SimElectronics™

NPN - Model Gummel-Poon NPN Transistor

Library

SPICE-Compatible Semiconductors

Description

The NPN block represents a SPICE-compatible four-terminal Gummel-Poon NPN transistor. The substrate port is connected to the transistor body using a capacitor, so these devices are equivalent to a three-terminal transistor when you connect the substrate port to any other port and use the default value of zero for the C-S junction capacitance, CJS parameter.

The NPN block model includes the following components:

• Current-Voltage and Base Charge Model

• Base Resistance Model

• Transit Charge Modulation Model

• Junction Charge Model

• Temperature Dependence

Current-Voltage and Base Charge Model

The current-voltage relationships and base charge relationships for the transistor are calculated adjusting the applicable model parameters for temperature as described in the following sections:

• Base-Emitter and Base-Collector Junction Currents

• Terminal Currents

• Base Charge Model

Base-Emitter and Base-Collector Junction Currents

The base-emitter junction current is calculated using the following equations:

• When :

  

• When

  

The base-collector junction current is calculated using the following equations:

• When :

  

• When

  

In the preceding equations:

• V_BE is the base-emitter voltage and V_BC is the base-collector voltage.

• 

• ISC and ISE are the B-C leakage current, ISC and B-E leakage current, ISE parameter values, respectively.

• NE, NC, NF, and NR are the B-E emission coefficient, NE, B-C emission coefficient, NC, Forward emission coefficient, NF and Reverse emission coefficient, NR parameter values, respectively.

• q is the elementary charge on an electron.

• k is the Boltzmann constant.

• T is the transistor temperature:

  • If you select Device temperature for the Model temperature dependence using parameter, T is the sum of the Circuit temperature value plus the Offset local circuit temperature, TOFFSET parameter value. The Circuit temperature value comes from the SPICE Environment Parameters block, if one exists in the circuit. Otherwise, it comes from the default value for this block.

  • If you select Fixed temperature for the Model temperature dependence using parameter, T is the Fixed circuit temperature, TFIXED parameter value.

• G_min is the minimum conductance. By default, G_min matches the Minimum conductance GMIN parameter of the SPICE Environment Parameters block, whose default value is 1e-12. To change G_min, add a SPICE Environment Parameters block to your model and set the Minimum conductance GMIN parameter to the desired value.

Terminal Currents

The terminal currents, I_B and I_C are the base and collector currents, defined as positive into the device. They are calculated as:

where BF and BR are the Forward beta, BF and Reverse beta, BR parameter values, respectively.

Base Charge Model

The base charge, q_b, is calculated using the following equations:

where

• VAF and VAR are the Forward Early voltage, VAF and Reverse Early voltage, VAR parameters, respectively.

• IKF and IKR are the Forward knee current, IKF and Reverse knee current, IKR parameter values, respectively.

• eps is 1e-4.

Base Resistance Model

The block models base resistance in one of two ways:

• If you use the default value of infinity for the Half base resistance cur, IRB parameter, the NPN block calculates the base resistance r_bb as

  

  where:

  • RBM is the Minimum base resistance, RBM parameter value.

  • RB is the Zero-bias base resistance, RB parameter value.

• If you specify a finite value for the Half base resistance cur, IRB parameter, the NPN block calculates the base resistance r_bb as

  

  where

  

Transit Charge Modulation Model

If you specify nonzero values for the Coefficient of TF, XTF parameter, the block models transit charge modulation by scaling the Forward transit time, TF parameter value as follows:

where ITF is the Coefficient of TF, ITF parameter value.

Junction Charge Model

The block lets you model junction charge. The base-collector charge Q_bc and the base-emitter charge Q_be depend on an intermediate value, Q_dep as follows, after adjusting the applicable model parameters for temperature:

• For the internal base-emitter junctions:

  

• For the internal base-collector junctions:

  

• For the external base-collector junctions:

  

Q_dep depends on the junction voltage, V_jct (V_BE for the base-emitter junction and V_BC for the base-collector junction) as follows.

Applicable Range of Vjct Values	Corresponding Qdep Equation

Where:

• FC is the Capacitance coefficient FC parameter value.

• VJ is:

  • The B-E built-in potential, VJE parameter value for the base-emitter junction.

  • The B-C built-in potential, VJC parameter value for the base-collector junction.

• MJ is:

  • The B-E exponential factor, MJE parameter value for the base-emitter junction.

  • The B-C exponential factor, MJC parameter value for the base-collector junction.

