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*Mathematical Analysis*

Basically, the hybrid-pi model represents the dynamic incremental variation of the
stored charge in the base upon the incremental change of the applied emitter voltage. A
change of *DV _{E}* gives rise to an increase of

*g _{m} = dI_{c} / dV_{E}*

We have,

*n _{p}(0) = n_{p0}e^{(V}E^{
/ V}T^{)}*,

*|I _{C}| = {qAD_{n}n_{p}(0)} / x_{B}
*

Thus, we derive,

*g _{m} = |I_{C}| / V_{T} = qI_{C} /
kT*

The input resistance *r _{p}* relates

*rp = dV _{BE} / dI_{B }= kT / qI_{B }*

The output resistance *r _{0}* relates

*r0 = dV _{CE} / dI_{C}*

The capacitance are designated by

*Cm = C _{dBC}*

and

*C _{p} = C_{dBE} + C_{DE}*