Ebers-Moll model and ac T-model of BJT

Ebers-Moll model

The large-signal model uses two diodes (the emitter-base and collector-base junctions) and two current sources that show the transport of carriers between the junctions.

  C o---+-----------+
        |           |
       ( ) αF·IF   DC | IR
        |           |
  B o---+-----------+
        |           |
       ( ) αR·IR   DE | IF
        |           |
  E o---+-----------+

Simplified form: DE (BE diode) carries IF = IES[exp(VBE/VT) - 1] and DC (BC diode) carries IR = ICS[exp(VBC/VT) - 1]. The collector gets αF IF from the emitter diode, and the emitter gets αR IR from the collector diode:

IC = αF IF - IR ,    IE = -(IF - αR IR) ,    IB = (1-αF) IF + (1-αR) IR

AC equivalent T-model

For small signals in the active region, the model is:

        C
        |
       ( )  α ie   (current source)
        |
 B -----+
        |
       re  (between base and emitter)
        |
        E

• A resistor re = VT/IE (the dynamic resistance of the forward-biased BE junction) is placed between the emitter and the base.
• The collector current source is α ie, directed from collector to base (equivalently ic = α ie).
• The base current is ib = ie/(β+1) = (1-α) ie.
• ro = VA/IC may be added in parallel with the source.

This model is best suited to circuits with resistance in the emitter (CB, CC and CE with RE), because re appears directly in the emitter path.