• C_jct is:

  • The B-E depletion capacitance, CJE parameter value for the base-emitter junction.

  • The B-C depletion capacitance, CJC parameter value for the base-collector junction.

• 

• 

• 

The collector-substrate charge Q_cs depends on the collector-substrate voltage V_cs as follows, after adjusting the applicable model parameters for temperature.

Applicable Range of Vcs Values	Corresponding Qcs Equation

where:

• CJS is the C-S junction capacitance, CJS parameter value.

• VJS is the Substrate built-in potential, VJS parameter value.

• MJS is the Substrate exponential factor, MJS parameter value.

Temperature Dependence

Several transistor parameters depend on temperature. There are two ways to specify the transistor temperature:

• When you select Device temperature for the Model temperature dependence using parameter, the transistor temperature is

  

  where:

  • T_C is the Circuit temperature parameter value from the SPICE Environment Parameters block. If this block doesn't exist in the circuit, T_C is the default value of this parameter.

  • T_O is the Offset local circuit temperature, TOFFSET parameter value.

• When you select Fixed temperature for the Model temperature dependence using parameter, the transistor temperature is the Fixed circuit temperature, TFIXED parameter value.

The block provides the following relationship between the saturation current IS and the transistor temperature T:

where:

• IS is the Transport saturation current, IS parameter value.

• T_meas is the Parameter extraction temperature, TMEAS parameter value.

• XTI is the Temperature exponent for IS, XTI parameter value.

• EG is the Energy gap, EG parameter value.

• V_t = kT/q.

The block provides the following relationship between the base-emitter junction potential VJE and the transistor temperature T:

where:

• VJE is the B-E built-in potential, VJE parameter value.

• 

• 

The block uses the VJE(T) equation to calculate the base-collector junction potential by substituting VJC (the B-C built-in potential, VJC parameter value) for VJE.

The block provides the following relationship between the base-emitter junction capacitance CJE and the transistor temperature T:

where:

• CJE is the B-E depletion capacitance, CJE parameter value.

• MJE is the B-E exponential factor, MJE parameter value.

The block uses the CJE(T) equation to calculate the base-collector junction capacitance by substituting CJC (the B-C depletion capacitance, CJC parameter value) for CJE and MJC (the B-C exponential factor, MJC parameter value) for MJE.

The block provides the following relationship between the forward and reverse beta and the transistor temperature T:

where:

• β is the Forward beta, BF or Reverse beta, BR parameter value.

• XTB is the Beta temperature exponent, XTB parameter value.

The block provides the following relationship between the base-emitter leakage current ISE and the transistor temperature T:

where:

• ISE is the B-E leakage current, ISE parameter value.

• NE is the B-E emission coefficient, NE parameter value.

The block uses this equation to calculate the base-collector leakage current by substituting ISC (the B-C leakage current, ISC parameter value) for ISE and NC (the B-C emission coefficient, NC parameter value) for NE.

Basic Assumptions and Limitations

The model is based on the following assumptions:

• The NPN block does not support noise analysis.

• The NPN block applies initial conditions across junction capacitors and not across the block ports.

Dialog Box and Parameters

Main Tab

Device area, AREA

The transistor area. This value multiplies the following parameter values:

• Transport saturation current, IS

• Forward knee current, IKF

• B-E leakage current, ISE

• Reverse knee current, IKR

• B-C leakage current, ISC

• Half base resistance cur, IRB

• B-E depletion capacitance, CJE

• Coefficient of TF, ITF

• B-C depletion capacitance, CJC

• C-S junction capacitance, CJS

It divides the following parameter values:

• Zero-bias base resistance, RB

• Minimum base resistance, RBM

• Emitter resistance, RE

• Collector resistance, RC

The default value is 1 m². The value must be greater than 0.

Number of parallel devices, SCALE

The number of parallel transistors the block represents. This value multiplies the output current and device charges. The default value is 1. The value must be greater than 0.

Forward Gain Tab

Transport saturation current, IS

The magnitude of the current at which the transistor saturates. The default value is 1e-16 A/m². The value must be greater than or equal to 0.

Forward beta, BF

The ideal maximum reverse beta. The default value is 100. The value must be greater than 0.

Forward emission coefficient, NF

The reverse emission coefficient or ideality factor. The default value is 1. The value must be greater than 0.

B-E leakage current, ISE

The base-emitter leakage current. The default value is 0 A/m². The value must be greater than or equal to 0.

B-E emission coefficient, NE

The base-collector emission coefficient or ideality factor. The default value is 1.5. The value must be greater than 0.

