Waveguide Loop Coupling

Waveguide Loop Coupling

Waveguide loop coupling is a method of transferring microwave energy between an external transmission line and a waveguide by using the magnetic field. The coupling loop is a conducting loop connected to a transmission line, and when a high frequency current flows through the loop, it produces a time varying magnetic field around the conductor. This magnetic field interacts with the magnetic field already present inside the waveguide. The interaction allows electromagnetic energy to be transferred into the waveguide and used to excite a particular propagation mode. The same principle also works in the reverse direction, where an electromagnetic wave propagating inside the waveguide induces current in the loop and transfers microwave energy from the waveguide to the external circuit.

Principle of Waveguide Loop Coupling

The operation of loop coupling is based on Faraday's law of electromagnetic induction. When a changing magnetic field passes through the area enclosed by a conducting loop, magnetic flux is linked with the loop and an electromotive force is induced in the conductor. In a microwave system, the current supplied to the loop produces a changing H field, and this field extends into the interior of the waveguide. If the generated magnetic field has the correct orientation and frequency, it interacts with the magnetic field distribution of the waveguide mode. The amount of energy transferred depends mainly on the magnetic flux linked with the loop. Therefore, the loop must be positioned and oriented carefully so that a large amount of the magnetic field passes through its enclosed area.

The magnetic flux linked with the loop can be expressed as:

$ \Phi = \int_S \mathbf{B}\cdot d\mathbf{S} $

where \(\Phi\) is the magnetic flux through the loop, \(\mathbf{B}\) is the magnetic flux density, and \(d\mathbf{S}\) represents an elemental area normal to the surface of the loop. Since the magnetic flux density is related to the magnetic field intensity by \(\mathbf{B}=\mu\mathbf{H}\), the flux linkage depends directly on the strength of the magnetic field and the orientation and area of the loop. A stronger magnetic field produces greater flux linkage when the loop is correctly oriented. This is the fundamental reason why the position and orientation of a coupling loop are important in waveguide systems.

Why the Loop Is Placed at the Magnetic Field Maximum?

The coupling loop is placed at a point where the magnetic field strength is maximum because the objective is to obtain the largest possible magnetic flux linkage with the loop. The induced electromotive force is proportional to the rate of change of magnetic flux through the loop. Therefore, when the loop is located in a region where the H field is strong, a greater amount of magnetic flux passes through the loop and a larger induced voltage is produced. This results in stronger coupling between the loop and the waveguide. If the loop is moved toward a point where the magnetic field is weaker, the amount of linked magnetic flux decreases and the coupling becomes weaker. Thus, the magnetic field maximum provides the most effective location for transferring microwave energy through a loop.

For a particular waveguide mode, the electric and magnetic fields are distributed throughout the cross section according to the field equations of that mode. The fields do not have the same magnitude at every point. Some regions contain electric field maxima, while other regions contain magnetic field maxima. Since a coupling loop responds primarily to the magnetic field, it must be located according to the H field distribution rather than simply being placed at an arbitrary position. The correct coupling position is therefore determined by studying the magnetic field pattern of the mode that is intended to be excited. This field based placement ensures that the loop interacts strongly with the desired mode and avoids unnecessarily weak coupling.

Orientation of the Coupling Loop

The orientation of the loop is equally important because maximum coupling does not depend only on the magnitude of the magnetic field. The direction of the magnetic field relative to the plane of the loop also determines the amount of magnetic flux passing through it. For maximum magnetic flux linkage, the plane of the loop should be normal to the magnetic flux lines. In this orientation, the magnetic field passes through the enclosed area of the loop as effectively as possible. If the loop is rotated away from this position, the effective component of the magnetic field passing through the loop decreases. As a result, the magnetic flux linkage and induced electromotive force decrease, causing the coupling between the loop and the waveguide to become weaker.

The orientation can be understood from the magnetic flux expression:

$ \Phi = BA\cos\theta $

where \(B\) is the magnetic flux density, \(A\) is the area of the loop, and \(\theta\) is the angle between the magnetic field and the normal to the plane of the loop. Maximum flux occurs when:

$ \theta=0^\circ $

Therefore:

$ \Phi_{\max}=BA $

This means that the magnetic field is normal to the plane of the loop when maximum flux linkage is obtained. If the loop is rotated so that the magnetic field becomes parallel to the plane of the loop, the magnetic flux passing through the loop approaches zero and the magnetic coupling becomes very small.

Controlling the Coupling by Rotating the Loop

The orientation of the loop can also be used to control the amount of microwave energy transferred between the external circuit and the waveguide. When the loop is positioned at the magnetic field maximum and its plane is normal to the magnetic flux lines, coupling is strongest. If the loop is gradually rotated away from this position, the effective magnetic flux passing through the loop decreases. Consequently, the induced voltage and the coupling coefficient also decrease. This provides a simple method of obtaining controlled or weak coupling without changing the waveguide itself. In practical microwave systems, mechanical adjustment of the loop angle can therefore be used when only a small portion of the available waveguide energy needs to be coupled into an external circuit.

Location of the Loop in a Short Circuited Waveguide

A coupling loop can be installed in the end wall of a short circuited waveguide or positioned along the top or bottom wall at a suitable distance from the short circuit. The correct location is determined by the standing wave pattern established inside the guide. When the waveguide is terminated by a short circuit, the forward and reflected waves combine to form a standing wave. This standing wave produces fixed locations of maximum and minimum electric and magnetic field strength. The loop is positioned at a magnetic field maximum because this location provides the greatest magnetic flux linkage and therefore the strongest possible magnetic coupling.

The positions of equivalent magnetic field maxima repeat along the waveguide at intervals related to the guide wavelength. These positions can be represented by:

$ d=n\frac{\lambda_g}{2} $

where \(d\) is the distance from the reference position, \(n\) is an integer, and \(\lambda_g\) is the guide wavelength. The use of \(\lambda_g\), rather than the free space wavelength \(\lambda_0\), is important because the field pattern inside a waveguide is determined by the guided wave. Therefore, the physical position of the loop must be selected using the guide wavelength corresponding to the operating mode and frequency.