Start Presentation October 18, 2012 Modeling of Bipolar Transistors In this class, we shall deal with an application of mixed electrical and thermal modeling:

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Presentation transcript:

Start Presentation October 18, 2012 Modeling of Bipolar Transistors In this class, we shall deal with an application of mixed electrical and thermal modeling: the Bipolar Junction Transistor (BJT). We shall start out with a SPICE-style model of the BJT, then convert the model to a bond graph. We shall recognize that the SPICE-model of the BJT is problematic. We shall convert the bond graph to obtain a modified BJT model that makes sense from a thermodynamic point of view.

Start Presentation October 18, 2012 Table of Contents BJT modelBJT model Vertical and lateral npn-transistorVertical and lateral npn-transistor Non-linear current sourceNon-linear current source Junction diodeJunction diode BJT bond graphBJT bond graph Power-flow interpretationPower-flow interpretation Modified BJT bond graphModified BJT bond graph

Start Presentation October 18, 2012 SPICE-style BJT Model SPICE models the BJT by three junction diodes, one from the base to the collector, the second from the base to the emitter, and the third to the substrate. The figure to the left shows a laterally diffused npn-transistor.

Start Presentation October 18, 2012 Vertical and Lateral npn-Transistors The pn junction diodes connect positively doped regions with negatively doped regions. In the laterally diffused BJT, all three junction diodes have their anodes in the base. verticallateral for p-region (acceptors): boron or aluminum for n-region (donors): phosphorus or arsenic Dopants:

Start Presentation October 18, 2012 Non-linear Current Sources The model contains two non-linear current sources that inject currents into the circuit: The current injected into the collector is a function of the base-emitter Voltage, and the current injected into the emitter is a function of the base-collector Voltage.

Start Presentation October 18, 2012 The Junction Diode Model The pn junction diode is modeled as follows: JdJd

Start Presentation October 18, 2012 The BJT Bond Graph  Converted using the diamond property

Start Presentation October 18, 2012 Problems With BJT Bond Graph Where does the power for these current sources come from? The sources are internal to the model. Hence there is no place where these sources could possibly draw power from.

Start Presentation October 18, 2012 Conversion of the BJT Bond Graph

Start Presentation October 18, 2012 The Non-linear Resistor The two current sources are really a power sink, rather than a power source. They can be interpreted as a single non-linear resistor.

Start Presentation October 18, 2012 Dissipated Power I The power dissipated by the RS-element of the junction diodes (i.e., the two former current “sources”) is: and therefore: We still need to show that P BJT > 0.

Start Presentation October 18, 2012 Dissipated Power II We need to show that V C’E’ and i CE always point in the same direction. 

Start Presentation October 18, 2012 References Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York, Chapter 6.Continuous System ModelingChapter 6 Schweisguth, M.C. (1997), Semiconductor Modeling with Bondgraphs, MS Thesis, Dept. of Electr. & Comp. Engr., University of Arizona, Tucson, AZ.Semiconductor Modeling with Bondgraphs Schweisguth, M.C. and F.E. Cellier (1999), A Bond Graph Model of the Bipolar Junction Transistor, Proc. SCS Intl. Conf. on Bond Graph Modeling, San Francisco, CA, pp A Bond Graph Model of the Bipolar Junction Transistor