BJT T-model

The T-model is the BJT small-signal model rearranged so that the resistance between base and emitter is the [[Emitter resistance|$r_e$]] instead of $r_{\pi }$. It is fully equivalent to the BJT hybrid-pi model — same device, same answers — but its topology makes circuits where the emitter is the signal node much easier to analyse.

Its elements:

• A resistance $r_e$ between base and emitter, carrying the full emitter current $i_e$. Recall $r_e=\alpha /g_m\approx 1/g_m\approx 25\Omega$ at 1 mA — much smaller than $r_{\pi }$, because the emitter sees the full current while the base sees only $i_b=i_c/\beta$ (see Emitter resistance).
• A controlled current source between collector and emitter, $g_m{v}_{be}\equiv \alpha i_e$ (equivalently $\beta i_b$). Since $v_{be}=i_e{r}_e$ and $r_e=\alpha /g_m$, $g_m{v}_{be}=g_m{i}_e{r}_e=g_m{i}_e(\alpha /g_m)=\alpha i_e$ — the same current as in the hybrid-π, just written in terms of $i_e$.
• An optional $r_o=V_A/I_C$ in parallel for the Early effect.

T-model: $r_e$ between base and emitter, controlled source $g_m{v}_{be}\equiv \alpha i_e$ collector-to-emitter; add $r_o$ in parallel for the Early effect. Equivalent to the hybrid-π but more convenient when the emitter is the signal node.

The shape (named for the “T” the resistor and the two branches make) puts $r_e$ directly in the signal path when you feed the emitter. That makes it the model of choice for the Common-base amplifier (input at the emitter — input resistance falls straight out as $r_e$) and for the Emitter follower (output taken at the emitter — output resistance ≈ $r_e$ drops out cleanly). It also makes the Resistance reflection rule obvious: a resistor in the emitter is in series with the full $i_e$, while the base only carries $i_b=i_e/(\beta +1)$, so that resistor looks $(\beta +1)$ times larger from the base. Use the hybrid-π when the base is the input (common-emitter), the T-model when the emitter is.