# apr12

The 430 MHz line feed on the carriage  house illuminates the 1000 foot dish when the ch is at za=0. As the ch goes up in za, the illumination on the dish spills over onto the ground/ground screen. Since the gain is proportional to the illuminated area (assuming uniform illumination) the gain will also go down. To figure out how the spillover increases with za, a simulation was done. This simulation used:
• compute rgrid which is a 600x600 grid of points spaced by 1 meter.
• Fill rgrid with the distance from each point to the center.
• Generate a aperture plane agrid(600x600) for za = 0
• use  rgrid to find all of the points in agrid that have a radius between 305/2 meters and 91/2 meters (300 foot diameter).
• This is the part of the aperture plane illuminated by the linefeed when za=0.
• Fill these points with unity.
• integrate over the entire agrid0
• Figure out how much the aperture plane moves in the x direction when the feed moves to a non zero zenith angle.
• Approximate this by looking at the triangle :
• angleEdge=asin(305/2 / radiusCurvature) = 35.0795 degrees .. angle to edge of dish.
• r1=radiusCurvature*cos(angleEdge)  .. height edge of dish to center of curvature
• r2=305/2 :  radius of dish
• th=angleEdge + za
• solve tan(th)=(r2+dx)/r1  this give the x shift of the aperture plane.
• compute rgrid1(600,600). this has the radius for each point to the center of the dish, with the x coordinate shifted by dx.
• Find all of the points in rgrid1 within 305/2 meters of the center.
• Use these indices to integrate over agrid0 (the aperture plane at za=00
• The normalized gain(za)= total(aperature plane at za)/total(aperture plane za=0).
The plots  show the change in area (gain) as a function of za. (.ps) (.pdf):
• Page 1: Illuminated area (gain) vs za.
• The black line is the simulated data. The red line is a linear fit to the data.
• The slope of the fit is -.0326 per deg za.
• Page 2: Measured gain vs za for linefeed.
• Data is from 20050301 thru 20120229
• black is the measured gain. The red line is a linear fit to the data: gain= C0 + C1*za
• The data is centered at 430 MHz.
• Each frame is a different bandwidth: 12.5,6.25,3.125,1.5625 MHz.
• the fractional  slope : C1/C0  should match the slope of the line from the simulation:
• simulation: -.0326
• measured data:-.0288 to -.0295 ..
• so the match is pretty good.
• The gain increases as the bandwidth narrows since the linefeed has a fwhm response of about 9.5 MHz. centered close to 430MHz.

## Summary:

• simulation shows that the fractional change in gain with za for the line feed is:
• Using the measured gain from the carriage house we get a normalized slope of:
• -.0288 to -.0295  * zaDeg. This agrees pretty well with the simulation
• The measured  gain of the linefeed has a fwhm of about 9.5 MHz (centered at 429.5 MHz).
• What was not included in the simulation.
• The true illumination patter probably has a taper. This would weight the area spilling over at the edge with a smaller value
• So the simulation would come closer to the measured value.
processing: x101/430ch/herbc/sim430LinefeedGainVsZa.pro
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