The Past and Present Infrared Spectrum of BD+30 3639

We present a radiative-transfer calculation which reproduces the infrared spectrum of the planetary nebula BD+30${}^{\circ }$3639, fitting both the spectral energy distribution and the spatial extent at infrared wavelengths. We obtain an acceptable fit to most of the spectrum, including the infrared bands. The fit requires a distance of $\ge 2\text{kpc}$, which implies that BD+30${}^{\circ }$3639 has evolved from a massive progenitor of several solar masses. Two surprising results are (1) a very low dust-to-gas ratio, (2) an absence of the smallest PAH molecules. Extrapolating back in time, we calculate the previous infrared evolution of BD+30${}^{\circ }$3639.