Synchronous delta-modulation systems are used to control resonant voltage link inverters, where switching has to be synchronized with the zero crossings of the link voltage. This paper shows that output current harmonic distortion and average switching frequency of such systems can be calculated analytically in spite of the quasistochastic behavior of the modulators output. Under the assumption of constant link frequency and large ratio of link to output frequency, results are derived for three-phase sigma-delta modulation, space-vector based sigma-delta modulation, and current-regulated delta modulation. The results hold for any shape of the inverter input voltage (including DC). The output current harmonic distortion of resonant link inverters is compared with conventional hard switching PWM inverters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>