SPICE NPN
SPICE-compatible Gummel-Poon NPN Transistor
Libraries:
Simscape /
Electrical /
Additional Components /
SPICE Semiconductors
Description
The SPICE NPN block represents a SPICE-compatible
four-terminal Gummel-Poon NPN bipolar junction transistor. A capacitor connects the
substrate port, sx, to the transistor base,
bx. Therefore, the device is equivalent to a three-terminal
transistor when you use the default value of 0
for the C-S
junction capacitance, CJS parameter and connect the substrate port to any
other port, including the emitter port, ex, or the collector port,
cx.
SPICE, or Simulation Program with Integrated Circuit Emphasis,
is a simulation tool for electronic circuits. You can convert some SPICE subcircuits into
equivalent Simscape™
Electrical™ models using the Environment Parameters block and
SPICE-compatible blocks from the Additional Components library. For more
information, see subcircuit2ssc
.
Equations
Variables for the SPICE NPN block equations include:
Variables that you define by specifying parameters for the SPICE NPN block. The visibility of some of the parameters depends on the value that you set for other parameters. For more information, see Parameters.
Geometry-adjusted variables, which depend on several values that you specify using parameters for the SPICE NPN block. For more information, see Geometry-Adjusted Variables.
Temperature, T, which is
300.15
K
by default. You can use a different value by specifying parameters for the SPICE NPN block or by specifying parameters for both the SPICE NPN block and an Environment Parameters block. For more information, see Transistor Temperature.Temperature-dependent variables. For more information, see Temperature Dependence.
Minimal conductance, GMIN, which is
1e–12
1/Ohm
by default. You can use a different value by specifying a parameter for an Environment Parameters block. For more information, see Minimal Conduction.
Several variables in the equations for the SPICE NPN bipolar junction transistor model consider the geometry of the device that the block represents. These geometry-adjusted variables depend on variables that you define by specifying SPICE NPN block parameters. The geometry-adjusted variables depend on these variables:
AREA — Area of the device
SCALE — Number of parallel connected devices
The associated unadjusted variable
The table includes the geometry-adjusted variables and the defining equations.
Variable | Description | Equation |
---|---|---|
ISd | Geometry-adjusted transport saturation current |
|
IKFd | Geometry-adjusted forward knee current |
|
ISd | Geometry-adjusted base-emitter leakage current |
|
IKRd | Geometry-adjusted reverse knee current |
|
ISCd | Geometry-adjusted base-collector leakage current |
|
IRBd | Geometry-adjusted half base resistance current |
|
CJEd | Geometry-adjusted base-emitter depletion capacitance |
|
ITFd | Geometry-adjusted forward transit time coefficient |
|
CJCd | Geometry-adjusted base-collector depletion capacitance |
|
CJSd | Geometry-adjusted collector-substrate junction capacitance |
|
RBd | Geometry-adjusted zero-bias base resistance |
|
RBMd | Geometry-adjusted minimum base resistance |
|
REd | Geometry-adjusted emitter resistance |
|
RCd | Geometry-adjusted collector resistance |
|
You can use these options to define transistor temperature, T:
Fixed temperature — The block uses a temperature that is independent from the circuit temperature when the Model temperature dependence using parameter in the Temperature settings of the SPICE NPN block is set to
Fixed temperature
. For this model, the block sets T equal to TFIXED.Device temperature — The block uses a temperature that depends on circuit temperature when the Model temperature dependence using parameter in the Temperature settings of the SPICE NPN block is set to
Device temperature
. For this model, the block defines temperature asWhere:
TC is the circuit temperature.
If there is no Environment Parameters block in the circuit, TC is equal to 300.15 K.
If there is an Environment Parameters block in the circuit, TC is equal to the value that you specify for the Temperature parameter in the SPICE settings of the Environment Parameters block. The default value for the Temperature parameter is
300.15
K
.TOFFSET is the offset local circuit temperature.
Minimal conductance, GMIN, has a default value of
1e–12
1/Ohm
. To specify a different value:
If there is not an Environment Parameters block in the circuit, add one.
In the SPICE settings of the Environment Parameters block, specify the desired GMIN value for the GMIN parameter.
The current-voltage relationships and base charge relationships for the transistor are described in terms of Base-Emitter and Base-Collector Junction Currents, Terminal Currents, and Base Charge Model. As applicable, the model parameters are first adjusted for temperature.
The base-emitter junction current depends on the base-emitter voltage, VBE such that:
When :
When :
The base-collector junction current depends on the base collector voltage, VBC, such that:
When :
When :
Where:
VBE is the base-emitter voltage.
VBC is the base-collector voltage.
VTE is the emitter thermal voltage, such that .
VTC is the collector thermal voltage, such that .
VTF is the forward thermal voltage, such that .
VTR is the reverse thermal voltage, such that .
