Determining BJT SPICE Parameters
Background
Assume one wants to use SPICE to determine the frequency response for
and
for the amplifier below.
Figure 1. Common-collector amplifier.
After creating a schematic, the next step is to provide the proper SPICE parameters for the BJT.
Appendix A documents SPICE’sparameters. The hybrid- model that we use to analyze circuits
are different from the models SPICE uses. The
and
hybrid- parameters, important for
frequency analysis, do not have corresponding SPICE parameters. However, SPICE computes
and
at the Q-point from its parameters. Thus, we need determine SPICE parameters so
that when it simulates, the simulation values match the values in the problem statement.
How SPICE Simulates BJTs
SPICE first does a dc or Q-point (
) analysis. SPICE then determines the
junction collector-base junction capacitance ( ) and then the junction capacitance ( ) and the
diffusion capacitance
for the base-emitter junction. Then SPICE computes
and :
SPICE does the Q-point analysis first, because all the capacitances depend on the Q-point.
Micro-Cap SPICE saves the values in the *.TNO file, where ―*‖ represents the base name of the
simulation file. It is instructive to examine this file.
SPICE DC Analysis Parameters
For the dc analysis, BF (=
is obviously the most important. Other significant parameters are
the Early voltage VAF
, the built-in junction potential of the base-emitter junction
,
and saturation current IS (
. Since the transistor part number is not specified, one can pick a
generic or common part such as the 2N2222 npn BJT and modify the BF and VAF SPICE
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parameters. Unless additional information on
SPICE default values or typical values.
or junction voltages are available, use the
Data sheets usually list the built-in junction potential of the base-emitter junction
.
Regardless, for a Si transistor,
is a reasonable choice. Data sheets list BF (=
explicitly, or as
. Data sheets normally do not specify the Early voltage explicitly, but one
can deduce it from the output family of curves. Many transistor data sheets contain the output
resistance measured at some collector current, and from this one can compute , since
Alternatively, VAF =100 V is a reasonable default for most transistors.
Regarding the saturation current, most transistor data sheets contain the information needed to
find IS. For example, below is a plot of
vs. for a transistor.
Figure 2. Sample
From the plot,
at
and
for a small BJT.
. Thus
However, in most cases IS is not critical, and for many transistors, IS = 10 fA (
good value to use.
SPICE AC Analysis Parameters:
) is a
Known
For an ac analysis, we need to provide SPICE with enough information so that it can compute
and
at the operating point.
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Incorporating
For
SPICE determines collector-base capacitance from
is the Q-point collector-base voltage that SPICE will determine during the dc analysis.
We need to specify MJC, VJC, and CJC so that when SPICE runs a simulation, the resulting
will match the desired value. Reasonable values for MJC and VJC are MJC = 0.5, VJC =0.7 V.
Example 1
Specify MJC, VJC, and CJC for the circuit in Figure 1 so that the resulting
is 4 pF.
Solution
Use VJC = 0.7 V, and MJC = 0.5. A dc analysis reveals that
for the circuit is 11 V.
Incorporating
For , SPICE determines the base-emitter junction capacitance
capacitance
and add these:
To incorporate
and the diffusion
, start with1
Here is the forward transit time. We need to specify MJE, VJE, CJE, and , so that when
SPICE runs a simulation, the resulting
will match the desired value. As before, unless
additional information is available, assume MJE = 0.5 and VJE = 0.7 V. This still leaves us with
CJE and and many combinations of these will result in the desired . Unless additional
information is available, there are three strategies:
1
Even though SPICE uses
, this equation gives poor results when we estimate
from
, and
generally works better for most discrete circuits that are biased at relatively large collector currents.
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1. Pick a reasonable value for and the determine CJE. For example,
purpose npn BJTs lie in the range 150—400 ps.
2. Set
and model
by the junction capacitance alone.
3. Set CJE = 0 and model
with the diffusion capacitance alone.
for general-
Example 2
For the circuit in Figure 1, use the three different strategies and determine the SPICE parameters
so that resulting
is 35 pF.
Solution
Strategy 1: pick
the operating point. Then
, then from
it follows that
at
Thus, one would provide SPICE with TF = 200 ps, CJE = 14 pF, MJE = 0.5, and VJE = 0.7 V. As
a check, using these values, SPICE computed
Strategy 2: set
. Then
Thus, one would provide SPICE with TF = 0 ps, CJE = 17 pF, MJE = 0.5, and VJE = 0.7 V. As a
check, using these values, SPICE computed
Strategy 3: set
Thus
Thus, one would provide SPICE with TF = 1.12 ns, CJE = 0 pF, and MJE, VJE does not matter
with respect to . As a check, using these values, SPICE computed
Simulating Small-Signal Model in SPICE
One can simulate the small-signal model of the amplifier in Figure directly in SPICE. Since the
small-signal parameters depend on the Q-point, the first step is to do a dc analysis. Micro-Cap
SPICE’s Dynamic DC Analysis reveals
,
and
. Next determine
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Then construct a small-signal model, using SPICE’s IofV dependent source (see Figure below).
Figure 3. Left: SPICE’s IofV dependent source. Right: small-signal model of
the amplifier in Figure 1. One would set the value for the IofV dependent source
to the transconductance
. Further,
.
Next, one can run the ac analysis and determine the frequency response. However, imagine one
want to explore how the amplifier behaves for different values of . Every value of
will
give a different
and thus new values for and
, so that one has to recalculate the smallsignal values, update the SPICE file, and rerun the analysis. This quickly becomes impractical
with circuits that contain more than one BJT.
