Analysis of Rectangular and Circular Wave Guide. - Wong, Eric Vun Shiung (2016)
Waveguides are generally used to channel the weak cosmic wave to the receiver in a radio telescope. The most commonly used waveguide is the rectangular and circular waveguides. Cosmic waves from distant sources are extremely weak. Hence it is important to minimize the loss in the waveguide. To allow the engineers and scientists to efficiently design a waveguide, it is important to develop a formulation which is able to compute the attenuation in a waveguide accurately. The transcendental equations developed by Stratton and Yeap to compute losses in waveguides are derived from the first principle. Hence, the equations are able to predict losses with higher accuracy. However, these equations are difficult to solve analytically. Solution to the transcendental equation can only be obtained using a root finding algorithm. Depending on the compiler and the algorithm used, solution may converge or diverge. Besides, it may require long computation time to solve. On the other hand, closed form solutions are simpler and give more intuitive insights. The resulting equation takes much less time to solve compared to the transcendental equation. Closed form solutions often use assumptions to simplify the equations. Equations such as the power loss method assumes the wall to be perfectly conducting. Such assumption is able to approximate the solution provided the metal is of sufficiently high conductivity. However, the assumption of perfect wall result in an infinite attenuation at cut-off frequency. An infinite conductivity metal prevents wave to propagate when the frequency is below the cut-off frequency. Such case is of course not accurate. Based on the experimental result, the attenuation of the wave increases as the frequency is reduced from the cut-off frequency. However, the attenuation constant is finite. vii This thesis primarily focuses on the formulation of a closed form equation that is able to describe wave beyond as well as below the cut-off frequency with reasonable accuracy. The new method developed is based on modification from Yeap’s transcendental equation. Unlike Stratton’s transcendental equation, which is only restricted to the case of a circular waveguide. Yeap’s method is able to be used for circular as well as rectangular waveguide. Hence, the new method proposed here has also the advantage of being applied in waveguides with circular or rectangular geometry. Finite Difference Method is used to approximate the transcendental equation to transform it into a closed form solution. The resulting equation is simpler and gives more intuitive insights than Yeap’s transcendental equation. It also requires less computation time. The results show that the loss computed based on the new method agrees with the experimental result as well as existing theories.