ISCd is the geometry-adjusted base-collector leakage current.
ISEd is the geometry-adjusted base-emitter leakage current.
NE is the base-emitter emission coefficient.
NC is the base-collector emission coefficient.
NF is the forward emission coefficient.
NR is the reverse emission coefficient.
q is the elementary charge on an electron.
k is the Boltzmann constant.
T is the transistor temperature. For more information, see Transistor Temperature.
Gmin is the minimum conductance. For more information, see Minimal Conduction.
The terminal currents are calculated as:
Where:
IB is the base terminal current.
IC is the collector terminal current.
BF is the forward beta.
BR is the reverse beta.
The base charge, qb, is calculated using these equations:
Where:
qb is the base charge.
VAF is the forward Early voltage.
VAR is the reverse Early voltage.
IKFd is the geometry-adjusted forward knee current.
IKRd is the geometry-adjusted reverse knee current.
eps is 1e-4.
You can use these options to model base resistance, rbb:
If you use the default value of infinity for the Half base resistance cur, IRB parameter, the block calculates the base resistance as
Where:
rbb is base resistance.
RBMd is the geometry-adjusted minimum base resistance.
RBd is the geometry-adjusted zero-bias base resistance.
If you specify a finite value for the Half base resistance cur, IRB parameter, the block calculates the base resistance as
Where
If you specify nonzero values for the Coefficient of TF, XTF parameter, the block models transit charge modulation by scaling the forward transit time as
Where ITFd is the geometry-adjusted coefficient of the forward transit time.
The block lets you model junction charge. The base-collector charge, Qbc, and the base-emitter charge, Qbe, depend on an intermediate value, Qdep. As applicable, the model parameters are first adjusted for temperature.
For the internal base-emitter junctions
For the internal base-collector junctions
For the external base-collector junctions
Qdep depends on the junction voltage, Vjct (VBE for the base-emitter junction and VBC for the base-collector junction), as follows.
Applicable Range of Vjct Values | Corresponding Qdep Equation |
---|---|
Where:
FC is the capacitance coefficient.
VJ is:
The base-emitter built-in potential, VJE, for the base-emitter junction.
The base-collector built-in potential, VJC, for the base-collector junction.
MJ is:
The base-emitter exponential factor, MJE, for the base-emitter junction.
The base-collector exponential factor, MJC, for the base-collector junction.
Cjct is:
The geometry-adjusted base-emitter depletion capacitance, CJEd, for the base-emitter junction.
The geometry-adjusted base-collector depletion capacitance, CJCd, for the base-collector junction.
The collector-substrate charge, Qcs, depends on the collector-substrate voltage, Vcs. As applicable, the model parameters are first adjusted for temperature.
Applicable Range of Vcs Values | Corresponding Qcs Equation |
---|---|
Where:
CJSd is the geometry-adjusted collector-substrate junction capacitance.
VJS is the substrate built-in potential.
MJS is the substrate exponential factor.
The relationship between the saturation current, ISd, and the transistor temperature, T, is
Where:
ISd is the geometry-adjusted transport saturation current.
Tmeas is the parameter extraction temperature.
XTI is the transport saturation current temperature exponent.
EG is the energy gap.
Vt = kT/q.
The relationship between the base-emitter junction potential, VJE, and the transistor temperature, T, is
Where:
VJE is the base-emitter built-in potential.
The block uses the VJE(T) equation to calculate the base-collector junction potential by substituting VJC, the base-collector built-in potential, for VJE.
The relationship between the base-emitter junction capacitance, CJE, and the transistor temperature, T, is
Where:
CJEd is the geometry-adjusted base-emitter depletion capacitance.
MJE is the base-emitter exponential factor.
The block uses the CJE(T) equation to calculate the base-collector junction capacitance by substituting CJCd, geometry-adjusted base-collector depletion capacitance, for CJEd and MJC, base-collector exponential factor, for MJE.
The relationship between the forward and reverse beta and the transistor temperature, T, is
Where:
β is the forward beta or reverse beta.
XTB is the beta temperature exponent.
The relationship between the base-emitter leakage current, ISE, and the transistor temperature, T, is
Where:
ISEd is the geometry-adjusted base-emitter leakage current.
NE is the base-emitter emission coefficient.
The block uses this equation to calculate the base-collector leakage current by substituting, ISCd, the geometry-adjusted base-collector leakage current for ISEd and NC, the base-collector emission coefficient, for NE.
Assumptions and Limitations
The block does not support noise analysis.
The block applies initial conditions across junction capacitors and not across the block ports.
Ports
Conserving
Parameters
References
[1] G. Massobrio and P. Antognetti. Semiconductor Device Modeling with SPICE. 2nd Edition. New York: McGraw-Hill, 1993.
Extended Capabilities
Version History
Introduced in R2008a