The impedance matching model is built to optimize the performance of the PTC from both cold finger and compressor. Based on the thermoacoustic theory, a 1-D simulation model of the 30 K PTC is built by using DeltaEC software for optimizing the coupling working parameters of the cold finger and compressor. The effects of the regenerator material, the inertance tube and the reservoir on the impedance of the cold finger are investigated theoretically. The test system is set up and the results show that the lowest temperature of 24.24 K and cooling power of 1 W at 30 K with electric power of 227 W can be obtained, which satisfy the applications of the space infrared detectors.