Ed is the received field at a particular geometry. EdMax is the maximum value of Ed over a range of Rx heights, with Distance and Tx height held constant.
Regarding the complexity of the issue... Certainly it is easy enough to calculate the entire geometry for any combination of Distance, Tx height and Rx height. The various hints in this thread help a great deal to simplify the visualization and calculations. Things can get more interesting at the step of determining the Rx heights at which the maximum (in-phase) and minimum (out-of-phase) signal levels occur. The numerical approach that I took kept things simple. Step the Rx height from 1 to 4 meters (I chose a 0.01 m step size as this is on the order of the accuracy to which I could set the antenna height using reasonable care; the resulting resolution was quite adequate). Calculate Ed for each Rx height and store in an array. Find the maximum value of Ed; from the corresponding array index determine the Rx height. The geometry for the in-phase conditions can then be calculated. The same process can be used to find EdMin for the anti-phase conditions. An analytical solution could conceivably be found by taking the partial derivative of Ed with respect to Rx height, setting the derivative to zero, and solving for Rx height. At each solution, take the second partial derivative to determine which are maxima and which are minima. Find the highest maximum and the lowest minimum. The equations are going to get messy. I used LabVIEW, which includes complex arithmetic. I can confidently say that it took me far less time to write the program, run it and print out graphs, than would be needed for me to derive and solve the proposed analytical equations. A literature search shows that Manny Barron followed the same numerical approach, however he first derived analytical expressions (as functions only of real numbers) for the absolute values of the complex-number factors in the EdHoriz and EdVert equations. This enabled calculations to be performed in Excel. Various references: Smith, A. A., Jr., German, R., Pate, J., "Standard site method for determining antenna factors", IEEE Transactions on Electromagnetic Compatibility, EMC-24, pp. 316-322, no. 3, Aug. 1982. Smith, A. A., Jr., German, R., Pate, J., "Calculation of Site Attenuation from Antenna Factors", IEEE Electromagnetic Compatibilty", EMC-25, No. 3, August 1982, pp 301-316 Barron, M., "3-D Surface Plot of Theoretical Normalized Site Attenuation Calculation by Spreadsheet Analysis", 2001 IEEE International Symposium on EMC, Seattle, WA. Pp 133-138 Best Regards, Mike -----Original Message----- From: John Woodgate [mailto:j...@jmwa.demon.co.uk] Sent: Friday, July 31, 2015 2:34 PM To: EMC-PSTC@LISTSERV.IEEE.ORG Subject: Re: [PSES] Calculating Reflection Angles on OATS/SAC In message <dm2pr04mb8955244ee213552f09d187498...@dm2pr04mb895.namprd04.prod.outlook .com>, dated Fri, 31 Jul 2015, "Heckrotte, Michael" <michael.heckro...@ul.com> writes: >Perhaps someone with a postgraduate degree in mathematics could derive >an analytical formula, but as an engineer I used numerical methods by >calculating Ed over the range of Rx height variation. You seem to be addressing a much more complex issue than I understood the enquirer to be asking about. What is 'Ed'? -- OOO - Own Opinions Only. With best wishes. See www.jmwa.demon.co.uk When I turn my back on the sun, it's to look for a rainbow John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK - ---------------------------------------------------------------- This message is from the IEEE Product Safety Engineering Society emc-pstc discussion list. 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