The phase locked loop (PLL) frequency synthesizer includes a phase detector receiving a reference signal, a controlled oscillator (e.g. a voltage controlled oscillator) connected to the phase detector and generating a synthesized frequency output signal based upon the reference signal, a mixer (e.g. an in-phase and quadrature-phase (IQ) modulator) connected to the controlled oscillator, a divider connected between the mixer and the phase detector, and a signal source driving the mixer. The frequency synthesizer and method have narrow frequency steps (e.g. as low as fractions of a Hertz) while using a relatively high reference frequency to maintain low phase noise. Furthermore, the fine frequency tuning resolution is achieved while also reducing output spurs and using a relatively simple topology.