  The recently-introduced Topological Heavy Fermion (THF) model [Phys. Rev.
Lett. 129, 047601] of twisted bilayer graphene (TBG) aims to reconcile the
quantum-dot-like electronic structure of the latter observed by scanning
tunneling microscopy, with its electron delocalization seen in transport
measurements. The THF model achieves this by coupling localized (heavy)
fermions with anomalous conduction electrons. Originally, the parameters of the
THF model were obtained numerically from the Bistritzer-Macdonald (BM) model of
TBG [Phys. Rev. Lett. 129, 047601]. In this work, we derive analytical
expressions for the THF model parameters as a function of the twist angle, the
ratio between the tunneling amplitudes at the $AA$ and $AB$ regions ($w_0 /
w_1$), and the screening length of the interaction potential. By numerically
computing the THF model parameters across an extensive experimentally-relevant
parameter space, we show that the resulting approximations are remarkably good,
i.e. within the 30% relative error for almost the entire parameter space. At
the single-particle level, the THF model accurately captures the energy
spectrum of the BM model over a large phase space of angles and tunneling
amplitude ratios. When interactions are included, we also show that the THF
description of TBG is good around the magic angle for realistic values of the
tunneling amplitude ratios ($0.6 \leq w_0/w_1 \leq 1.0$), for which the
hybridization between the localized and conduction fermions $\gamma$ is smaller
than the onsite repulsion of the heavy fermions $U_1$ (i.e. $|\gamma| < U_1$).
