Substrate Integrated Waveguide (SIW) is a new type of wave guiding structure which can be applicable in microwave and millimeter-wave integrated circuits. It has advantages of conventional rectangular waveguide to some extent and doesn’t have many of its defects. High-Q, easy and low-cost fabrication, low volume, low weight and low profile, mass-producible, capability of integration by planar and non-planar circuits are some of its advantages. This is why in the recent years it has become very popular and different types of devices such as filters, couplers, resonators and etc have been fabricated with this structure. Here, we first speak about the necessity of using substrate integrated circuits and then properties of SIW such as propagation constant, attenuation constant, electromagnetic bandgap phenomenon and etc. Two different methods to find the rectangular equivalence of SIW have been introduced including an empirical and a method based on analytical method of moment (MOM). Our simulation shows that the latter is more exact. Then we talk about coupling from small apertures in a waveguide. In this thesis, design process of a 20dB wideband coupler on the basis of SIW using different methods including chebyshev and binomial polynomials and also modeling the coupler by distributed low-pass filter prototypes and using chebyshev coefficients for these prototypes have been done. A MATLAB program is used for generation of chebyshev polynomials of low-pass filter prototypes. The base of work is the Bethe coupling theory for small apertures that has been expanded for large apertures. The polarizabilities of different type of apertures have been changed to use for large apertures. The type of apertures for our designs includes circular, rectangular and square. For circular aperture two coefficients have used for correction of polarizabilities and for rectangular aperture new polarizabilities have been defined. The square aperture is a type of rectangular aperture. Aperture dimensions are being designed by several MATLAB programs that have been written based on different methods which we had introduced in this thesis.We also introduced a new method to calibrate aperture dimensions to obtain our desired coupling. The method is based on dimensional analysis. Also a Riblet-Saad coupler has been designed and simulated by a simple method that is based on dimensional analysis. Excellent results have been obtained from simulations Riblet-Saad has the flattest coupling. The error is 0.3dB on the X band. Finally, we see that the flattest coupling sequentially belongs to Riblet-Saad, circular aperture, square aperture and rectangular aperture couplers and the bigger isolation belongs to circular aperture,rectangular.... Keywords: Substrate Integrated Waveguide (SIW), coupler, coupling, large aperture, Riblet-Saad, wide-band