This paper proposes a new form of phase-locked loop (PLL) for improved synchronization of three-phase power converters with the grid, including applications operating at low ratios of sampling-to-fundamental frequency. First, a linear phase detector (PD) concept is introduced, enabling the construction of a new linear PLL (L-PLL). The proposed L-PLL exhibits well-behaved response to any step changes in phase or frequency including start-ups, responding as a linear system to any disturbances or transient conditions. As a result, the L-PLL gain can be tuned to low values for improved steady-state disturbance rejection and increased robustness in grid converters, especially in weak grids, while still retaining the ability to respond stably to large-amplitude transients. Both simulation and experimental results are presented to verify the improved performance characteristics of the proposed L-PLL.