Railroad signaling systems are to control intervals and routes of trains. There are ATS, ATP, ATO and ATC system. Trains are operated in the section which is met on the signaling system because various signaling systems are used in Korea. Hence, trains are not operated in the section which is used in the other signaling system. To solve this problem, recently combined on-board system has been developed. The combined on-board system designed by doubling the ATS, ATP and ATC system to ensure the safety of system. The inductance of antenna is change and in return the resonance frequency of antenna is varied by the electromagnetic induction. Therefore, the information signal is not received exactly in the combined on-board system and in return accidents between trains occur. In this paper, electric model of the combined on-board system for considering the ATS and ATP antenna is presented. Moreover, the mutual inductance including the distance between the ATS and ATP antenna is calculated. As a result of the frequency response of the antennas, the mutual inductance met on operation range of resonance frequency is defined.