Abstract: An object of the present invention provides a frequency synthesizer having a broad frequency entraining range which can finely set a frequency over a broad band by a novel principle. As s specific solving means, a sinusoidal signal of an output frequency of a voltage-controlled oscillator is subjected to orthogonal detection, a vector rotating at the differential frequency (speed) between the output frequency and the frequency of the frequency signal used for the detection is created, and the frequency of a vector when the output frequency of the voltage-controlled oscillator is equal to a set value is calculated in advance. The voltage signal corresponding to the difference between the frequency of the vector and the calculated frequency is fed back to the voltage-controlled oscillator when the voltage-controlled oscillator is driven, and PLL is formed so that the difference is equal to zero.