During the Northern Hemisphere winter months, the observed strengthening of the polar vortex during the westerly phase of the QBO and the weakening during the easterly phase (as described by Holton and Tan) are reproduced in the model. The extratropical QBO signal has been analyzed with and without stratification by phase of the 11-year solar cycle. We show that the Holton Tan relationship can reverse during solar maximum compared to solar minimum conditions in the 1950-2000 period, in good agreement with the observational record. However, the analysis of the longer 1850-2000 period does not show such a modulation and instead, the Holton Tan relationship stands independently of the phase of the 11-year solar cycle.