In order to interpret the radio data from extensive air shower detectors, we rely on accurate simulations.
The state-of-the-art simulation frameworks use Monte-Carlo techniques which pose computational challenges.
Therefore, we developed template synthesis, a novel, fast and accurate forward model to calculate the radio emission, which achieves the same accuracy as full microscopic simulations in only a fraction of the time.
This speeds up the simulation-heavy reconstruction techniques used in Auger and LOFAR by orders of magnitude.
Moreover, it can revolutionize the field by allowing efficient production of simulations for more advanced techniques such as interferometry and reconstruction of the longitudinal shape of the shower.

Our method synthesises the radio emission using a microscopically (Monte-Carlo) simulated origin shower and a set of semi-analytical scaling relations.
These relations were extracted from a large set of CoREAS simulations, thus capturing the behaviour of the microscopic models.
We divide the atmosphere into slices of constant atmospheric depth and synthesise the emission from each slice separately.
In this process we correct for the shower age inside each slice, which we found to be one of the crucial parameters determining the radio emission.
The computation time of the synthesis process is negligible compared to the runtime of the microscopic simulation.
Crucially, when comparing the synthesised traces to CoREAS simulations, the amplitudes are typically within 5% of each other.

Here we present the complete framework, which can be used for showers of all geometries without any modifications, addressing an important limitation in the previous iterations.
It can also account for different experimental conditions, such as the atmosphere and magnetic field, as well as the influence of the air shower geometry.
We also present the Python package implementing this method, called SMIET.