  Reconfigurable transmitarray antennas (RTAs) are rapidly gaining popularity,
but optimizing their performance requires systematic design theories. In
particular, establishing a performance limit theory for RTA elements is
valuable. This paper presents a transmission efficiency limit theory for
single-switch RTA elements and their cascaded extensions. Employing microwave
network analysis, we analytically investigate single-switch RTA elements,
demonstrating that their transmission coefficients under two states must lie on
or within a specific unit circle on the Smith chart. Therefore, the
transmission phase difference is tightly constrained by the transmission
amplitudes, indicating that the phase-shifting ability of a single-switch RTA
element is limited. Subsequently, this analysis is extended to cascaded RTA
elements. By cascading several single-switch layers, the phase variation range
is extended, enabling the realization of 1-bit phase shifts with high
transmission amplitudes. These findings have significant impact on the design
and optimization of RTA elements.
