Indian Journal of Radio & Space Physics Vol. 26, December 1997, pp.359-362 A new formula for the gain of open-ended rectangular waveguide K T Selvan & Sisir K Das SAMEER- Centre for Electromagnetics, 2nd Cross, CIT Campus, Taramani, Chennai 600113 Received 15 April 1997; accepted 26 August 1997 A new, simple formula is presented for the gain of the open-ended rectangular waveguide (OEG). The formula is derived by expressing the gain of the OEG in terms of the gains of its two constituent parallel plate waveguides, one supporting TEM mode and the other supporting TEIO mode. This new formula offers an improvement ofabout 1-2 dB over Schelkunoffs formula and compares with the more complicated formulas of Yaghjian to an accuracy of about 0.5 dB. 1 Introduction Open-ended, unflanged rectangular waveguides (OEG) are widely used as probes in near-field antenna measurements and as transmitting antennas to generate standard fields in anechoic chamber for performing electromagnetic interference (EMI) measurements. Consequently, an accurate lmowledge of their gain has been of significance. Since the measurement of gain is a rather tedious, time-consuming and costly operation, reliable gain formulas are of particular importance. Apart from reliability, it is often preferable to have formulas that are simple. In this paper, a' simple gain formula of 'reasonable accuracy is presented. The paper is constructed as follows: First, the available formulas for computing the gain of the OEG are examined with particular reference to their accuracy limits and computational requirements. Outlining the need for a simple formula of sufficient accuracy, it is then noted that an improvement in the classical gain formula for the OEG can be attempted by resolving it into parallel plate configurations. Subsequently the gain of the OEG is examined in the light of this possibility. This examination results in a new, simple formula for the gain ofthe OEG. 2 Examination of available formulas The classical Schelkunoffs formula for the far- field on-axis gain of the rectangular aperture of Fig. 1, with an in-phase field distribution uniform in the y direction and cosinusoidal in the x direction, is given byl 32ab G=--2 ... (1) 7tA; where A. is the free-space wavelength. This formula predicts values that are 2-3 dB lower than measuremenr. Noting that the Kirchoff theory only considers the TEIOmode and that 'fringe' currents strongly influence the H-plane pattern, Yaghjian2 constructed a 'fringe current method' by modifying the physical optics (PO) result of the Stratton-Chu formulas with a fringe current contribution to derive the OEG's H-plane pattern accurately. This method yields the following expression for the gain of the OEG: [ 2 ,2 ~k2ab k p P 2 G= x- l+-+r(l--)](-) +Co 8 (1-lfI2 ) P k k ~ ... (2) where f is the complex reflection coefficient at the y z Fig. I-Geometry of open-ended rectangular waveguide