Determination of Transmission Zero Frequency for Complementary Split-Ring Resonator/Split-Ring Resonator Unit Cells from Effective Permittivity and Permeability

In this work, complementary split-ring resonator (CSRR) and split-ring resonator (SRR) unit cells structures are investigated and simulations are performed in order to find out transmission zero frequency f
r
(S
21
) depending on frequency band of the negative permittivity or negative permeability. The proposed analytic method based on calculation of transmission zero frequency, f
r
(S
21
) in specific frequency band which is limited by lower and upper frequencies (f
1
, f
2
). In proposed CSRR unit cell, it is founded that the accuracy rate of the f
r
(S
21
) produced by the proposed analytic method is 99.62%, while the accuracy rate is 89.45% obtained by theoretical calculation. Similarly, in SRR unit cell, the proposed analytic accuracy rate produced is 98.7% while the accuracy rate is 98% obtained by theoretical calculation. Further validation of the proposed analytic method has been achieved by using, different substrate materials with different permittivity values (starting from the relative permittivity value, ε
r
=2.1 for Teflon to the permittivity value, ε
r
=6.15 for Roger RO 3006) for both unit cells. As results for this investigation; for CSRR unit cell the minimum analytic accuracy rate obtained by proposed method is 98.4%, while it is 88.66% obtained by theoretical calculation. Similarly, in SRR unit cell the minimum analytic accuracy recorded by proposed method is 98.5%, while it is 96.3% achieved by theoretical calculation. The proposed analytic method has effective performance for CSRRs than SRRs, in which it is very convenient to characterize structures have negative electric permittivity. Ansoft HFSS simulator has been used for all structures designed and simulation results.