SPICE Parameters for BJTs 1 Version 2.0

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

SPICE Parameters for BJTs 2 Version 2.0

parameters. Unless additional information on or junction voltages are available, use the

SPICE default values or typical values.

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 for a small BJT.

From the plot, at and . Thus

However, in most cases IS is not critical, and for many transistors, IS = 10 fA ( ) is a

good value to use.

SPICE AC Analysis Parameters: Known

For an ac analysis, we need to provide SPICE with enough information so that it can compute

and at the operating point.

SPICE Parameters for BJTs 3 Version 2.0

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 and the diffusion

capacitance and add these:

To incorporate , 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.

SPICE Parameters for BJTs 4 Version 2.0

1. Pick a reasonable value for and the determine CJE. For example, for general-

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.

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 , then from it follows that at

the operating point. Then

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

SPICE Parameters for BJTs 5 Version 2.0

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 small-

signal values, update the SPICE file, and rerun the analysis. This quickly becomes impractical

with circuits that contain more than one BJT.

SPICE Parameters for BJTs 6 Version 2.0

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 (or

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

(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)

SPICE Parameters for BJTs 7 Version 2.0

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 hybrid-

model:

(5a)

For moderate, large (5b)

where is the base-emitter junction capacitance given by equation (3), and is the base-

emitter diffusion capacitance given by equation (4).

The relationship between the transition frequency and , and is:

Data sheets normally list , and follows from . Using this and equation (5) one can

determine TF, which is what SPICE requires.

SPICE Parameters for BJTs 8 Version 2.0

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 . Thus

Solving yields . Thus, one would enter and in SPICE.

SPICE Parameters for BJTs 9 Version 2.0

Example A.2

For the same BJT as in Example 1, was measured as , measured at and

. To determine the forward transit time TF, use

is identical to the collector-base junction capacitance which the plot shows is about 3 pF

at so that

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

SPICE Parameters for BJTs 10 Version 2.0

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

SPICE Parameters for BJTs 11 Version 2.0

For the capacitances we need and . Since no other information is

available, estimate . Further, assume

For the transit time , use

Strictly speaking, one should recompute at , the bias voltage when

was measured. However, given that we estimated , this does not make much sense, and we

use . Now, at ,

Estimate at forward bias:

and

Finally,

SPICE Parameters for BJTs 12 Version 2.0

Appendix B

Static Parameters

Parameter 2N2222

BF Forward or 36.6 pF

VAF Forward Early voltage 42.4 pF

IS Saturation current in 0

RB Zero-bias base resistance 0

Zero-Bias Junction Capacitances

Parameter 2N2222

CJC Collector-base 36.6 pF

CJE Emitter-base 42.4 pF

CJS Collector-substrate 0 pF

Grading Coefficients

Parameter 2N2222

MJC Collector-base 0.56

MJE Emitter-base 0.64

MJS Collector-substrate 0

Built-In Potentials

Parameter 2N2222

VJE Base-emitter 0.7 V

VJC Collector-base 0.7 V

VJS Collector substrate 0.75

Relating Junction Capacitances and Hybrid-π Parameters

SPICE Parameters for BJTs 13 Version 2.0

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 .