Small-Signal Analysis: Analytical (Closed-Form) Approach

The JSX uses analytical (closed-form) small-signal formulas, not a transfer function approach. Here's what the code actually does, based on the source I extracted:

DC Bias (Thévenin Equivalent)

vth = vcc * r2 / (r1 + r2)
rth = (r1 * r2) / (r1 + r2)
ib  = (vth - vbe) / (rth + (1 + β) * re)
ic  = β * ib

Small-Signal Parameters

gm   = ic / vt
rpi  = β / gm
ro   = VA / ic
rc_eff = rc ∥ ro
av   = gm * rc_eff

Bandwidth — Miller Approximation (Dominant-Pole)

cMiller = Cμ * (1 + gm * rc_eff)     ← Miller effect on Cμ
cTotal  = Cπ + cMiller
rEff    = rth_rpi ∥ 10kΩ
fh      = 1 / (2π * rEff * cTotal)   ← single-pole -3dB estimate

Two-Stage Cascade

bw  = min(fh_stage1, fh_stage2)       ← dominant pole of the cascade
av  = av1_loaded * av2

Summary

So to directly answer your question: it is not a transfer function approach. There is no polynomial H(s), no root-finding, no Bode plot computation. Instead it uses:

1. Thévenin bias analysis for the DC operating point,
2. Miller's theorem to lump Cμ into a single equivalent input capacitance, and
3. A single-pole RC formula f = 1/(2πRC) to estimate the −3 dB bandwidth per stage.

The system bandwidth is then just the min() of the two stage bandwidths — a crude but fast approximation suitable for the A* optimizer loop, which needs thousands of fast evaluations. A proper transfer function (with all poles/zeros from Cπ, Cμ, CE bypass caps, etc.) would be far more accurate but much more expensive to compute.