  We propose an analytical framework to design actively tunable narrowband
thermal emitters at infrared frequencies. We exemplify the proposed design
rules using phase-change materials (PCM), considering dielectric-to-dielectric
PCMs (e.g. GSST) and dielectric-to-metal PCMs (e.g. $\mathrm{VO_2}$). Based on
these, we numerically illustrate near-unity ON-OFF switching and arbitrarily
large spectral shifting between two emission wavelengths, respectively. The
proposed systems are lithography-free and consist of one or several thin
emitter layers, a spacer layer which includes the PCM, and a back reflector.
Our model applies to normal incidence, though we show that the behavior is
essentially angle-independent. The presented formalism is general and can be
extended to \textit{any} mechanism that modifies the optical properties of a
material, such as electrostatic gating or thermo-optical modulation.
