Digital cores that are currently incorporated into advanced Systems on Chip (SoC) frequently include Logic Built-In Self-Test (LBIST) modules with the Self-Test Using MISR/Parallel Shift Register Sequence Generator (STUMPS) architecture. Such a solution always comprises a Pseudo-Random Pattern Generator (PRPG), usually designed as a Linear Feedback Shift Register (LFSR) with a phase shifter attached to the register and arranged as a network of XOR gates. This study discloses an original and innovative structure of such a PRPG unit referred to as the DT-LFSR-TPG module that needs no phase shifter. The module is designed as a set of identical linear registers of the DT-LFSR type with the same primitive polynomial. Each register has a form of a ring made up exclusively of D and T flip-flops. This study is focused on the investigation of those parameters of DT-LFSR registers that are essential to use these registers as components of PRPG modules. The investigated parameters include phase shifts and the correlation between sequences of bits appearing at outputs of T flip-flops, implementation cost, and the maximum frequency of the register operation. It is demonstrated that PRPG modules of the DT‑LFSR‑TPG type enable much higher phase shifts and substantially higher operation frequencies as compared to competitive solutions. Such modules can also drive significantly more scan paths than other PRPGs described in reference studies and based on phase shifters. However, the cost of the foregoing advantages of DT-LFSR-TPG modules is the larger hardware overhead associated with the implementation of the solution proposed.