Simultaneous multislice imaging using multiband RF pulses can accelerate image acquisition, particularly for single-shot imaging sequences used for diffusion and functional MRI ¹. However, designing multiband RF pulses remains a problem. This is because traditional multiband pulse design methods lead to high peak amplitudes in the waveform that can easily exceed the specification of RF transmission hardware ². Moreover, multiband waveforms have rapid amplitude and phase modulation (AM & PM) due to their increased frequency content. This rapid modulation can be close to the edge of what current MRI RF systems reproduce accurately; in particular we have found that systems specifying phase via frequency modulation introduce errors when pulses contain rapid phase modulation. In this scenario pulses that are solely amplitude modulated (AM) will yield the best performance. We examine three current methods for optimizing multiband pulses: phase-offsets ³, time-shifting ⁴ and root-flipping ⁵, we describe how each method can be modified to produce AM only waveforms, and examine relative performance.The relationship between RF pulses and magnetisation is governed by the Bloch equations, for which no analytic inversion exists. In the small-tip angle regime the inversion can be reduced to a Fourier relation. A key property is that conjugate-symmetric Fourier series have real coefficients. In all three methods (phase optimization, time shifting, root-flipping) peak amplitudes are reduced by manipulating the phase profiles of the desired slices without altering the magnitude profiles. To form pure AM waveforms the existing techniques were modified to produce conjugate-symmetric profiles across all excited slices. Phase-optimized RF pulses are created by finding the set of phase-offsets which minimise the peak amplitude. $$b(t)=p(t)\sum_{n=1}^{N}e^{i(\omega_nt + \phi_n)}$$ Where $$$b(t)$$$ and $$$p(t) $$$ are the multiband and single-band waveforms, $$$N$$$ is the multiband factor, $$$\omega_n$$$ is the inter-slice frequency off-set, symmetrically distributed around zero (the centre of the slice group) and $$$\phi_n$$$ is the set of phase variables which are optimized for. $$$b(t) $$$ can be made real valued (i.e. AM) if slices equidistant from the centre have anti-symmetric phase-offset (i.e. $$$\phi_i = -\phi_j$$$ for $$$\omega_i = -\omega_j$$$, for slices i and j) ⁶. Optimal $$$\phi_n$$$ are independent of the properties of $$$p(t)$$$. Time-shifting is an extension of this method in which individual single-band pulses are temporally off-set to minimise constructive interference: $$b(t)=\sum_{n=1}^{N} p(t-\tau_n)e^{i(\omega_nt + \phi_n)}$$ Where $$$\tau_n$$$ is the shift variable for each single-band pulse. To create AM pulses, time-shifting is constrained such that slices equidistant from the centre are shifted by the same amount (i.e. $$$\tau_i = \tau_j$$$ for $$$\omega_i = -\omega_j$$$) in addition to phase constraint $$$\phi_i = -\phi_j$$$ for these slices. Root-flipping differs from the above methods, in that it is a bottom-up design approach in which the desired multiband magnetisation profile is approximated by a polynomial of complex exponentials. The roots of this polynomial are distributed close to the unit circle in the complex plane. Flipping a root about the unit circle changes the phase profile in a non-linear way, without altering the magnitude slice profile. Temporally, root-flipping redistributes energy in the RF waveform lobes across its duration, so can be exploited to reduce peak amplitude. Flipping roots that are located symmetrically about the real axis leads to AM pulses after the inverse Shinnar-Le Roux transform. For all three techniques, both complex and AM pulses were designed using the same design specifications. Pulses were validated using Bloch simulations, and design specifications varied in both multiband factor and time-bandwidth product. Figure 1 verifies that the modifications lead to purely real-valued (AM) pulses. Figure 2 shows how the different AM-only methods interrelate, which resembles an earlier report for the complex case ⁵. Figure 3 shows the peak amplitudes of AM pulses relative to complex ones, averaged over a range of design parameters. The AM pulses were on average 28% longer in duration compared to equivalent pulses that allow both real and imaginary components. Phase-optimized results are independent of the single-band waveform, however this has a significant effect when time-shifting. An extreme case is shown in figure 4 where an AM pulse is virtually equivalent to its complex counterpart.We have demonstrated how phase-optimized, time-shifted and root-flipped pulses may be designed to have purely real-valued profiles. This is useful for overcoming hardware limitations of some RF systems. The constraint does lead to an increase in peak amplitude – as might be expected since the number of degrees of freedom are respected – however the increase is observed to be of the order of 20-25% for phase optimized and root-flipped pulses, with larger variability for time-shifted pulses.