Abstract:

The phase truncation in direct digital linear frequency modulation (LFM) synthesizer can cause the linearity error, which will degrade the performance of LFM signals in radar systems. The linearity error caused by the phase truncation is analyzed specifically for the first time by using the discrete mathematics theory. The necessary and sufficient condition of no linearity errors in the presence of phase truncation is obtained. The exact expressions of linearity and the FM slope error are derived under normal circumstance, and the distribution of the FM slope error on four candidate values is obtained by exploring Monte Carlo method. The effect of phase truncation on linearity is also numerically evaluated through simulation examples. Some practical design suggestions are proposed according to the conclusions obtained. Simulation results demonstrate the correctness of the theoretical derivation.