Strict proof and applicable range of the quarter-wavelength model for microwave absorbers

In the research and applications on microwave absorption materials and electromagnetic absorbers, the quarter-wavelength model is widely used in describing the dependence of the reflection loss (RL) peak frequency on electromagnetic parameters and thickness, and in the preparation and design of microwave absorption materials. However, the strict proof about this model based on transmission line theory is lacking. Moreover, a deviation between the absorption peaks obtained from the RL results and those from the quarter-wavelength model is observed in some materials, for which universal and reasonable theoretical explanation is also lacking. Hence, in this work, we derived strict proof of the quarter-wavelength model based on the transmission line theory, and developed a revised equation for this model to explain the abovementioned deviation. The revised equation could well fit the deviations observed in our experimental results. Combining with experimental results, we also discussed the applicable ranges for the quarter-wavelength model and the revised equation. Moreover, the results of this work showed that the appropriate value of phase angle is effective to reduce the absorber thickness.