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Appendix A
Junction and Diffusion Capacitances
SPICE BJTs model are complex (Ebers–Moll and Gummel-Poon) and capture behavior at both
small- and large signals. Broadly speaking, SPICE uses-physically based BJT parameters. For
example, the large-signal BJT model below shows
, and that are resistances associated
with the contact (and other) resistances at the base, collector, and emitter. The capacitance
refers to the collector-base junction capacitance, and
refers to the base-emitter junction
capacitance.
Figure A1. Left: BJT large signal model with junction capacitances. Right: SPICE
symbols.
is computed from
. In SPICE,
is TF.
Junction capacitances depend on the (reverse) voltage across the pn junction and
CJC, CJE in SPICE) are the zero-bias junction capacitances. The following describes the
dependence:
Reverse bias voltage
Built-in junction voltage
Zero-bias junction capacitance
Junction grading coefficient
(or
(1)
The parameters
depend on how the BJT was manufactured. Typical values for and
range between 0.33–0.5 and 0.55–0.7 V respectively.
is the junction capacitance at zero
bias. Using the SPICE notation:
Collector-base junction capacitance
(2)
Base-emitter junction capacitance
(3)
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Here CJC is the zero-bias junction capacitance, VJC is the built-in junction voltage (~0.65 V), and
MJC (~0.5) is the junction grading coefficient for the collector-base junction. CJE, VJE (~0.7 V),
and MJE (~0.33) are the corresponding SPICE parameters for the base-emitter junction. For
BJTs on a substrate (ICs) there is another set and equations for the collector-substrate junction.
Assuming the BJT operates in the forward-active mode, then the base-emitter junction is forward
biased and there is a diffusion capacitance associated with the base-emitter junction. In the
context of BJTs, this capacitance is designated with
(see Figure A.1) and depends on the
current and the transit time (see equation (4)).
Thermal voltage
Transit time of charge carriers
(4)
The base-emitter diffusion- and junction capacitances are parallel and lumped together and is
called the
capacitance in the hybrid
model.
AC Parameters CJC, CJE, MJC, MJC and TF
BJT data sheets normally do not list CJC, CJE, MJC, MJC, explicitly. Rather, they contain
capacitances measured at some
or plots of capacitances at different Q-points. Further, data
sheets seldom list the forward transit time TF, but list the transition frequency instead.
The collector-base junction capacitance at the Q-point in SPICE is same as the
capacitance in
the hybrid- model. The total capacitance of the forward-biased base-emitter junction is the sum
of the junction- and diffusion capacitances. This is also the
capacitance in the hybridmodel:
(5a)
For moderate, large
where
is the base-emitter junction capacitance given by equation (3), and
emitter diffusion capacitance given by equation (4).
The relationship between the transition frequency and
Data sheets normally list , and
follows from
determine TF, which is what SPICE requires.
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, and
(5b)
is the base-
is:
. Using this and equation (5) one can
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BJT data sheets often contain plots of the capacitances as a function of reverse voltage, and one
can use this to determine
and MJC. An example of such plots is shown below.
When plots are not available, one has to make educated guesses. The junction grading
coefficient MJE is 0.33, and for MJC a reasonable value is 0.5.
Figure A2. Junction Capacitances for a small BJT.
Some Examples
Example A.1
From the plot in Figure A.2, the collector-base junction capacitance is about 10 pF at 0.1 V
reverse bias, so it is reasonable to take this values as the zero-bias junction capacitance
. The
general relationship between the junction capacitance and reverse voltage is
From the plot the collector-base voltage is 3 pF at
Solving yields
. Thus, one would enter
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. Thus
and
in SPICE.
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Example A.2
For the same BJT as in Example 1,
was measured as
. To determine the forward transit time TF, use
is identical to the collector-base junction capacitance
at
so that
, measured at
and
which the plot shows is about 3 pF
Further, ignoring the base-emitter junction capacitance
Thus
Thus, one would enter
in SPICE.
To get a better estimate, do not ignore the base-emitter junction capacitance. Rather, one would
compute it from
However, values computed using this is not reliable. One problem is that for forward bias, the
sign of
is negative and the magnitude slightly less than 1. Thus, the numerator is
small—which amplifies small uncertainties in calculations. A good approximation is to take
. Figure A.2 shows that
at zero reverse voltage is about 24 pF. Thus, we take
= 24 pF, and
. Now
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Now one can determine the transition time
Example A.3
Below are the measured parameters for a BJT. Determine the main SPICE parameters.
Parameter
Value
Measurement Conditions
1
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For the capacitances
we need
available, estimate
For the transit time
and
. Further, assume
, use
Strictly speaking, one should recompute
at
was measured. However, given that we estimated
use
. Now, at
,
Estimate
. Since no other information is
, the bias voltage when
, this does not make much sense, and we
at forward bias:
and
Finally,
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Appendix B
Static Parameters
2N2222
36.6 pF
42.4 pF
0
0
Parameter
BF
VAF
IS
RB
Forward or
Forward Early voltage
Saturation current in
Zero-bias base resistance
Zero-Bias Junction Capacitances
2N2222
36.6 pF
42.4 pF
0 pF
Parameter
CJC
CJE
CJS
Collector-base
Emitter-base
Collector-substrate
Grading Coefficients
MJC
MJE
MJS
2N2222
0.56
0.64
0
Parameter
Collector-base
Emitter-base
Collector-substrate
Built-In Potentials
2N2222
0.7 V
0.7 V
0.75
Parameter
VJE
VJC
VJS
Base-emitter
Collector-base
Collector substrate
Relating Junction Capacitances and Hybrid-π Parameters
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Forward Transit Time TF
When determining
at a given
, one would use the following.
However, this does not give good results for (strongly) forward-biased junctions and a better
estimate when determining transit time is to use
.
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