Forward knee current, IKF

The current value at which forward-beta high-current roll-off occurs. The default value is Inf A/m². The value must be greater than or equal to 0.

Forward Early voltage, VAF

The forward Early voltage. The default value is Inf V. The value must be greater than or equal to 0.

Reverse Gain Tab

Reverse beta, BR

The ideal maximum reverse beta. The default value is 1. The value must be greater than 0.

Reverse emission coefficient, NR

The reverse emission coefficient or ideality factor. The default value is 1. The value must be greater than 0.

B-C leakage current, ISC

The base-collector leakage current. The default value is 0 A/m². The value must be greater than or equal to 0.

B-C emission coefficient, NC

The base-collector emission coefficient or ideality factor. The default value is 2. The value must be greater than 0.

Reverse knee current, IKR

The current value at which reverse-beta high-current roll-off occurs. The default value is Inf A/m². The value must be greater than or equal to 0.

Reverse Early voltage, VAR

The reverse Early voltage. The default value is Inf V. The value must be greater than or equal to 0.

Resistors Tab

Emitter resistance, RE

The resistance of the emitter. The default value is 0 m²*Ω. The value must be greater than or equal to 0.

Collector resistance, RC

The resistance of the collector. The default value is 0 m²*Ω. The value must be greater than or equal to 0.

Zero-bias base resistance, RB

The resistance of the collector. The default value is 0 m²*Ω. The value must be greater than or equal to 0.

Minimum base resistance, RBM

The resistance of the collector. The default value is 0 m²*Ω. The value must be less than or equal to the Zero-bias base resistance, RB parameter value.

Half base resistance cur, IRB

The base current at which the base resistance has dropped to half of its zero-bias value. The default value is Inf A/m². The value must be greater than or equal to 0. Use the default value of Inf if you do not want to model the change in base resistance as a function of base current.

Capacitance Tab

Model junction capacitance

Select one of the following options for modeling the junction capacitance:

• No — Do not include junction capacitance in the model. This is the default option.

• B-E Capacitance — Model the junction capacitance across the base-emitter junction.

• B-C Capacitance — Model the junction capacitance across the base-collector junction.

• C-S Capacitance — Model the junction capacitance across the collector-substrate junction.

Note   To include junction capacitance in the model: Select B-E Capacitance and specify the base-emitter junction capacitance parameters. Select B-C Capacitance and specify the base-collector junction capacitance parameters. Select C-S Capacitance and specify the collector-substrate junction capacitance parameters. You can specify or change any of the common parameters when you select any of the preceding options for the Model junction capacitance parameter.

B-E depletion capacitance, CJE

The depletion capacitance across the base-emitter junction. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is 0 F/m². The value must be greater than or equal to 0.

B-E built-in potential, VJE

The base-emitter junction potential. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is 0.75 V. The value must be greater than or equal to 0.01 V.

B-E exponential factor, MJE

The grading coefficient for the base-emitter junction. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is 0.33. The value must be greater than or equal to 0 and less than or equal to 0.9.

Forward transit time, TF

The transit time of the minority carriers that cause diffusion capacitance when the base-emitter junction is forward-biased. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is 0. The value must be greater than or equal to 0.

Coefficient of TF, XTF

The coefficient for the base-emitter and base-collector bias dependence of the transit time, which produces a charge across the base-emitter junction. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is 0. The value must be greater than or equal to 0. Use the default value of 0 if you do not want to model the effect of base-emitter bias on transit time.

VBC dependence of TF, VTF

The coefficient for the base-emitter bias dependence of the transit time. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is Inf V. The value must be greater than or equal to 0.

Coefficient of TF, ITF

The coefficient for the dependence of the transit time on collector current. This parameter is only visible when you select B-E Capacitance for the Model junction capacitance parameter. The default value is 0 A/m². The value must be greater than or equal to 0. Use the default value of 0 if you do not want to model the effect of collector current on transit time.

B-C depletion capacitance, CJC

The depletion capacitance across the base-collector junction. This parameter is only visible when you select B-C Capacitance for the Model junction capacitance parameter. The default value is 0 F/m². The value must be greater than 0.

B-C built-in potential, VJC

The base-collector junction potential. This parameter is only visible when you select B-C Capacitance for the Model junction capacitance parameter. The default value is 0.75 V. The value must be greater than or equal to 0.01 V.

B-C exponential factor, MJC

The grading coefficient for the base-collector junction. This parameter is only visible when you select B-C Capacitance for the Model junction capacitance parameter. The default value is 0.33. The value must be greater than or equal to 0 and less than or equal to 0.9.

