Empirical Quality Factor Prediction of Quarter-Mode Substrate Integrated Waveguide Resonators

Quarter-mode substrate integrated waveguide (QMSIW) is an effective technique to reduce the size of filters designed on SIW technology. An accurate prediction of the unloaded quality factor of QMSIW resonators helps to estimate the insertion loss of QMSIW filters. This article introduces new empirical equations to calculate the contribution of the finite conductor and radiation on the quality factors of QMSIW resonators. To show the accuracy of the equations, the calculated quality factor values are compared to values extracted from full-wave electromagnetic simulations for five different resonators at different frequencies and various substrate materials. For further comparison, these resonators were fabricated, and the quality factor values were extracted from measurements. The good agreement between simulations, measurements, and the predicted quality factors shows that accurate quality factor estimations can be made using the developed equations. Finally, a second-order filter is designed and fabricated to demonstrate the benefits of the proposed equations in microwave filter design.