# Applying hybrid-pi model of an npn-BJT to a pnp BJT in small signal analysis

When doing the small signal analysis of a circuit containing a pnp BJT connected to either the emitter or collector (or base?) of a npn BJT, is it possible to apply the hybrid-pi model for the npn-BJT and apply a minus sign to the current as in -gmVbe since current flows opposite?

simulate this circuit – Schematic created using CircuitLab

• I1 is 19 amps? Dang, that's going to produce some seriously high voltages in that circuit. – alex.forencich Nov 9 '13 at 2:16

## 1 Answer

simulate this circuit – Schematic created using CircuitLab

The model of each transistor is not dependent on what it will be connected.

Yes it is possible, but you must have into account the sign of the currents and which voltage controls the collector source current, Vbe or Veb.

You can take the NPN model and apply Vbe = -Veb (that's by definition). Then, on the equations for the NPN model you'll have ib = -Veb/rb, ic = -gm Veb and ie = ib + ie;

But now all currents are negative and the arrows pointing against the flow. Since that's not intuitive and we're free to choose the signs, we consider positive the currents that flow outwards and turn around the current source. That translates to the equations to multiply the right members of the equations by -1. This way, you have the PNP model.

As you see, It's a matter of avoiding minus signs. Just like in large signal analysis we say VEB = 0.6V instead VBE = -0.6V for a PNP transistor.