As a drop-in replacement of Continuous Electron Beam Accelerator Facility (CEBAF) 5kW CW klystron system, a 1497MHz, high efficiency magnetron using injection phase lock [1] and slow amplitude variation using magnetic field trimming and anode voltage modulation has been studied systematically using MatLab/Simulink simulations. The magnetron model is based the characteristics of experiment and manufacture chart on a 2.45GHz cooker type CW magnetron. To achieve high performance of a superconducting radio frequency (SRF) acceleration cavity with an electron beam loading, the magnetron's low level radio frequency (LLRF) control has been studied in two lock loops. In the frequency lock loop, the characterized anode V-I curve, output power (the tube electronic efficiency) and frequency dependence to the anode current (pushing by Vaughan model) and the Rieke diagram (frequency pulling by the reactive load) are simulated. The magnetic field B and anode voltage V in Hartree condition are satisfied and the effect of filament heater power to the frequency lock is also included. In the phase lock loop, the Adler equation governing injection phase stability is included in this study. The control of the magnet trim-coil power-supply and of the anode voltage modulation-switching power-supply has been also simulated to achieve the amplitude modulation. The result of linear responses to the amplitude and phase of SRF cavity will be presented in this paper. The requirement of LLRF control will be given by this result.