B-C capacitance fraction, XCJC

The fraction of the base-collector depletion capacitance that is connected between the internal base and the internal collector. The rest of the base-collector depletion capacitance is connected between the external base and the internal collector. This parameter is only visible when you select B-C Capacitance for the Model junction capacitance parameter. The default value is 0. The value must be greater than or equal to 0 and less than or equal to 1.

Reverse transit time, TR

The transit time of the minority carriers that cause diffusion capacitance when the base-collector junction is reverse-biased. This parameter is only visible when you select B-C Capacitance for the Model junction capacitance parameter. The default value is 0 s. The value must be greater than or equal to 0.

Capacitance coefficient FC

The fitting coefficient that quantifies the decrease of the depletion capacitance with applied voltage. This parameter is only visible when you select B-E Capacitance or B-C Capacitance for the Model junction capacitance parameter. The default value is 0.5. The value must be greater than or equal to 0 and less than or equal to 0.95.

Specify initial condition

Select one of the following options for specifying an initial condition:

• No — Do not specify an initial condition for the model. This is the default option.

• Yes — Specify the initial transistor conditions.

  Note   The NPN block applies the initial transistor voltages across the junction capacitors and not across the ports.

This parameter is only visible when you select B-E Capacitance or B-C Capacitance for the Model junction capacitance parameter.

Initial condition voltage ICVBE

Base-emitter voltage at the start of the simulation. This parameter is only visible when you select B-E Capacitance or B-C Capacitance for the Model junction capacitance and Yes for the Specify initial condition parameter. The default value is 0 V.

Initial condition voltage ICVCE

Base-collector voltage at the start of the simulation. This parameter is only visible when you select B-E Capacitance or B-C Capacitance for the Model junction capacitance and Yes for the Specify initial condition parameter. The default value is 0 V.

C-S junction capacitance, CJS

The collector-substrate junction capacitance. This parameter is only visible when you select C-S Capacitance for the Model junction capacitance parameter. The default value is 0 F/m². The value must be greater than or equal to 0.

Substrate built-in potential, VJS

The potential of the substrate. This parameter is only visible when you select C-S Capacitance for the Model junction capacitance parameter. The default value is 0.75 V.

Substrate exponential factor, MJS

The grading coefficient for the collector-substrate junction. This parameter is only visible when you select C-S Capacitance for the Model junction capacitance parameter. The default value is 0. The value must be greater than or equal to 0 and less than or equal to 0.9.

Temperature Tab

Model temperature dependence using

Select one of the following options for modeling the transistor temperature dependence:

• Device temperature — Use the device temperature, which is the Circuit temperature value plus the Offset local circuit temperature, TOFFSET value. The Circuit temperature value comes from the SPICE Environment Parameters block, if one exists in the circuit. Otherwise, it comes from the default value for this block.

• Fixed temperature — Use a temperature that is independent of the circuit temperature to model temperature dependence.

Beta temperature exponent, XTB

The forward and reverse beta temperature exponent that models base current temperature dependence. This parameter is only visible when you select Device temperature for the Model temperature dependence using parameter. The default value is 0. The value must be greater than or equal to 0.

Energy gap, EG

The energy gap that affects the increase in the saturation current as temperature increases. This parameter is only visible when you select Device temperature for the Model temperature dependence using parameter. The default value is 1.11 eV. The value must be greater than or equal to 0.1.

Temperature exponent for IS, XTI

The order of the exponential increase in the saturation current as temperature increases. This parameter is only visible when you select Device temperature for the Model temperature dependence using parameter. The default value is 3. The value must be greater than or equal to 0.

Offset local circuit temperature, TOFFSET

The amount by which the transistor temperature differs from the circuit temperature. This parameter is only visible when you select Device temperature for the Model temperature dependence using parameter. The default value is 0 K.

Parameter extraction temperature, TMEAS

The temperature at which the transistor parameters were measured. The default value is 300.15 K. The value must be greater than 0.

Fixed circuit temperature, TFIXED

The temperature at which to simulate the transistor. This parameter is only visible when you select Fixed temperature for the Model temperature dependence using parameter. The default value is 300.15 K. The value must be greater than 0.

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.

S

Electrical conserving port associated with the transistor substrate terminal.

Examples

See the Creating a SPICE-Compatible Circuit with the Extended Electrical Library demo.

References

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

See Also

NPN Bipolar Transistor

NJFET

NPN Bipolar Transistor