Bipolar Junction Transistor
NCollector
NCollector
NBase
bjtpnp
NBase
NSubstrate
NSubstrate
NEmitter
NEmitter
(b)
(a)
Figure 1: Q — Bipolar Polar Junction Transistor: (a) NPN transistor; (b) PNP transistor.
fREEDATM Form: bjtpnp:hinstance namei n1 n2 n3 hparameter listi
n1 is the base node
n2
is the collector node
n3
is the emitter node
SPICE Form:
Qname NCollector NBase NEmitter [NSubstrate] ModelName [Area] [OFF] [IC=Vbe,Vce]
where
NCollector is the collector node.
NBase
NEmitter
NSubstrate
ModelName
Area
OFF
IC
is the base node.
is the emitter node.
is the optional substrate node. If not specified, then the ground is used as the
substrate node. If NSubstrate is a name as allowed in it must be enclosed in
square brackets, e.g. [NSubstrate], to distinguish it from ModelName.
is the model name.
is the area factor. If the area factor is omitted, a value of 1.0 is assumed.
(Units: none; Optional; Default: 1; Symbol: Area)
indicates an (optional) initial condition on the device for the dc analysis. If
specified the dc operating point is calculated with the terminal voltages set to
zero. Once convergence is obtained, the program continues to iterate to obtain
the exact value of the terminal voltages. The OFF option is used to enforce
the solution to correspond to a desired state if the circuit has
more than one stable state.
is the optional initial condition specification using IC=VBE , VCE is intended
for use with the UIC option on the .TRAN line, when a transient analysis is
desired starting from other than the quiescent operating point. See the .IC
line description for a better way to set transient initial conditions.
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Example:
bjtpnp:Q20 10 50 0
bjtpnp:QFAST IC=0.65,15.0
bjtpnp:Q5PUSH 10 29 14 200 MODEL1
Model Parameters:
Name
AREA
BF
BR
C2
C4
CJC
CJE
EG
FC
IKF
IKR
IS
ISC
ISE
IRB
ITF
MJC
MJE
NC
NE
NF
NR
RB
RBM
RE
RC
T
TF
TNOM
TR
TRB1
TRB2
TRC1
TRC2
TRE1
TRE2
TRM1
TRM2
Description
Current multiplier
Ideal maximum forward beta (BF )
Ideal maximum reverse beta (BR )
Base-emitter leakage saturation coefficient
Base-collector leakage saturation coefficient
Base collector zero bias p-n capacitance (CJC )
Base emitter zero bias p-n capacitance (CJE )
Bandgap voltage (EG )
Forward bias depletion capacitor coefficient (FC )
Corner of forward beta high-current roll-off (IKF )
Corner for reverse-beta high current roll off (IKR )
Transport saturation current (IS )
Base collector leakage saturation current (ISC )
Base-emitter leakage saturation current (ISE )
Current at which RB falls to half of RBM (IRB )
Transit time dependency on IC (IT F )
Base collector p-n grading factor (MJC )
Base emitter p-n grading factor (MJE )
Base-collector leakage emission coefficient (NC )
Base-emitter leakage emission coefficient (NE )
Forward current emission coefficient (NF )
Reverse current emission coefficient (NR )
Zero bias base resistance (RB )
Minimum base resistance (RBM )
Emitter ohmic resistance (RE )
Collector ohmic resistance (RC )
Operating Temperature T
Ideal forward transit time (TS )
Nominal temperature (TN OM )
Ideal reverse transit time (TR )
RB temperature coefficient (linear) (TRB1 )
RB temperature coefficient (quadratic) (TRB2 )
RC temperature coefficient (linear) (TRC1 )
RC temperature coefficient (linear) (TRC2 )
RE temperature coefficient (linear) (TRE1 )
RE temperature coefficient (quadratic) (TRE2 )
RBM temperature coefficient (linear) (TRM 1 )
RBM temperature coefficient (quadratic) (TRM 2 )
2
Units
F
F
eV
A
A
A
A
A
A
Ω
Ω
Ω
Ω
K
secs
K
S
Default
1.0
100.0
1.0
ISE /IS
(ISC /IS )
0.0
0.0
1.11
