###### Abstract  
A split-ring resonator (SRR)-based power tiller wheel-shaped quad-band \(\epsilon\)-negative metamaterial is presented in this research article. This is a new compact metamaterial with a high effective medium ratio (EMR) designed with three modified octagonal split-ring resonators (OSRRs). The electrical dimension of the proposed metamaterial (MM) unit cell is 0.086\(\lambda\) 0.086\(\lambda\), where \(\lambda\) is the wavelength calculated at the lowest resonance frequency of 2.35 GHz. Dielectric RT6002 materials of standard thickness (1.524 mm) were used as a substrate. Computer simulation technology (CST) Microwave Studio simulator shows four resonance peaks at 2.35, 7.72, 9.23 and 10.68 GHz with magnitudes of \(-43.23\) dB - 31.05 dB, \(-44.58\) dB and \(-31.71\) dB, respectively. Moreover, negative permittivity (\(\epsilon\)) is observed in the frequency ranges of 2.35-3.01 GHz, 7.72-8.03 GHz, 9.23-10.02 GHz and 10.69-11.81 GHz. Additionally, a negative refractive index is observed in the frequency ranges of 2.36-3.19 GHz, 7.74-7.87 GHz, 9.26-10.33 GHz and 10.70-11.81 GHz, with near-zero permeability noted in the environments of these frequency ranges. The medium effectiveness indicator effective medium ratio (EMR) of the proposed MM is an estimated 11.61 at the lowest frequency of 2.35 GHz. The simulated results of the anticipated structure are validated by authentication processes such as array orientation, HFSS and ADS for an equivalent electrical circuit model. Given its high EMR and compactness in dimensions, the presented metamaterial can be used in S-, C- and X-band wireless communication applications. E 2023 16 1137 1137 1137 1137 1137 1137 1137 1137 1137 1137 1137 1137 1137 1137 1137 13  
4.8 was designed for sensing applications in the microwave range [13]. A dual-band flexible metamaterial was designed on a nickel aluminate (NiAl2O4) substrate with a 42% aluminum concentration and dimensions of 12.5 \(\times\) 10 mm\({}^{2}\), covering the X and Ku bands [14]. Recently, a metamaterial was reported that a contained rectangular-shaped SRR. This metamaterial was utilized to sense concrete, temperature and humidity [15]. [PERSON] et al. in [16] introduced a SNG metamaterial that shows triple band resonance for microwave application. Moreover, [PERSON] et al. proposed a three-dimensional metamaterial built on reedy wire, along with a split-ring resonator [17]. In numerical simulation, the MM exhibited a double-negative characteristic with a wideband spectrum. A triple-band polarization-dependent MM with dimensions of 8 \(\times\) 8 mm\({}^{2}\) was designed on an RT6002 substrate and yielded at 0.92 GHz, 7.25 GHz and 14.83 GHz, covering the S, C and Ku bands [18]. A tri-band MM with dimensions of 10 \(\times\) 10 mm\({}^{2}\) and a Greek key shape was designed on an RT 5880 dielectric. In numerical simulation, it showed triple resonance peaks at 2.40, 3.50 and 4.0 GHz [19]. An epsilon-negative, delta-shaped metamaterial comprising an SSR (square ring resonator) exhibited tri-resonance crests that covered the C and X bands [20]. Another triple-band metamaterial with dimensions of 5 \(\times\) 5 mm\({}^{2}\) was presented by [PERSON] et al. in 2016 [21] with an RCER (reformed circular electric resonator). This MM with a low (5.45) effective medium ratio (EMR) was resonant in the frequency ranges of 9.70 GHz to 10.50 GHz and 15 GHz to 15.70 GHz. A different metamaterial with a pie-shaped metallic resonator surrounded by an SRR was presented in [22]. This tri-band MM was designed on a substrate with dimensions of 8 \(\times\) 8 mm\({}^{2}\) and covered the microwave S, C and X bands. An SRR-based triple-band metamaterial was designed with a double circular ring [23]. This multiunit cell-based MM was resonant at 5.6 GHz of Wi-MAX and 2.45 of WLAN. In 2019, [PERSON] et al. [24] designed a metamaterial based on a CSRR (complementary split-ring resonator) with dimensions of 5 \(\times\) 5 mm\({}^{2}\). It showed resonance at 7.5 GHz with an EMR of 8.