1. Consider a partially loaded waveguide without sidewalls as shown in the figure below. We would like to look at the TMy guided modes existing in the structure. Take the direction of propagation to be the z-axis. Let ko=woco be the wavenumber in free-space. (i) Find the characteristic equation for determining the propagation constant k of the modes. (30 points) (ii) For operation at 600 MHz and er = 2, r = 2, b = 10 cm, t = 1 cm determine the normalized propagation constant kz/ko for the first two modes. (15 points) (10 points) (iii) What is the form of the characteristic equation in the limit as b . (iv) What is the power flow per unit length (in the x direction) at the plane z = zo > 0 for an arbitrary mode. (10 points) PEC PEC (0, 0) (Er, fr) y b t Figure 1: Partially loaded parallel plate waveguide. N