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NPN Bipolar Transistor - Model NPN bipolar transistor using enhanced Ebers-Moll equations

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Semiconductor Devices

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:

Where:

I_B and I_C are base and collector currents, defined as positive into the device.
V_be is the base-emitter voltage and V_bc is the base-collector voltage.
β_F is the ideal maximum current gain BF
β_R is the ideal maximum 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 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 or , the corresponding exponential terms in the equations are replaced with and , respectively. This helps prevent numerical issues associated with the steep gradient of the exponential function e^x at large values of x. Similarly, if or then the corresponding exponential terms in the equations are replaced with and , respectively.

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

Basic Assumptions and Limitations

The NPN Bipolar Transistor model has the following limitations:

This block does not model temperature-dependent effects. SimElectronics simulates the block at the temperature at which the component behavior was measured, as specified by the Measurement temperature parameter value.
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.

Dialog Box and Parameters

Main Tab

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. 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 [2]. 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.

Forward current transfer ratio h_fe

Small-signal current gain. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 100.

Output admittance h_oe

Derivative of the collector current with respect to the collector-emitter voltage for a fixed base current. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 5e-05 1/Ω.

Collector current at which h-parameters are defined

The h-parameters vary with operating point, and are defined for this value of the collector current. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 1 mA.

Voltage Vbe

Base-emitter voltage when the collector current is zero and the base current is Ib. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 0.55 V.

Current Ib for voltage Vbe

Base current when the base-emitter voltage is Vbe and the collector current is zero. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 0.5 mA.

Forward current transfer ratio BF

Ideal maximum forward current gain. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 100.

Saturation current IS

Transistor saturation current. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 1e-14 A.

Forward Early voltage VAF

In the standard Ebers-Moll equations, the gradient of the Ic versus Vce curve is zero in the normal active region. The additional forward Early voltage term increases this gradient. The intercept on the Vce-axis is equal to –VAF when the linear region is extrapolated. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 200 V.

Reverse current transfer ratio BR

Ideal maximum reverse current gain. This value is often not quoted in manufacturer datasheets, because it is not significant when the transistor is biased to operate in the normal active region. When the value is not known and the transistor is not to be operated on the inverse region, use the default value of 1.

Measurement temperature

Temperature at which Vbe and Ib or IS are measured. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 25 °C.

Ohmic Resistance Tab

Collector resistance RC: Resistance at the collector. The default value is 0.1 Ω.
Emitter resistance RE: Resistance at the emitter. The default value is 0.1 Ω.
Zero bias base resistance RB: Resistance at the base at zero bias. The default value is 0.1 Ω.

Junction Capacitance Tab

Base-collector capacitance: Parasitic capacitance across the base-collector junction. The default value is 5 pF.
Base-emitter capacitance: Parasitic capacitance across the base-emitter junction. The default value is 5 pF.

Ports

The block has the following ports:

B: Electrical conserving port associated with the transistor base terminal.
C: Electrical conserving port associated with the transistor collector terminal.
E: Electrical conserving port associated with the transistor emitter terminal.