We aim to reproduce the DCO$^+$ emission in the disk around HD163296 using a simple 2D chemical model for the formation of DCO$^+$ through the cold deuteration channel and a parametric treatment of the warm deuteration channel. We use data from ALMA in band 6 to obtain a resolved spectral imaging data cube of the DCO$^+$ $J$=3--2 line in HD163296 with a synthesized beam of 0.53$times$ 0.42. We adopt a physical structure of the disk from the literature that reproduces the spectral energy distribution. We then apply a simplified chemical network for the formation of DCO$^+$ that uses the physical structure of the disk as parameters along with a CO abundance profile, a constant HD abundance and a constant ionization rate. Finally, from the resulting DCO$^+$ abundances, we calculate the non-LTE emission using the 3D radiative transfer code LIME. The observed DCO$^+$ emission is reproduced by a model with cold deuteration producing abundances up to $1.6times 10^{-11}$. Warm deuteration, at a constant abundance of $3.2times 10^{-12}$, becomes fully effective below 32 K and tapers off at higher temperatures, reproducing the lack of DCO$^+$ inside 90 AU. Throughout the DCO$^+$ emitting zone a CO abundance of $2times 10^{-7}$ is found, with $sim$99% of it frozen out below 19 K. At radii where both cold and warm deuteration are active, warm deuteration contributes up to 20% of DCO$^+$, consistent with detailed chemical models. The decrease of DCO$^+$ at large radii is attributed to a temperature inversion at 250 AU, which raises temperatures above values where cold deuteration operates. Increased photodesorption may also limit the radial extent of DCO$^+$. The corresponding return of the DCO$^+$ layer to the midplane, together with a radially increasing ionization fraction, reproduces the local DCO$^+$ emission maximum at $sim$260 AU.
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