The use of high-frequency input signals from room-temperature microwave sources makes it difficult to scale up the number of quantum bits in universal quantum computers. To address this issue, superconducting single flux quantum (SFQ) integrated circuits are being explored as suitable candidates for qubit manipulation in universal quantum computers. Previously, we designed a low-power SFQ qubit control circuit (SQCC) to produce an equidistant SFQ pulse train without high-frequency input. It was reported that the fidelity of qubit control could be further improved if the pattern of SFQ pulse train could be adjustable. In this paper, we present optimized designs for different pattern requirements of qubit control, building upon the SQCC without high-frequency input. These designs feature segmented frequency modulation circuits, as well as circuits capable of outputting arbitrary patterns. The circuit capable of generating arbitrary patterns currently achieves a maximum adjustable number of 400, with a corresponding frequency output of 20 GHz. It has been successfully fabricated using the SIMIT Nb03 process and has passed functionality measurement tests. The optimized circuit opens up possibilities for improved qubit control and advancements in quantum computing applications.