# Improved SPICE Models for MJL3281A and MJL1302A Power Transistors

Section 1: Background

*Author's note: This article should be considered historical in nature. For more information about recent developments, see the notes on the background of this article*.

## Introduction

The MJL3281A and MJL1302A power transistors have become very popular for use in the output stages of high-performance audio power amplifiers due to their high f_{T}, good safe operating area, and reasonably high β that holds up well at high collector currents [1]. With the increasing popularity of SPICE simulators, many designers will want to simulate their designs that use these devices. Those interested in doing so will likely obtain their SPICE models from the manufacturer, ON Semiconductor. However, when performing simulations using the manufacturer-provided models, experience shows that the simulated behavior is much poorer than what would be expected in an actual circuit given the specifications and measured performance of the devices. This naturally leads to an investigation of whether the SPICE model parameters accurately reflect the datasheet performance.

The results of that investigation show that there are significant discrepancies between device parameters predicted by the manufacturer-provided SPICE models and the measured device parameters. This document is intended to address those issues. The purpose of this document is to point out the areas of trouble and provide new models that more accurately represent the measured data of the devices. Those who are only interested in getting the models can download them here. Those who are curious to see what the errors are and how the new model was developed will probably want to read through at least some of the information presented in the sections that follow.

The information in this document is structured as follows.

- Compare graphs of measured device parameters with parameters predicted from the manufacturer-provided SPICE models.
- Identify the discrepancies between measured and simulated device parameters.
- Outline a procedure for computing the new SPICE parameters from the datasheet graphs.
- Provide new models with SPICE parameters computed from this procedure.
- Show graphs of the simulated parameters using the new models to demonstrate the improved accuracy.

The process for determining the SPICE parameters proceeds roughly as below.

- Compute preliminary values for the SPICE parameters that affect simulated data corresponding to a given measurement.
- Plug these preliminary values into the model and perform a simulation that outputs data in the same form as the corresponding datasheet measurement.
- Compare the simulated data with the measured datasheet performance.
- Recompute the relevant SPICE parameters if the simulated and measured data are not close enough.
- Repeat steps (1)-(4) as necessary to obtain the closest possible match between simulated and measured data.

## SPICE Modeling Issues

The details of the Gummel-Poon SPICE BJT model extraction have been obtained from the book *Semiconductor Device Modeling with SPICE* (second edition) by Giuseppe Massobrio and Paolo Antognetti [2]. In some cases, such as plots of f_{T} vs. collector current, the data predicted by the SPICE model can be obtained directly from the simulator. In the freeware LTspice simulator, f_{T} can be obtained by looking in the SPICE error log after doing an operating point simulation. For other parameters, such as junction capacitances vs. reverse voltage, checking simulated vs. measured data requires substitution of the SPICE model parameter values into the equations used internally by SPICE models. These equations are documented in reference [2], equations 2-50 and 2-51. The relevant equations will be presented in the device extraction section.

However, some of the model extraction procedures defined in [2] require device data that is not present in the datasheets in any form. Parameters such as reverse β (BR) and reverse Early voltage (VAR), which describe device operation in the reverse active region, cannot be obtained from any information in the datasheet. In such a case, one has the choice of either using the parameters provided by the manufacturer, or not specifying them at all. Not specifying them will cause SPICE to use default values for these parameters. In the case of audio power amplifiers, the reverse active region is not normally used. However, evaluating the equations that determine forward β vs. I_{C} and I_{C} vs. V_{BE} shows that the reverse Early voltage VAR strongly affects the data. For this reason, the manufacturer-provided data for the reverse parameters will be retained.

Still other model extraction procedures assume device data is available in a certain form that is not present in the datasheet, but can be obtained indirectly from other data. One such example concerns the model's prediction of β vs. I_{C}. This involves the SPICE parameters IKF, ISE and NE. Massobrio and Antognetti define a procedure for obtaining these parameters from plots of ln(I_{B}) and ln(I_{C}) vs. V_{BE}. The datasheets show plots of I_{C} vs. V_{BE}, but not I_{B} vs. V_{BE}. However, by combining information from the plots of I_{C} vs. V_{BE} and β vs. I_{C}, one can obtain the equivalent information. This requires a revised procedure that will be described in the model extraction section.

In addition, certain aspects of power BJT performance cannot be predicted by the standard Gummel-Poon model at all. One such property is *quasi-saturation*. Reference [2] goes into detail about behavior of certain types of power BJT in the quasi-saturation region. The behavior can be seen in the characteristic curves shown in the MJL3281A and MJL1302A datasheets. The characteristic curves appear to gradually bend in the transition region between the active region and saturation rather than making an abrupt transition. This is best shown with the graph below in Figure 1, captured from the ON Semiconductor MJL1302A datasheet.

Because the β of the device remains reasonably large even at high currents, the base currents shown are large enough that the device is not in the active region at all. What the graph actually shows is the quasi-saturation region. The characteristic curves can be made to look much more like what one expects for a device in the active region by reducing the base currents. More recent device models such as VBIC [3] are designed to handle quasi-saturation, but so far this model does not enjoy the widespread popularity of Gummel-Poon. Since the Gummel-Poon model cannot predict quasi-saturation behavior, it will be neglected in the derivation of the model parameters here. This will have the side effect of causing the simulated characteristic curves to look more idealized than Figure 1 with large base currents. In an actual audio power amplifier, the base currents would only reach the values shown in Figure 1 under overload conditions such as the approach of clipping. Normally, amplifier clipping is determined by the stages prior to the output stage, so quasi-saturation of the output stage is a secondary consideration.