In this paper, an autonomous tuning method is proposed to realize optimal adaptive voltage positioning (AVP) scheme for the buck converter. The optimal AVP scheme can perform linearly fast transient response with less output capacitors compared to the traditional buck converter. The conventional wisdom of realizing the optimal AVP is to make the current sensing resistor (R i) equal to the equivalent series resistor (Rc) of the output capacitor. However, such approach usually requires on-line system-identification algorithms or sensors that are complex and costly. Alternatively, this paper proposes a novel approach to implement the optimal AVP using a linear transition approximation (LTA) algorithm. Without using any parameter identification technique, the LTA algorithm only observes the output voltage response to adaptively adjust controller for realizing optimal linear transition during transient. The result of the proposed approach is very close to the effect of approximating Ri to Rc for an optimal AVP scheme. A buck converter using a FPGA controller that embeds the proposed algorithm is implemented. Experiment results show that the linear transient response is achieved in response to a 1-5 A step load change within 20μs. A comparative result also shows that the optimal AVP performance is superior to the case without using the proposed algorithm.