I have design a split ring resonator with dielectric substrate Roger RO 4350 and we have extracted the equivalent capacitance and inductance value at from S-parameter. But how we can add the value of Resistance also and how we can consider dielectric substrate in the equivalent circuit model ?
The value of resistance would be different at different frequencies. You can convert the S parameters to Z parameters to have an estimate of the resistance. The real part will give you resistance value at your desired frequency, while the imaginary value will provide you information about the capacitive or inductive behavior at that particluar frequency.
In a model of ring resonator, the resistance can be assumed in series with the inductor for simplicity.
The circuit model is based on passive components i.e. R, L and C. The effect of dielectric constant can be reflected in the change of the the values of the three components. The shift in resonance frequency is observed for a fixed shape/design with the change in dielectric constant. The circuit model doesn't specifically have any component for dielectric constant. An equivalent circuit model for dielectrics can be developed but it will again contain the same R, L and C components. Researchers usually estimate and present a lumped model.
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