In this paper, we present SoDa, an irradiance-based synthetic Solar Data generation tool to generate realistic sub-minute solar photovoltaic (PV) output power time series, that emulate the weather pattern for a certain geographical location. Our tool relies on the National Solar Radiation Database (NSRDB) to obtain irradiance and weather data patterns for the site. Irradiance is mapped onto a PV model estimate of a solar plant's 30-min power output, based on the configuration of the panel. The working hypothesis to generate high-resolution (e.g. 1 second) solar data is that the conditional distribution of the time series of solar power output given the cloud density is the same for different locations. We therefore propose a stochastic model with a switching behavior due to different weather regimes as provided by the cloud type label in the NSRDB, and train our stochastic model parameters for the cloudy states on the high-resolution solar power measurements from a Phasor Measurement Unit (PMU). In the paper we introduce the stochastic model, and the methodology used for the training of its parameters. The numerical results show that our tool creates synthetic solar time series at high resolutions that are statistically representative of the measured solar power and illustrate how to make use of the tool to create synthetic data for arbitrary sites in the footprint covered by the NSRDB.