This paper presents an ultra-small physical unclonable function (PUF) chip structure to protect data in compact IoT sensor devices. The proposed PUF has far fewer transistors and a reduced active area compared to the conventional strong PUF with multiple challenge response pairs (CRPs). According to the manufacturing process variations, the conventional SRAM-based PUF uses a switching transistor and a main transistor to implement multiple CRPs, whereas the proposed structure adds the function of a switching transistor to a single main transistor, controlling the body voltage to switch the transistor. This unified and simple PUF structure results in significant silicon area reduction. For a PUF with a 32-bit challenge, the number of transistors is significantly reduced by 40%; the active area of the conventional structure is <inline-formula> <tex-math notation="LaTeX">$57.78~\mu m^{2}$ </tex-math></inline-formula> while the area of the proposed structure is <inline-formula> <tex-math notation="LaTeX">$36.4~\mu m^{2}$ </tex-math></inline-formula>. Overall, an active area reduction of 38% is realized with the same number of CRPs. Here, we implemented an SRAM-based PUF system with a 32-bit challenge, a 1024-bit response, and 160 million CRPs. PUF core cell shows energy efficiency of 0.09 pJ/bit. The inter-Hamming distance is 48.89%, while the intra-Hamming distance is 1.2% after data post-processing, i.e., discarding unstable bits. A prototype chip is implemented in the 65nm CMOS process with a supply voltage of 1.2V. Compared to the prior arts, the proposed prototype is shown effective silicon area reduction while maintaining remarkable energy efficiency.