Simulations with the HAMMONIA general circulation and chemistry model are analyzed to improve the understanding of the atmospheric response to solar cycle variations and the role of the quasi-biennial oscillation of equatorial winds (QBO) for this response. The focus is on the Northern Hemisphere winter stratosphere. Owing to the internally produced QBO, albeit with a too short period of 24 months, the model is particularly suited for such an exercise. The simulation setup with only solar and QBO forcing allows an unambiguous attribution of the simulated signals. Two separate simulations have been performed for perpetual solar maximum and minimum conditions. The simulations confirm the plausibility of dynamical mechanisms, suggested earlier, that propagate the solar signal from the stratopause region downward to the troposphere. One feature involved in this propagation is a response maximum of temperature and ozone in the lower equatorial stratosphere. In our model, this maximum appears as a pure solar signal independent of the QBO and of other forcings. As observed, the simulated response of the stratospheric polar vortex to solar cycle forcing depends on the QBO phase. However, in the model this is statistically significant only in late winter. The simulation for early and mid winter suffers probably from a too strong internal variability of the polar vortex in early winter.