If you are working (either as an employee or self-employed), then you are entitled to a residence permit independent of your wife.
The law that covers residency rights for EU citizens and their family members in Germany is called the Freizügigkeitsgesetz. Paragraph 3, section 4 covers the rights of the husband or wife if the EU citizen they are married to leaves Germany. Here you can read it via online translation:
The requirements it refers to is about having to work. You can additional support from, for example, the Jobcenter (Bürgergeld) or the Sozialamt (Wohngeld) but you do need to be working. You need to apply for a new permit on the basis of this law with your local Ausländerbehörde.
After 5 years in Germany fulfilling the working condition, you are entitled to permanent EU residency.