The main drawback of the transmissive focusing metasurface (TFM) is its low operational bandwidth and aperture efficiency. Increasing both of these radiation characteristics simultaneously is a major challenge for these structures. This paper introduces a novel multi-state coding metasurface that utilizes system-level and element-level synthesis approaches to enhance frequency bandwidth and aperture efficiency. Unlike most of the TFMs proposed in this field, the proposed novel element consists of only two dielectric layers. The multi-frequency phase synthesis (MFPS) approach, a well-established broadband technique, is utilized for the system-level synthesis approach. An optimization algorithm is utilized to balance the phase error in the whole band in terms of gain variations and aperture efficiency. At the element design level, a PCT-based wideband technology is utilized and implemented by a subwavelength non-resonant element. The element is composed of three C-shaped metallic patterns, and the metal layers are printed on both sides of two identical dielectric layers without using any metalized via in the configuration. By simply changing the angle of arc curves in all layers, eight states of phase quantization are achieved. The amplitude of the transmitted wave with rotated polarization is larger than 0.9 from 12.3 to 16.5 GHz, except for state 4, which has an amplitude greater than 0.5 at the beginning of the band. A 25\documentclass[12pt]{minimal}
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				\begin{document}$$\times $$\end{document}×25-element TFM was designed, fabricated, and tested using the aforementioned broadband technique (MFPS along with PCT-based wideband technology). The measurement results show that the 1-dB gain bandwidth of the antenna is 12.3–16.5 GHz, which is equivalent to 29%. The maximum measured aperture efficiency is 53.6%, occurring at 12.8 GHz. The proposed metasurface is classified in the group of broadband high-efficiency TFMs.