In message
<dm2pr04mb895279e532e2efe5d2d034d98...@dm2pr04mb895.namprd04.prod.outlook
.com>, dated Sat, 1 Aug 2015, "Heckrotte, Michael"
<michael.heckro...@ul.com> writes:
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.
You mean constructive or destructive interference between the direct
Tx-Rx path and the indirect path with one reflection?
I agree it's a valid topic but the original enquirer didn't ask about
it.
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.
Agreed.
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.
Perhaps not so very 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.
Obviously there is a choice. I wouldn't just assume that the analytical
approach is unwieldy.
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.
I think complex numbers can be avoided by using trig functions. But I
don't think I'm going to pursue the topic further, because at present I
don't expect ever to need the results.
--
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
-
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