We present a novel method for generating small, accurate PLL macromodels that capture transient response and jitter performance with unprecedented accuracy, while offering large speedups. The method extracts and uses a highly accurate oscillator phase macromodel termed the TP-PPV macromodel. The core idea behind the novel extraction procedure is to combine concepts from strongly nonlinear trajectory piecewise macromodeling techniques together with PPV-based timeshifted nonlinear phase macromodels. As a result, TP-PPV generated macromodels offer excellent global as well as local fidelity. These properties are necessary for handing large excursions in PLL control voltages during capture/lock in, e.g., hopping frequency synthesizers. We validate TP-PPV on a 5-stage interpolative ring VCO based PLL and compare results against full simulation, as well as against prior macromodels. We show that, unlike prior macromodels that only work well when the control voltage of the VCO has small excursions, the TP-PPV macromodel provides near-perfect matches against full SPICElevel simulation over a wide range of design scenarios, while achieving speedups of about three orders of magnitude.