Determining BJT SPICE Parameters

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Griffin Wilkins
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1 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 1 Version 2.0

2 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 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 ( good value to use. ) is a 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 2 Version 2.0

3 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 with 1 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 3 Version 2.0

4 1. Pick a reasonable value for and the determine CJE. For example, for generalpurpose npn BJTs lie in the range 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 4 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.

5 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. SPICE Parameters for BJTs 5 Version 2.0

6 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: (or 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 and 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 6 Version 2.0

7 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 (5b) where is the base-emitter junction capacitance given by equation (3), and is the baseemitter 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 7 Version 2.0

8 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 8 Version 2.0

9 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 at is identical to the collector-base junction capacitance so that 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 SPICE Parameters for BJTs 9 Version 2.0

10 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 10 Version 2.0

11 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 11 Version 2.0

12 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 12 Version 2.0

13 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. SPICE Parameters for BJTs 13 Version 2.0

University of Southern C alifornia School Of Engineering Department Of Electrical Engineering

University of Southern C alifornia School Of Engineering Department Of Electrical Engineering EE 348: Homework Assignment #05 Spring, 2002 (Due 03/05/2002) Choma Problem #18: The biasing circuit in Fig.