0.5
10−10
10−10
10−16
0.0
0.0
10−10
0.0
0.33
0.33
2.0
1.5
1.0
1.0
0.0
RB
0.0
0.0
300
0.0
300
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Name
VA
VAF
VAR
VB
VJC
VJE
VTF
XCJC
XTB
XTF
XTI
Description
alternative keyword for VAF (VA )
Forward early voltage (VAF )
Reverse early voltage (VAR )
alternative keyword for VAR (VB )
Base collector built in potential (VJC )
Base emitter built in potential (VJE )
Transit time dependency on VBC (VT F )
Fraction of CBC connected internal to RB (XCJC )
Forward and reverse beta temperature coefficient (XT B )
Transit time bias dependence coefficient (XT F )
IS temperature effect exponent (XT I )
3
Units
V
V
V
V
V
Default
10−10
10−10
10−10
10−10
0.75
0.75
10−10
1.0
0.0
0.0
3.0
ELEMENT Model
R
C
V
VBX
BC
C BX
NBase
I
B
CBC
B
RB
VBE
CBE
NCollector
C
I
C
ICE
IBC
I BE
NX
IC=
gm VBE
RO
VCJS
E
R
IE
NSubstrate
E
NEmitter
Figure 2: Schematic of the BJT Model
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CJS
Standard Calculations
The physical constants used in the model evaluation are
k
q
Boltzman’s constant
electronic charge
1.3806226 10−23 J/K
1.6021918 10−19 C
Absolute temperatures (in kelvins, K) are used. The thermal voltage
VT H (TN OM ) = k TN OM /q.
(1)
IBE = IBF /βF + ILE
(2)
IBC = IBR /βR + ILC
(3)
ICE = IBF − IBR /KQB
(4)
³
´
IBF = IS eVBE /(NF VT H ) − 1
(5)
³
´
ILE = ISE eVBE /(NE VT H ) − 1
(6)
³
´
IBR = IS eVBC /(NR VT H ) − 1
(7)
³
´
ILC = ISC eVBC /(NC VT H ) − 1
(8)
Current Characteristics
The base-emitter current,
the base-collector current,
and the collector-emitter current,
where the forward diffusion current,
the nonideal base-emitter current,
the reverse diffusion current,
the non-ideal base-collector current,
and the base charge factor,
−1
KQB = 1/2 [1 − VBC /VAF − VBE /VAB ]
³
1+
p
´
1 + 4 (IBF /IKF + IBR /IKR )
(9)
Thus the conductive current flowing into the base,
IB = IBE + IBC
(10)
the conductive current flowing into the collector,
IC = ICE − IBC
(11)
and the conductive current flowing into the emitter,
IC = IBE + ICE
(12)
Capacitances
CBE = Area(CBEτ + CBEJ ) where the base-emitter transit time or diffusion capacitance
CBEτ = τF,EF F ∂IBF /∂VBE
5
(13)
the effective base transit time is empirically modified to account for base puchout, space-charge limited
current flow, quasi-saturation and lateral spreading which tend to increase τF
h
i
(14)
τF,EF F = τF 1 + XT F (3x2 − 2x3 )e(VBC /(1.44VT F )
and x = IBF /(IBF + AreaIT F ).
The base-emitter junction (depletion) capacitance
(
−MJE
CJE (1 − VBE /VJE )
VBE ≤ FC VJE
CBEJ =
−(1 + MJE )
CJE (1 − FC )
(1 − FC (1 + MJE ) + MJE VBE /VJE ) VBE > FC VJE
(15)
The base-collector capacitance, CBC = Area(CBCτ + XCJC CBCJ ) where the base-collector transit time
or diffusion capacitance
CBCτ = τR ∂IBR /∂VBC
(16)
The base-collector junction (depletion) capacitance
(
−MJC
CJC (1 − VBC /VJC )
VBC ≤ FC VJC
CBCJ =
−(1 + MJC )
CJC (1 − FC )
(1 − FC (1 + MJC ) + MJC VBC /VJC ) VBC > FC VJC
The capacitance between the extrinsic base and the intrinsic collector

−MJC

Area(1 − XCJC )CJC (1 − VBX /VJC )
VBX ≤ FC VJC



CBX =
−(1 + MJC )


VBX > FC VJC
 (1 − XCJC )CJC (1 − FC )

× (1 − FC (1 + MJC ) + MJC VBX /VJC )
(17)
(18)
Bugs:
Parameters: OFF and IC are not functional.
Version:
2002.09.01
Credits:
Name
Senthil Velu
Affiliation
North Carolina State University
Date
Sept 2002
Publications:
1. C. Christoffersen, S. Velu and M. B. Steer, “ A Universal Parameterized Nonlinear Device Model
Formulation for Microwave Circuit Simulation,” 2002 IEEE Int. Microwave Symp. Digest, June 2002,
pp 2189-2192.
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