My product is a combination of CE-compliant components, this means my product is automatically CE compliant

Only an end-user can combine CE-compliant products into a system (such as a home cinema system) without needing to comply with CE. If however, you intend to sell a system, this needs to comply with all applicable legislation. This is harder to achieve than CE-compliance for each of its separate parts.

For example, you combine 4 ventilators into a ventilation system and bring it to the market as one entity. As the system performs the same functionality as a single ventilator, the legislation remains the same. This means that the limits for e.g. radiated emission are the same. In this example, the ventilators of the ventilation system can emit 4 times less than a single ventilator to meet the EMC-requirements.