Module 6 : Wave Guides. Lecture 46 : The Surface Current on the Waveguide Walls. Objectives. In this course you will learn the following

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1 Objectives In this course you will learn the following Procedure for obtaining current distribution on the waveguide walls. Surface current for mode inside Parallel Plane Waveguide. Surface current on the walls of the rectangular waveguide for mode.

2 Procedure for obtaining current distribution on the waveguide walls The modal fields inside the waveguide induce surface charges and surface currents on the walls of the waveguide. In other words we can say that the modal fields are supported by the surface charges and surface currents on the inner walls of the waveguide. Since the fields are time varying the surface charges and surface currents also vary to time. It should be emphasized that power carried inside the waveguide is by the fields and not by the surface charges and surface currents. The direction of power flow and the direction of the current in general need not be same. The following procedure for finding surface currents is similar to that used in visualizing the modal fields inside the waveguide: (a) (b) (c) (d) First we fix time to get instantaneous current distribution on the walls of the waveguide. Then we allow the current distribution to drift along the waveguide with the phase velocity. Since the surface currents are related to tangential components of magnetic fields first, we obtain the distribution of magnetic fields on the walls of the waveguide. The surface current that is obtained through (6.75) where unit vector and is the outward normal on the repective inner surfaces of the waveguide.

3 Surface current for The magnetic fields for mode inside Parallel Plane Waveguide mode are given as (6.76) (6.77) Now in wall the normal is oriented in direction and magnetic field is oriented in direction. The current direction then is given by direction. Similarly on wall the magnetic field is oriented in -direction nad the unit normal is oriented in -direction. The direction of the current wall then is direction. The currents on both the walls do not have any variation in -direction and have sinosoidal variation in the direction. The interesting things to note are : (a) Both the walls have the currents flowing in the same direction i.e, -direction with equal amplitude. (b) The current always flow perpendicular to the direction of the power flow which is in of the current in the direction of the power flow. direction i.e, there is no component The current direction reverses for every distance in the direction of the wave propagation. The surface current distribution is shown in figure below

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5 Surface current on the walls of the rectangular waveguide for mode The magnetic field for mode has two components in and directions which are given as (6.78) (6.79) For obtaining the surface current only tangential component of the magnetic field is needed. For vertical walls the tangential component is only where as for the horizontal wall both and components are tangential. For vertical walls the tangential components of the magnetic fields are (6.80) (6.81) The outward unit normal is along -direction for wall. The current direction then on this wall is on wall the unit normal is in -direction and the magnetic field is in -direction. Giving the direction of the current. That means in both the vertical walls at this instant of time the current flows vertically downwards and since have any variation in -direction the current amplitude remains constant along the height of the wave. does not On horizontal walls the surface current is due to both components and. On lower horizontal wall,, outward normal is in -direction. Vector current distribution on the lower wall then is given as (6.82) (6.83) (6.84) The and components of the current are in space quardrat in the -direction and also in space quardration in - direction. When we systematically draw the vector current we get the vector current distribution on the horizontal waveguide wall On wall the magnetic field directions remains same as that on the wall but the direction of normal is reversed i.e, it is along -direction. The current distribution on the upper wall then is the minor image of the current distribution of the lower wall (fig)

6 The figure shows the current distribution at same instance of time for mode inside a rectangular waveguide. The current distribution drifts inside the waveguide with a phase velocity of the mode.

7 Recap In this course you have learnt the following Procedure for obtaining current distribution on the waveguide walls. Surface current for mode inside Parallel Plane Waveguide. Surface current on the walls of the rectangular waveguide for mode. Congratulations! You have finished Module 6. To view the next Module select it from left hand side of the page.