In this paper the theoretical bases to design a true random bit generator (TRBG) circuit with a predefined minimum entropy are discussed. The approach is tailored to TRBGs based on a one-dimensional piecewise-linear chaotic map, and it is based on a feedback control procedure that allows to dynamically changing the system parameters. For this purpose, the procedure just exploits the TRBG output observation without requiring bit throughput reduction. The design approach was validated by an hardware prototype implemented on a field programmable analog array (FPAA