameters directly.

If qV_BC / (kT_m1) > 40 or qV_BE / (kT_m1) > 40, the corresponding exponential terms in the equations are replaced with (qV_BC / (kT_m1) – 39)e⁴⁰ and (qV_BE / (kT_m1) – 39)e⁴⁰, respectively. This helps prevent numerical issues associated with the steep gradient of the exponential function e^x at large values of x. Similarly, if qV_BC / (kT_m1) < –39 or qV_BE / (kT_m1) < –39 then the corresponding exponential terms in the equations are replaced with (qV_BC / (kT_m1) + 40)e^–39 and (qV_BE / (kT_m1) + 40)e^–39, respectively.

Optionally, you can specify fixed capacitances across the base-emitter and base-collector junctions. You also have the option to specify base, collector, and emitter connection resistances.

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 saturation current, IS, and the forward and reverse gains (β_F and β_R) become a function of temperature according to the following equations:

$I S_{T s} = I S_{T m 1} \cdot {(T_{s} / T_{m 1})}^{X T I} \cdot \exp (- \frac{E G}{k T_{s}} (1 - T_{s} / T_{m 1}))$

$β_{F s} = β_{F m 1} {(\frac{T_{s}}{T_{m 1}})}^{X T B}$

$β_{R s} = β_{R m 1} {(\frac{T_{s}}{T_{m 1}})}^{X T B}$

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.
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.
β_Fm1 and β_Rm1 are the forward and reverse gains at the measurement temperature.
β_Fs and β_Rs are the forward and reverse gains at the simulation temperature. These are the values used in the bipolar transistor equations when temperature dependence is modeled.
EG is the energy gap for the semiconductor type measured in Joules. The value for silicon is usually taken to be 1.11 eV, where 1 eV is 1.602e-19 Joules.
XTI is the saturation current temperature exponent.
XTB is the forward and reverse gain temperature coefficient.
k is the Boltzmann constant (1.3806503e–23 J/K).

Appropriate values for XTI and EG depend on the type of transistor and the semiconductor material used. In practice, the values of XTI, EG, and XTB need tuning to model the exact behavior of a particular transistor. Some manufacturers quote these tuned values in a SPICE Netlist, and you can read off the appropriate values. Otherwise you can determine values for XTI, EG, and XTB by using a datasheet-defined data at a higher temperature T_m2. The block provides a datasheet parameterization option for this.

You can also tune the values of XTI, EG, and XTB yourself, to match lab data for your particular device. You can use Simulink^® Design Optimization™ software to help tune the values.

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 prior to 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.

Nominal values provide a way 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 which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

NPN Bipolar Transistor Characteristics

Generation of the Ic versus Vce curve for an NPN bipolar transistor. Define the vector of base currents and minimum and maximum collector-emitter voltages by double clicking on the block labeled 'Define Conditions (Ib and Vce)'. Run the tests and generate plots of the curves by clicking in the model on hyperlink 'plot curves'.

Open Model

Assumptions and Limitations

The block does not account for temperature-dependent effects on the junction capacitances.
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.

Ports

Conserving

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B — Base terminal
electrical

Electrical conserving port associated with the transistor base terminal

C — Collector terminal
electrical

Electrical conserving port associated with the transistor collector terminal

E — Emitter terminal
electrical

Electrical conserving port associated with the transistor emitter terminal

H — Thermal port
thermal

Thermal conserving port.

Dependencies

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

Parameters

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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. The block calculates the forward Early voltage VAF as Ic/h_oe, where Ic is the Collector current at which h-parameters are defined parameter value, and h_oe is the Output admittance h_oe parameter value [1]. The block sets BF to the small-signal Forward current transfer ratio h_fe value. The block calculates the saturation current IS from the specified Voltage Vbe value and the corresponding Current Ib for voltage Vbe value when Ic is zero. This is the default method.
Specify using equation parameters directly — Provide equation parameters IS, BF, and VAF.