We study electromagnetic wave propagation in a system that is periodic both in space and in time, namely, a discrete (``lumped'') transmission line with capacitors (``varactors'') that are modulated in time harmonically. These periodicities result in exotic electromagnetic band structures that are periodic in the angular frequency ω and in the phase advance ka of the wave. Depending on the strength of modulation m and the reduced modulation frequency Ω/ω0 (where ω0 is the resonant frequency of a unit cell of the transmission line), this band structure can display frequency or wave vector band gaps, both, or neither. Moreover, minor changes in or the modulation strength can control the aperture or closure of a gap and even transform a k-gap to an ω-gap. Such phase transitions are intimately associated with exceptional or critical points in the (ω, k, Ω, m) space.
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