Since SARS-CoV-2 started spreading in Europe in early 2020, there has been a strong call for technical solutions to combat or contain the pandemic, with contact tracing apps at the heart of the debates. The EU's General Daten Protection Regulation (GDPR) requires controllers to carry out a data protection impact assessment (DPIA) where their data processing is likely to result in a high risk to the rights and freedoms (Art. 35 GDPR). A DPIA is a structured risk analysis that identifies and evaluates possible consequences of data processing relevant to fundamental rights and describes the measures envisaged to address these risks or expresses the inability to do so. Based on the Standard Data Protection Model (SDM), we present a scientific DPIA which thoroughly examines three published contact tracing app designs that are considered to be the most "privacy-friendly": PEPP-PT, DP-3T and a concept summarized by Chaos Computer Club member Linus Neumann, all of which process personal health data. The DPIA starts with an analysis of the processing context and some expected use cases. Then, the processing activities are described by defining a realistic processing purpose. This is followed by the legal assessment and threshold analysis. Finally, we analyse the weak points, the risks and determine appropriate protective measures. We show that even decentralized implementations involve numerous serious weaknesses and risks. Legally, consent is unfit as legal ground hence data must be processed based on a law. We also found that measures to realize the rights of data subjects and affected people are not sufficient. Last but not least, we show that anonymization must be understood as a continuous process, which aims at separating the personal reference and is based on a mix of legal, organizational and technical measures. All currently available proposals lack such an explicit separation process.