Figure 5.

Absolute values and phases of the $a_{\mathit{\chi }}\left(t\right)$ coefficients characterizing the interaction frame trajectory of the ${\widehat{I}}_z$ operator during a nutation experiment with rf irradiation along the $x$  axis. A nominal rf field strength of 100  $\mathrm{kHz}$ and a MAS frequency of 30  $\mathrm{kHz}$ was assumed. The magnitude and phase of the coefficients are shown as a function of the $A_n^{\left(\mathrm{A}\right)}$  (a, b) and $A_n^{\left(\mathrm{P}\right)}$  (c, d) magnitude coefficients for rf amplitude modulations, with ${\mathit{\omega }}_{\mathrm{r}}$  (a) and $\mathrm{2}\cdot {\mathit{\omega }}_{\mathrm{r}}$  (b), as well as phase modulations with ${\mathit{\omega }}_{\mathrm{r}}$  (c) and $\mathrm{2}\cdot {\mathit{\omega }}_{\mathrm{r}}$  (d). Sidebands due to the MAS modulation of the rf amplitude at ${\mathit{\nu }}_{\mathrm{1}}\pm m\cdot {\mathit{\nu }}_{\mathrm{r}}$ , with $m$ being any integer for modulations with ${\mathit{\omega }}_{\mathrm{r}}$ ( $A_{\mathrm{1}}^{\left(\mathrm{A}\right)}$ ), and any even integer for modulations with $\mathrm{2}\cdot {\mathit{\omega }}_{\mathrm{r}}$ ( $A_{\mathrm{2}}^{\left(\mathrm{A}\right)}$ ) is observed. The intensity of these sidebands increases with the strength of the modulation. For rf phase modulations, sidebands at $\mathrm{0}\pm n\cdot {\mathit{\nu }}_{\mathrm{r}}$ arise for modulations with $n\cdot {\mathit{\omega }}_{\mathrm{r}}$ . The intensity of these sidebands increases with the strength of the modulation and considerably higher intensities are observed for higher $n$ (note the different scaling of the colour bars for $A_{\mathrm{1}}^{\left(\mathrm{P}\right)}$ and $A_{\mathrm{2}}^{\left(\mathrm{P}\right)}$ in c and d). The frequency axes in (c, d) were restricted to 0–90  $\mathrm{kHz}$ since the phase modulation sidebands are significantly weaker than the main band contribution to $a_z\left(t\right)$ at the nominal rf amplitude of 100  $\mathrm{kHz}$ .